PHYSICS - accueil › iso... · 1 About Phywe Founded in Göttingen, Germany in 1913 by Dr. Gotthelf Leimbach, Phywe Systeme GmbH & Co. KG quickly advanced to one of the leading manufacturers

PHYSICSL A B O R ATO RY E X P E R I M E N TS

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Dear customer,

this catalogue of physics laboratory experiments for universities, colleges, high schools etc. is a valuable and

extensive work of scientific literature for experiment-oriented education purposes. It includes numerous successful

and classical experiments playing an essential role in every physics laboratory course. The experiments have been

field-tested over and over again and countless enthusiastic customers all over the world have been inspired

by them.

Our team of experienced scientists has set great store on using both classical equipment, such as oscilloscopes,

recorders etc., and modern interface systems like our Cobra3 system for the experiments. This is why you will often

find several versions for one experiment. Just choose the experiment version which best meets your specific

requirements.

If you need help in selecting the right experiments, our sales representatives in your country would be more than

happy to assist you.

We hope you enjoy our manual and look forward to your questions.

Phywe Systeme GmbH & Co. KG

PHYWE Systeme GmbH & Co. KGRobert-Bosch-Breite 10D-37079 Göttingen · GermanyPhone + 49/551/604- 0Fax + 49/551/604 [email protected]


1

About Phywe

Founded in Göttingen, Germany in 1913 by Dr. Gotthelf Leimbach, Phywe Systeme GmbH & Co. KG quickly advanced

to one of the leading manufacturers of scientific equipment.

Over this period of more than 90 years Phywe has been putting quality and innovation into its products as a

fundamental requirement.

As a well known international supplier in the fields of science and engineering we have made a significant impact on

the market through high quality equipment.

Phywe products are made in Germany and in use throughout the world in the fields of education und research, from

primary schools right through to university level.

Up-to-date educational systems, planning and commissioning of scientific and engineering laboratories to meet

specific requirements are our daily business.

As a supplier of complete, fully developed and established systems, Phywe provides teaching and learning systems

for students as well as teacher demonstration experiments. The system ranges from simple, easy to operate

equipment intended for student use up to coverage of highly sophisticated and specialised university equipment

demands.

Phywe Systeme GmbH & Co. KG has achieved a very high standard based on research and technology and through

exchange of experiences with universities and high schools as well as with professors and teachers.

As experienced and competent manufacturer, we would gladly assist you in the

selection of the "right" experiments for your particular curricula.


2

Mechanics Measurement techniques Phywe in the University City of Göttingen –

Natural sciences have a longstanding

tradition in Göttingen. More than 40 Nobel

prizewinners coming from all sorts of

scientific disciplines and numerous university

institutes successfully conduct research in

practically all areas of science.

The following research institutions and

university institutes are located in Göttingen:

Academy of Science, several Max-Planck

institutes, the German Primate Centre, the

Centre of Molecular Physiology of the Brain,

the Centre of Molecular Life Science –

to name just a few.

We are in contact with these institutions and

exchange our views with them to ensure that

the latest trends and scientific innovations

are always reflected in the product range of

Phywe Systeme GmbH & Co. KG.


3

A Center of Natural Sciences in Germany

GÖTTINGEN is a city of teaching and research. Scientific equipment, teaching

equipment and laboratory installations developed and produced in this city are famous

throughout the world.

Göttingen would not be what it is without its university.

“Georgia Augusta” was founded in 1734 and by 1777 it was Germany‘s largest

university, with 700 students. It still is one of the leading universities in Germany, with

14 faculties, significant scientific facilities and more than 30,000 students.

The gracious Goose Girl (“Gänseliesel”) on the market place well is the most kissed girl

in Germany. Why? Because every newly graduated doctor must kiss the cold beauty on

her bronze mouth. That is Göttingen tradition.

Doctor’s kiss for the “Goose Girl”

Nobel Price winner Prof. Otto Hahn visitingPHYWE in 1966


4

PHYSICS – CHEMISTRY – BIOLOGYThe comprehensive catalogue for physics, chemistry

and biology. Additionally you can find a large number of

laboratory materials and an insight in our particularly

successful teaching systems TESS, Cobra3 and

Natural Sciences on the board.

Available in English and Spanish.

Laboratory ExperimentsThe experiments in the Phywe publication series “Laboratory Experiments”

are intended for the heads of laboratories,colleges of advanced technology, technical

colleges and similar institutions and alsofor advanced courses in high schools.

Laboratory Experiments Physics isalso available on CD-ROM.

Available in English.

For the student system “Advanced Opticsand Laser Physics” a special brochure

is available in English.

Special brochuresAdditionally there are special brochu-res for our particularly successfulteaching systems TESS (available inGerman, English, French and Spanish),Cobra3 (available in German, English)and Natural Sciences on the board(available in German, English).

– catalogues, brochures and more…


5PHYWE Systeme GmbH & Co. KG · D-37070 Göttingen Laboratory Experiments Physics

Physics HandbooksPhywe is uncomplicated

To help you in selecting your experiments, we have added pictograms to several of our experiments.

These pictograms give you a quick overview of the most important features of the experiments and provide

you with all the essential information at a glance.

New Products

New products which have been launched in the last few months. Here

you will also find particularly successful experiments with new additional

features to offer you even more measurement and experiment

possibilities.

Our Best-Sellers

Particularly successful and reliable products which have been field-tested

over and over again in numerous countries - some for many years. We

would be more than happy to provide you with references upon request.

Computer-Assisted Experiments with our Cobra3 PC Interface

A large number of experiments can be performed in a particularly comfor-

table and elegant way with the help of our Cobra3 measurement interfa-

ce. All you need is a PC. The advantage is that you can process the data

particularly well using a PC.

PC interfaced instruments

Some Phywe devices already have an interface included.

These instruments can be connected directly to a PC where you can use

the Phywe measure Software to work with the data.


6 PHYWE Systeme GmbH & Co. KG · D-37070 GöttingenLaboratory Experiments, Physics

Laboratory Experiments, Physics

Picture andEquipment List guarantee time-savingand easy conducting of the experiment.

Theory and evaluation states full theoryinvolved and shows graphical and numericalexperimental results including error calcules.

Example ofmeasurementparameters

All experiments are uniformly built-upand contain references such asRelated topics and Principle and taskto introduce the subject.

LEP5.3.01-11 Hall effect in p-germanium with Cobra3

25301-11PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany

2

Set-up and procedureThe experimental set-up is shown in Fig.1. The test piece on

the board has to be put into the hall-effekt-modul via the guide-

groove. The module is directly connected with the 12V~ output

of the power unit over the ac-input on the backside of the mod-

ule.The connection to the Analog In 2 – port of the Cobra3 Basic-

Unit is realized via a RS232 cable from the RS232-port of the

module.The Tesla-module is connected to the module-port of the

Interface.The plate has to be brought up to the magnet very carefully, so

as not to damage the crystal in particular, avoid bending the

plate. It has to be in the centre between the pole pieces.

The different measurements are controlled by the software.

The magnetic field has to be measured with a hall probe, which

can be directly put into the groove in the module as shown in

Fig.1. So you can be sure that the magnetic flux is measured

directly on the Ge-sample.

To perform the measurements, start the software and choose

as gauge the Cobra3 Hall-Effect.You will receive the following window (Fig.3):

This is the start-screen which appears before every measure-

ment. Here, you can choose, which parameters have to be

measured, displayed, etc., e.g. Hall voltage as a function of

Sample current (Fig.4)

You can also calibrate the Tesla-module via ”options” (Fig.5).

Start the measurement-screen by pressing the ”continue”-but-

ton.

1. Choose The Hall voltage as the measurement-channel and

the Sample current as x-axis.Choose the measurement on ”key press”.Continue. Set the magnetic field to a value of 250 mT by

changing the voltage and current on the power supply.

Determine the hall voltage as a function of the current from

-30 mA up to 30 mA in steps of nearly 5 mA.

You will receive a typical measurement like in Fig.6.

Fig. 3: Start menu of the software Cobra3 Hall effect.

Fig. 4: Example of measurement parameters.

Fig. 5: Calibration menu.

Fig. 2: Hall effect in sample of rectangular section. The polar-

ity sign of the Hall voltage shown applies when the car-

riers are negatively charged.

Fig. 6: Hall voltage as a function of current.

LEP5.3.01

-11Hall effect in p-germanium with Cobra3

25301-11 PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany4

Theory and evaluationIf a current I flows through a conducting strip of rectangularsection and if the strip is traversed by a magnetic field at rightangles to the direction of the current, a voltage – the so-calledHall voltage – is produced between two superposed points onopposite sides of the strip.This phenomenon arises from the Lorentz force: the chargecarriers giving rise to the current flowing through the sampleare deflected in the magnetic field B as a function of their signand their velocity v:

(F = force acting on charge carriers, e = elementary charge).

Since negative and positive charge carriers in semiconductorsmove in opposite directions, they are deflected in the samedirection.

The type of charge carrier causing the flow of current cantherefore be determined from the polarity of the Hall voltage,knowing the direction of the current and that of the magneticfield.

1. Fig. 6 shows that there is a linear relationship between thecurrent I and the Hall voltage UB:

UH = a · I

where a = proportionality factor.2. The change in resistance of the sample due to the magnet-

ic field is associated with a reduction in the mean free pathof the charge carriers. Fig. 7 shows the non-linear, clearlyquadratic, change in resistance as the field strength in-creases. Therefore us the channel modification in theanalysis-menu.

3. In the region of intrinsic conductivity, we have

where s = conductivity, Eg = energy of bandgap, k = Boltz-mann constant, T = absolute temperature.If the logarithm of the conductivity is plotted against T-1 astraight line is obtained with a slope

from which Eg can be determined.

From the measured values used in Fig. 8, the slope of theregression line

is

with a standard deviation sb = ±0.07 · 103 K.

3. To receive the necessary graph, do as follows:Choose the channel modification in the analysis-menu. Setthe parameters as shown in Fig.11. Continue. Rememberthe procedure with the parameters in Fig.12. Now, you havethe desired graph. To determine the regression line, choosethe ”Regression”-icon.(Since the measurements were made with a constant cur-rent, we can put s ~ U–1, where U is the voltage across thesample.)

Since

we getEg = b · 2k = (0.72 ± 0.03) eV.

k � 8.625 · 10�5 eVK

b � �Eg

2 k � � 4.18 · 103 K

ln s � ln s0 �Eg

2 k · T�1

b � �Eg

2 k .

s � s0 · exp a �Eg

2 kTb

F �

� e 1v � � B 2

Fig. 11: Parameters for the first channel modification.

Fig. 12: Parameters for the second channel modification.

LEP5.3.01

-11Hall effect in p-germanium with Cobra3

PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany 25301-11 1

Related topics

Semiconductor, band theory, forbidden zone, intrinsic conduc-

tivity, extrinsic conductivity, valence band, conduction band,

Lorentz force, magnetic resistance, mobility, conductivity, band

spacing, Hall coefficient.

PrincipleThe resistivity and Hall voltage of a rectangular germanium

sample are measured as a function of temperature and mag-

netic field. The band spacing, the specific conductivity, the type

of charge carrier and the mobility of the charge carriers are

determined from the measurements.

Equipment

Hall effect module,11801.00 1

Hall effect, p-Ge, carrier board 11805.01 1

Coil, 600 turns06514.01 2

Iron core, U-shaped, laminated 06501.00 1

Pole pieces, plane, 30330348mm, 2 06489.00 1

Hall probe, tangent., prot. cap 13610.02 1

Power supply 0-12 V DC/6 V, 12 V AC 13505.93 1

Tripod base -PASS- 02002.55 1

Support rod -PASS-, square, l = 250 mm 02025.55 1

Right angle clamp -PASS- 02040.55 1

Connecting cord, 100 mm, red 07359.01 1

Connecting cord, 100 mm, blue 07359.04 1



Connecting cord, 500 mm, black 07361.05 2

Cobra3 BASIC-UNIT12150.00 1

Cobra3 power supply unit12151.99 1

Tesla measuring module12109.00 1

Cobra3 Software Hall14521.61 1

RS 232 data cable14602.00 2

Tasks1. The Hall voltage is measured at room temperature and con-

stant magnetic field as a function of the control current and

plotted on a graph (measurement without compensation for

defect voltage).

2. The voltage across the sample is measured at room tem-

perature and constant control current as a function of the

magnetic induction B.

3. The voltage across the sample is measured at constant

control current as a function of the temperature. The band

spacing of germanium is calculated from the measure-

ments.

4. The Hall voltage UH is measured as a function of the mag-

netic induction B, at room temperature. The sign of the

charge carriers and the Hall constant RH together with the

Hall mobility mH and the carrier concentration p are calcu-

lated from the measurements.

5. The Hall voltage UH is measured as a function of tempera-

ture at constant magnetic induction B and the values are

plotted on a graph.

Fig.1: Experimental set-up

LABORATORY EXPERIMENTSPHYSICS

1650

2.12

Laboratory Experiments

Klaus HermbeckerLudolf von Alvensleben

Regina ButtAndreas Grünemaier

Robin Sandvoß

Experimental literature

Laboratory Experiments Physics

Print Version No. 16502.32

CD No. 16502.42

The experiments in the PHYWE Publication Series “Laboratory Experiments Physics” are intended for the

heads of physics laboratory courses at universities, colleges of advanced technology, technical colleges and

similar institutions and also for advanced courses in high schools.



Laboratory Experiments, Physics

The present volume which has been developed by PHYWE, complements the previously existing collection

of about 230 experiments in twenty-six chapters as the following comprehensive Table of Contents shows.

In this brochure we present the experiments in short form. The experiments can be ordered or offered

completely or partially, if desired, in accordance with the Comprehensive Equipment Lists. On request, we

will gladly send you detailed experimental descriptions.

You can order the experiments as follows:

� Didactically adap-ted descriptions ofexperiments – easy,direct preparationby the students ispossible

� Comprehensive experiments – cover the entire range of classicaland modern physics

� Developed and proven bypracticians – unproblematical andreliable performance

� Complete equipment offeringmodular experimental set-up –multiple use of individual devices,cost effective and flexible

� Excellent measurement accuracy – results agree with theory

� Computer-assisted experiments –simple, rapid assessement of theresults

Quantity

Order No.

Please specify thisOrder No. if you wouldlike to order the completeexperiment.

Hall effect module, 11801.00 1


Coil, 600 turns 06514.01 2


Pole pieces, plane 06489.00 1






Connecting cord, l = 100 mm, red 07359.01 1

Connecting cord, l = 100 mm, blue 07359.04 1



Connecting cord, l = 500 mm, black 07361.05 2

Cobra3 Basic Unit 12150.00 1

Power supply, 12 V 12151.99 1

Tesla measuring module 12109.00 1

Cobra3 Software Hall 14521.61 1

RS 232 data cable 14602.00 2

PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in p-germanium with Cobra3 P2530111

You can order the experiments as follows:


8 PHYWE Systeme GmbH & Co. KG · D-37070 GöttingenLaboratory Experiments Physics

Summary

1.4.05-00 Surface tension by the ring method (Du Nouy method)

1.4-06-11 Surface tension by the pull-out method with Cobra3

1.4.07-00 Barometric height formula

1.4.08-00 Lift and drag (resistance to flow)

1.5 Mechanical Vibration Acoustics

1.5.01-00 Vibration of strings

1.5.03-11 Velocity of sound in air with Cobra3

1.5.04-01 Acoustic Doppler effect

1.5.04-11 Acoustic Doppler effect with Cobra3

1.5.06-01 Velocity of sound using Kundt’s tube

1.5.07-00 Wavelengths and frequencies with a Quincke tube

1.5.08-11 Resonance frequencies of Helmholtz resonators with Cobra3

1.5.09-11 Interference of acoustic waves, stationary waves and diffraction at a slot with Cobra3

1.5.10-00 Optical determination of velocity of sound in liquids

1.5.11-00 Phase and group velocity of ultrasonics in liquids

1.5.12-00 Temperature dependence of the Velocity of sound in liquids

1.5.13-01 Stationary ultrasonic waves, determination of wavelength

1.5.14-01 Absorption of ultrasonic in air

1.5.15-11 Ultrasonic diffraction at different single and double slit systems with Cobra3

1.5.16-11 Ultrasonic diffraction at different multiple slit systems with Cobra3

1.5.17-11 Diffraction of ultrasonic waves at a pin hole and a circular obstacle with Cobra3

1.5.18-01 Ultrasonic diffraction at Fresnel lenses / Fresnel zone contruction

1.5.19-11 Interference by two identical ultrasonic transmitterswith Cobra3

1.6 Handbooks

Physics Demonstration Experiments –Magnet Board Mechanics 1

Magnet Board Mechanics 2

Optics2.1 Geometrical Optics

2.1.01-00 Measuring the velocity of light

2.1.02-00 Laws of lenses and optical instruments

2.1.03-00 Dispersion and resolving power of the prism and grating spectroscope

2.2 Interference

2.2.01-00 Interference of light

2.2.02-00 Newton’s rings

2.2.03-00 Interference at a mica plate according to Pohl

2.2.04-00 Fresnel’s zone construction / zone plate

2.2.05-00 Michelson interferometer

2.2.06-00 Coherence and width of spectral lines with Michelsoninterferometer

2.2.07-00 Refraction index of air and CO2 with Michelson interferometer

2.3 Diffraction

2.3.01-00 Diffraction at a slit and Heisenberg’s uncertainty principle

2.3.02-00 Diffraction of light at a slit and an edge

2.3.03-00 Intensity of diffractions due to pin hole diaphragms and circular obstacles

Mechanics1.1 Measurement Techniques

1.1.01-00 Measurement of basic constants: length, weight and time

1.2 Statics

1.2.01-00 Moments

1.2.02-00 Modulus of elasticity

1.2.03-00 Mechanical hysteresis

1.3 Dynamics

1.3.01-01 Hooke’s law

1.3.01-11 Hooke’s law with Cobra3

1.3.03-01 Newton’s 2nd Law / Air track

1.3.03-11 Newton’s 2nd Law / Air track with Cobra3

1.3.05-01 Laws of Collision / Air track

1.3.05-11 Laws of collision with Cobra3

1.3.07-01 Free fall

1.3.07-11 Free fall with Cobra3

1.3.09-11 Determination of the gravitational constant / Computerized Cavendish balance

1.3.11-00 Projectile motion

1.3.12-00 Ballistic Pendulum

1.3.13-01 Moment of inertia and angular acceleration

1.3.13-11 Moment of inertia and angular acceleration with Cobra3

1.3.15-00 Moment and angular momentum

1.3.16-01 Centrifugal force

1.3.16-11 Centrifugal force with Cobra3

1.3.18-00 Mechanical conservation of energy / Maxwell’s wheel

1.3.19-00 Laws of gyroscopes / 3-axis gyroscope

1.3.20-00 Laws of gyroscopes / cardanic gyroscope

1.3.21-00 Mathematical pendulum

1.3.22-00 Reversible pendulum

1.3.23-01 Pendulum oscillations / variable g pendulum

1.3.23-11 Pendulum oscillations with Cobra3

1.3.25-01 Coupled Pendula

1.3.25-11 Coupled Pendula with Cobra3

1.3.26-11 Harmonic oscillations of spiral springs – Springs linked in parallel and series

1.3.27-01 Forced Oscillations – Pohl’s pendulum

1.3.27-11 Forced Oscillations – Pohl’s pendulum; Determination of resonance frequencies by Fourier analysis

1.3.28-01 Moments of inertia of different bodies / Steiner’s theorem

1.3.28-11 Moments of inertia of different bodies / Steiner’s theorem with Cobra3

1.3.30-00 Torsional vibrations and torsion modulus

1.3.31-00 Moment of inertia and torsional vibrations

1.3.32-00 The propagation of a periodically excited continuous transverse wave

1.3.33-00 Phase velocity of rope waves

1.4 Mechanics of Liquids and Gaseous Bodies

1.4.01-00 Density of liquids

1.4.02-00 Surface of rotating liquids

1.4.03-00 Viscosity of Newtonian and non-Newtonian liquids (rotary viscometer)

1.4.04-00 Viscosity measurements with the falling ball viscometer

1

2



Summary

3

4

2.3.04-00 Diffraction intensity for multiple slits and grids

2.3.05-00 Determination of the diffraction intensity at slit and double slit systems

2.3.06-00 Diffraction intensity through a slit and a wire – Babinet’s theorem

2.4 Photometry

2.4.02-01 Photometric law of distance

2.4.02-11 Photometric law of distance with Cobra3

2.4.04-00 Lambert’s law

2.5 Polarisation

2.5.01-00 Polarisation by quarterwave plates

2.5.02-00 Polarimetry

2.5.03-00 Fresnel’s equations – theory of reflection

2.5.04-00 Malus’ law

2.6 Applied Optics

2.6.01-00 Faraday effect

2.6.02-00 Kerr effect

2.6.03-00 Recording and reconstruction of holograms

2.6.04-00 CO2-laser

2.6.05-11 LDA – Laser Doppler Anemometry with Cobra3

2.6.07-00 Helium Neon Laser

2.6.08-00 Optical pumping

2.6.09-00 Nd-YAG laser

2.6.10-00 Fibre optics

2.6.11-00 Fourier optics – 2f Arrangement

2.6.12-00 Fourier optics – 4f Arrangement – Filtering and reconstruction

2.7 Handbooks

Advanced Optics and Laser Physics – Handbook 1–3

Physics Demonstration Experiments – Magnet Board Optics

Thermodynamics3.1 Thermal Expansion

3.1.01-00 Thermal expansion in solids and liquids

3.2 Ideal and Real Gases

3.2.01-00 Equation of state of ideal gases

3.2.02-01 Heat capacity of gases

3.2.02-11 Heat capacity of gases with Cobra3

3.2.03-00 Maxwellian velocity distribution

3.2.04-00 Thermal equation of state and critical point

3.2.05-00 Adiabatic coefficient of gases – Flammersfeld oscillator

3.2.06-00 Joule-Thomson effect

3.3 Calorimetry, Friction Heat

3.3.01-01 Heat capacity of metals

3.3.01-11 Heat capacity of metals with Cobra3

3.3.02-00 Mechanical equivalent of heat

3.4 Phase Transitions

3.4.01-00 Vapour pressure of water at high temperature

3.4.02-00 Vapour pressure of water below 100°C Molar heat of vaporization

3.4.03-00 Boiling point elevation

3.4.04-00 Freezing point depression

3.5 Transport and Diffusion

3.5.01-00 Stefan-Boltzmann’s law of radiation

3.5.02-00 Thermal and electrical conductivity of metals

3.6 Applied Thermodynamics

3.6.01-00 Solar ray Collector

3.6.02-00 Heat pump

3.6.03-00 Heat insulation / Heat conduction

3.6.04-00 Stirling engine

3.7 Handbooks

Glas jacket system

Air Cushion Table

Demonstration Experiments Physics – Magnetic Board Heat

Electricity4.1 Stationary Currents

4.1.01-00 Measurement of low resistance

4.1.02-00 Wheatstone Bridge

4.1.03-00 Internal resistance and matching in voltage source

4.1.04-00 Temperature dependence of different resistors and diodes

4.1.06-00 Current balance / Force acting on a current-carrying conductor

4.1.07-00 Semiconductor thermogenerator

4.1.08-00 Peltier heat pump

4.1.09-00 Characteristic curves of a solar cell

4.1.11-00 Characteristic and efficiency of PEM fuel cell and PEM electrolyser

4.1.12-00 Faraday’s law

4.2 Electric Field

4.2.01-00 Electrical fields and potentials in the plate capacitor

4.2.02-00 Charging curve of a capacitor

4.2.03-00 Capacitance of metal spheres and of a spherical capacitor

4.2.04-00 Coulomb’s law / Image charge

4.2.05-00 Coulomb potential and Coulomb field of metal spheres

4.2.06-00 Dielectric constant of different materials

4.3 Magnetic Field

4.3.01-00 Earth’s magnetic field

4.3.02-00 Magnetic field of single coils / Biot-Savart’s law

4.3.03-00 Magnetic field of paired coils in Helmholtz arrangement

4.3.04-00 Magnetic moment in the magnetic field

4.3.05-00 Magnetic field outside a straight conductor

4.3.06-00 Magnetic field inside a conductor

4.3.07-11 Ferromagnetic hysteresis

4.3.08-00 Magnetostriction with the Michelson interferometer

4.4 Electrodynamics

4.4.01-00 Transformer

4.4.02-00 Magnetic induction

4.4.03-01 Inductance of solenoids

4.4.03-11 Inductance of solenoids with Cobra3

4.4.04-01 Coil in the AC circuit

4.4.04-11 Coil in the AC circuit with Cobra3



Summary

4.4.05-00 Capacitor in the AC circuit

4.4.06-01 RLC Circuit

4.4.06-11 RLC Circuit with Cobra3

4.4.07-00 Rectifier circuits

4.4.08-00 RC Filters

4.4.09-00 High-pass and low-pass filters

4.4.10-00 RLC measuring bridge

4.4.11-00 Resistance, phase shift and power in AC circuits

4.4.12-11 Induction impulse

4.5 Electromagnetic Oscillations and Waves

4.5.02-00 Coupled oscillating circuits

4.5.04-00 Interference of microwaves

4.5.05-00 Diffraction of microwaves

4.5.06-00 Diffraction and polarization of microwaves

4.5.08-00 Radiation field of a horn antenna / Microwaves

4.5.09-00 Frustrated total reflection / Microwaves

4.6 Handbooks

Demonstration Experiments Physics – Electricity/Electronics on the Magnetic Board 1 + 2

Physical Structure of Matter5.1 Physics of the Electron

5.1.01-00 Elementary charge and Millikan experiment

5.1.02-00 Specific charge of the electron – e/m

5.1.03-11 Franck-Hertz experiment with Hg-tube

5.1.03-15 Franck-Hertz experiment with Ne-tube

5.1.04-00 Planck’s “quantum of action” from photoelectric effect (line separation by interference filters)

5.1.05-00 Planck’s “quantum of action” from the photoelectric effect (line separation by defraction grating)

5.1.06-00 Fine structure, one-electron and two-electron spectra

5.1.07-00 Balmer series / Determination of Rydberg’s constant

5.1.08-00 Atomic spectra of two-electron systems: He, Hg

5.1.10-05 Zeeman effect with CCD-Camera incl. measurement software

5.1.11-00 Stern-Gerlach experiment

5.1.12-00 Electron spin resonance

5.1.13-00 Electron diffraction

5.2 Radioactivity

5.2.01-01 Half-life and radioactive equilibrium

5.2.01-11 Half-life and radioactive equilibrium with Cobra3

5.2.02-11 Law of radioactive decay with Cobra3

5.2.03-11 Poisson’s distribution and Gaussian distribution of radioactive decay with Cobra3 – Influence of the dead time of the counter tube

5.2.04-00 Visualisation of radioactive particles / Diffusion cloud chamber

5.2.21-00 Rutherford experiment

5.2.22-01 Fine structure of the �-spectrum of 241Am

5.2.22-11 Fine structure of the �-spectrum of 241Am w. Cobra3

5.2.23-01 Study of the �-energies of 226Ra

5.2.23-11 Study of the �-energies of 226Ra with Cobra3

5.2.24-01 Energy loss of �-particles in gases

5.2.24.11 Energy loss of �-particles in gases with Cobra3

5.2.31-00 Electron absorption

5.2.32-00 �-spectroscopy

5.2.41-01 Law of distance and absorption of gamma or beta rays

5.2.41-11 Law of distance and absorption of gamma or beta rays with Cobra3

5.2.41-01 Energy dependence of the �-absorption coefficient

5.2.42-11 Energy dependence of the �-absorption coefficient with Cobra3

5.2.44-01 Compton effect

5.2.44-11 Compton effect with Cobra3

5.4.45-01 Internal conversion in 137mBa

5.2.45-11 Internal conversion in 137mBa with Cobra3

5.2.46-01 Photonuclear cross-section / Compton scattering cross-section

5.2.46-11 Photonuclear cross-section / Compton scattering cross-section with Cobra3

5.2.47-01 X-ray fluorescence and Moseley’s law

5.2.47-11 X-ray fluorescence and Moseley’s law with Cobra3

5.3 Solid-state Physics

5.3.01-01 Hall effect in p-germanium

5.3.01-11 Hall effect in p-germanium with Cobra3

5.3.02-01 Hall effect in n-germanium

5.3.02-11 Hall effect in n-germanium with Cobra3

5.3.03-00 Hall effect in metals

5.3.04-01 Band gap of germanium

5.3.04-11 Band gap of germanium with Cobra3

5.4 X-ray Physics

5.4.01-00 Characteristic X-rays of copper

5.4.02-00 Characteristic X-rays of molybdenum

5.4.03-00 Characteristic X-rays of iron

5.4.04-00 The intensity of characteristic X-rays as a function of anodecurrent and anode voltage

5.4.05-00 Monochromatization of molybdenum X-rays

5.4.06-00 Monochromatization of copper X-rays

5.4.07-00 K� doublet splitting of molybdenum X-rays / fine structure

5.4.08-00 K� doublet splitting of iron X-rays / fine structure

5.4.09-00 Duane-Hunt displacement law and Planck's “quantum of action”

5.4.10-00 Characteristic X-ray lines of different anode materials / Moseley's Law; Rydberg frequency and screening constant

5.4.11-00 Absorption of X-rays

5.4.12-00 K- and L-absorption edges of X-rays / Moseley's Law and the Rydberg constant

5.4.13-00 Examination of the structure of NaCl monocrystals withdifferent orientations

5.4.14-00 X-ray investigation of cubic crystal structures / Debye-Scherrer powder method

5.4.15-00 X-ray investigation of hexagonal crystal structures / Debye-Scherrer powder method

5.4.16-00 X-ray investigation of crystal structures / Laue method

5.4.17-00 Compton scattering of X-rays

5.4.18-00 X-ray dosimetry

5.4.19-00 Contrast medium experiment with a blood vessel model

5.4.20-00 Determination of the length and position of an object whichcannot be seen

5.4 Handbooks

X-Ray Experiments

Cobra3 Physics and Chemistry/Biology

5


1Mechanics

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 11


Contents

1.1 Measurement Techniques

1.1.01-00 Measurement of basic constants: length, weight and time

1.2 Statics

1.2.01-00 Moments

1.2.02-00 Modulus of elasticity


1.3 Dynamics

1.3.01-01 Hooke’s law


1.3.03-01 Newton’s 2nd Law / Air track


1.3.05-01 Laws of Collision / Air track


1.3.07-01 Free fall


1.3.09-11 Determination of the gravitational constant / Computerized Cavendish balance


1.3.12-00 Ballistic Pendulum


1.3.13-11 Moment of inertia and angular acceleration with Cobra3


1.3.16-01 Centrifugal force


1.3.18-00 Mechanical conservation of energy / Maxwell’s wheel


1.3.20-00 Laws of gyroscopes / cardanic gyroscope


1.3.22-00 Reversible pendulum


1.3.23-11 Pendulum oscillations with Cobra3


1.3.25-11 Coupled Pendula with Cobra3


1.3.27-01 Forced Oscillations – Pohl’s pendulum

1.3.27-11 Forced Oscillations – Pohl’s pendulum; Determination of resonance frequencies by Fourier analysis

1.3.28-01 Moments of inertia of different bodies / Steiner’s theorem


Mechanics

1.3.30-00 Torsional vibrations and torsion modulus


1.3.32-00 The propagation of a periodically excited continuous transverse wave


1.4 Mechanics of Liquids and Gaseous Bodies

1.4.01-00 Density of liquids


1.4.03-00 Viscosity of Newtonian and non-Newtonian liquids (rotary viscometer)


1.4.05-00 Surface tension by the ring method (Du Nouy method)

1.4-06-11 Surface tension by the pull-out method with Cobra3

1.4.07-00 Barometric height formula


1.5 Mechanical Vibration Acoustics

1.5.01-00 Vibration of strings


1.5.04-01 Acoustic Doppler effect


1.5.06-01 Velocity of sound using Kundt’s tube


1.5.08-11 Resonance frequencies of Helmholtz resonators with Cobra3


1.5.10-00 Optical determination of velocity of sound in liquids


1.5.12-00 Temperature dependence of the Velocity of sound in liquids


1.5.14-01 Absorption of ultrasonic in air


1.5.16-11 Ultrasonic diffraction at different multiple slit systems with Cobra3

1.5.17-11 Diffraction of ultrasonic waves at a pin hole and a circular obstaclewith Cobra3

1.5.18-01 Ultrasonic diffraction at Fresnel lenses / Fresnel zone contruction

1.5.19-11 Interference by two identical ultrasonic transmitters with Cobra3

1.6 Handbooks

Physics Demonstration Experiments – Magnet Board Mechanics 1


1LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 12


Measurement of basic constants: length, weight and time 1.1.01-00

Measurement Techniques Mechanics

Principle:Caliper gauges, micrometers andspherometers are used for the accu-rate measurement of lengths, thick-nesses, diameters and curvatures. Amechanical balance is used forweight determinations, a decadecounter is used for accurate timemeasurements. Measuring proce-dures, accuracy of measurement andreading accuracy are demonstrated.

Vernier caliper

Tasks:1. Determination of the volume of

tubes with the caliper gauge.

2. Determination of the thickness ofwires, cubes and plates with themicrometer.

3. Determination of the thickness ofplates and the radius of curvatureof watch glasses with the sphe-rometer.

What you can learn about …

� Length� Diameter� Inside diameter thickness� Curvature� Vernier� Weight resolution� Time measurement

Vernier caliper 03010.00 1Micrometer 03012.00 1Spherometer 03017.00 1Light barrier 11207.20 1Digital counter, 4 decades 13600.93 1Alternative to 13600.93:Digital counter, 6-decade 13603.93 1

Precision balance, 2 pans, 500 g 44011.50 1Set of precision weights, 1 mg–200 g 44070.20 1Iron column 03913.00 1Iron cylinder 03914.00 1Iron wire, d = 1.0 mm, l = 10 m 06104.01 1Aluminium foil, set of 4 sheets 06270.00 1Glass plate, 100�85�1 mm 08203.00 1Watch glass, dia. 80 mm 34572.00 1Watch glass, dia. 100 mm 34574.00 1Watch glass, dia. 125 mm 34575.00 1Glass tubes, straight, 80 mm, 10 36701.65 1Glass tube, d = 24/21 mm, l = 120 mm 45158.00 1Cubes, set of 8 02214.00 1Fish line, l = 100 m 02090.00 1Steel ball with eyelet, d = 32 mm 02466.01 1Rod with hook 02051.00 1Support rod -PASS-, square, l = 630 mm 02027.55 1Tripod base -PASS- 02002.55 1Right angle clamp -PASS- 02040.55 2Measuring tape, l = 2 m 09936.00 1Connecting cord, l = 500 mm, red 07361.01 2Connecting cord, l = 500 mm, blue 07361.04 2

What you need:

Complete Equipment Set, Manual on CD-ROM includedMeasurement of basic constants: length, weight and time P2110100

Knife-edge measuring facesfor inside measurement

Slide Guide barDepth measuring

Measuring facesfor depthmeasurement

Graduated scaleVernier

Movable jaw blade

Measuring facesfor outsidemeasurement

Fixedjawblade

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 13


1.2.01-00 Moments

Principle:Coplanar forces (weight, spring bal-ance) act on the moments disc oneither side of the pivot. In equilibri-um, the moments are determined asa function of the magnitude anddirection of the forces and of thereference point.

Moment as a function of the distance between the origin of the coordinatesand the point of action of the force.

Tasks:1. Moment as a function of the dis-

tance between the origin of thecoordinates and the point of ac-tion of the force,

2. moment as a function of the anglebetween the force and the posi-tion vector to the point of actionof the force,

3. moment as a function of the force.

Moments disk 02270.00 1

Spring Balance 1 N 03060.01 2


Barrel base -PASS- 02006.55 1



Swivel clamp -PASS- 02041.55 1

Bolt with pin 02052.00 1

Weight holder f. slotted weights 02204.00 1

Slotted weight, 10 g, black 02205.01 4


Fish line, l = 100 m 02090.00 1

Rule, plastic, l = 200 mm 09937.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMoments P2120100

Mechanics Statics


� Moments� Couple� Equilibrium� Statics� Lever� Coplanar forces

m = 0.1 kg

r2 = 0.12 m

� = �/2.

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 14


Modulus of elasticity 1.2.02-00

Statics Mechanics

Principle:A flat bar is supported at two points.It is bent by the action of a forceacting at its centre. The modulus ofelasticity is determined from thebending and the geometric data ofthe bar.

Table 1: The modulus of elasticity for different materials.

Tasks:1. Determination of the characteris-

tic curve of the dial gauge

2. Determination the bending of flatbars as a function

● of the force

● of the thickness, at constantforce

● of the width, at constant force

● of the distance between thesupport points at constant force

3. Determination the modulus ofelasticity of steel, aluminium andbrass.


� Young’s modulus� Modulus of elasticity� Stress� Deformation� Poisson’s ratio� Hooke’s law

Dial gauge 10/0.01 mm 03013.00 1

Holder for dial gauge 03013.01 1

Flat bars, set 17570.00 1

Knife-edge with stirrup 03015.00 1

Bolt with knife-edge 02049.00 2









Measuring tape, l = 2 m 09936.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedModulus of elasticity P2120200

Material Dimensions [mm] E �N · m-2�

Steel 10�1.5 2.059 · 1011

Steel 10�2 2.063 · 1011

Steel 10�3 2.171· 1011

Steel 15�1.5 2.204 · 1011

Steel 20�1.5 2.111 · 1011

Aluminium 10�2 6.702 · 1010

Brass 10�2 9.222 · 1010

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 15



Principle:The relationship between torque andangle of rotation is determined whenmetal bars are twisted. The hystere-sis curve is recorded.

Mechanical hysteresis curve for the torsion of a copper rod of 2 mm diameterand 0.5 m long.

Tasks:1. Record the hysteresis curve of

steel and copper rods.

2. Record the stress-relaxation curvewith various relaxation times ofdifferent materials.

Torsion apparatus 02421.00 1

Torsion rod, steel, l = 500 mm, d = 2 mm 02421.01 1

Torsion rod, Al, l = 500 mm, d = 2 mm 02421.02 1





Torsion rod, brass, l = 500 mm, d = 2 mm 02421.07 1

Torsion rod, Cu, l = 500 mm, d = 2 mm 02421.08 1


Spring balance 2.5 N 03060.02 1

Stopwatch, digital, 1/100 sec. 03071.01 1

Support base -PASS- 02005.55 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedMechanical hysteresis P2120300

Mechanics Statics


� Mechanical hysteresis� Elasticity� Plasticity� Relaxation� Torsion molulus� Plastic flow� Torque� Hooke’s law

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 16


Hooke’s law 1.3.01-01

Statics Mechanics

2,0

1,5

1,0

0,5

0

X

0 2 4 6 8 � lcm

FwN

10 12 14 16 18

XX

XX

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

B

A

Principle:The validity of Hooke's law is deter-mined for two helical springs withdifferent spring constants. The elon-gation of the helical spring, whichdepends on the deforming force, isstudied by means of the weights ofmasses. For comparison, a rubberband, for which no proportionalityexists between the exerted force andthe resulting elongation, is submit-ted to the same forces.

Acting weight Fw as a function of the extension �l for a rubber band (elastic hysteresis).

Tasks:1. Determining the spring constants

of helical springs

2. Study of the elongation of a rub-ber band


� Hooke's law� Spring constant� Limit of elasticity� Elastic hysteresis� Elastic after-effect





Cursors, 1 pair 02201.00 1



Slotted weight, 10 g, silver bronze 02205.02 2



Helical spring, 3 N/m 02220.00 1


Silk thread, 200 m 02412.00 1

Meter scale, demo, l = 1000 mm 03001.00 1

Holding pin 03949.00 1

Square section rubber strip, l = 10 m 03989.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedHooke’s law P2130101

Theory (Hook’s Law)

Experiment

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 17



Principle:The validity of Hooke’s Law is provenusing various helical springs withdifferent spring constants. In com-parison, the behaviour of a stretchedrubber band is examined, for whichthere is no proportionality betweenacting force and resulting extension.

Characteristic elongation curve for a helical spring with D = 20 N/m.

Tasks:1. Calibration of the system (move-

ment sensor and force sensor).

2. Measurement of the tensile forceas a function of the path for threedifferent helical springs and a rub-ber band.

3. Determination of the spring con-stant and evaluation of a hystere-sis curve.

4. Verification of Hooke’s law.

Cobra3 Basic Unit 12150.00 1Power supply, 12 V– 12151.99 1RS232 cable 14602.00 1Cobra3 Force/Tesla Software 14515.61 1Square section rubber strip, l = 10 m 03989.00 1Newton Measuring module 12110.00 1Newton sensor 12110.01 1Movement sensor with cable 12004.10 1Adapter, BNC-socket/4 mm plug pair 07542.27 1Adapter, BNC socket - 4 mm plug 07542.20 1Helical spring, 3 N/m 02220.00 1Helical spring, 20 N/m 02222.00 1Helical spring, 30 N/m 02224.00 1Right angle clamp -PASS- 02040.55 2Support rod -PASS-, square, l = 1000 mm 02028.55 1Stand tube 02060.00 1Barrel base -PASS- 02006.55 1Bench clamp -PASS- 02010.00 1Plate holder 02062.00 1Meter scale, demo, l = 1000 mm 03001.00 1Nylon thread, l = 50 m 02095.00 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedHooke’s law with Cobra3 P2130111

Mechanics Statics


� Spring constant� Limit of elasticity� Extension and compression

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 18


Newton’s 2nd Law / Air track 1.3.03-01

Principle:The distance-time law, the velocity-time law, and the relationship be-tween mass, acceleration and forceare determined with the aid of theair track rail for uniformly accelerat-ed motion in a straight line.


� Velocity� Acceleration� Force� Acceleration of gravity

Tasks:Determination of:

1. Distance travelled as a function oftime

2. Velocity as a function of time

3. Acceleration as a function of theaccelerated mass

4. Acceleration as a function offorce.

Air track rail 11202.17 1

Blower 13770.97 1

Pressure tube, l = 1.5 m 11205.01 1

Glider f. air track 11202.02 1

Screen with plug, l = 100 mm 11202.03 1

Hook with plug 11202.07 1

Starter system 11202.13 1

Magnet w. plug f. starter system 11202.14 1

Precision pulley 11201.02 1

Stop, adjustable 11202.19 1

Fork with plug 11202.08 1

Endholder for air track rail 11202.15 1

Light barrier, compact 11207.20 4

Timer 4-4 13605.99 1



Weight holder 1 g 02407.00 1

Silk thread, 200 m 02412.00 1

Slotted weight, 1 g, natur.colour 03916.00 20

Portable balance Mod. LS2000 46002.93 1

Barrel base 02006.55 4




Connecting cord, l = 1000 mm, yellow 07363.02 4




What you need:

Complete Equipment Set, Manual on CD-ROM includedNewton’s 2nd Law / Air track P2130301

The distance travelled s plotted as a function of the time t ; m1 = 10 g, m2 = 201 g.

Dynamics Mechanics

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 19



Principle:According to Newton’s 2nd law ofmotion for a mass point, the rela-tionship between mass, accelerationand force are investigated.

Path-time law.

Tasks:The distance-time law, the velocity-time law and the relationship be-tween mass, acceleration and forceare determined. The conservation ofenergy can be investigated.


Power supply, 12 V- 12151.99 1

RS232 cable 14602.00 1

Cobra3 Translation/Rotation Software 14512.61 1


Air track 11202.17 1

Blower 13770.97 1


Glider for air track 11202.02 1

Slotted weight, 1 g, polished 03916.00 9




Starter system, mechanical, with trigger 11202.13 1

Magnet with plug for starter system 11202.14 1

Tube with plug 11202.05 1

Plasticine 03935.03 1

Hook with plug 11202.07 1

Silk thread, l = 200 m 02412.00 1

Weight holder, 1 g 02407.00 1

Bench clamp -PASS- 02010.00 1

Right-angle clamp 02043.00 2

Support rod, l = 250 mm 02031.00 1

Support rod, l = 10 cm 02030.00 1


Portable balance, Mod. LS2000 46002.93 1

Block battery, 9 V 07496.10 1

Connecting cord, l = 100 cm, red 07363.01 1

Connecting cord, l = 100 cm, blue 07363.04 1

Connecting cord, l = 100 cm, yellow 07363.02 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedNewton’s 2nd Law / Air track with Cobra3 P2130311

Mechanics Dynamics


� Linear motion� Velocity� Acceleration� Conservation of energy

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:48 Uhr Seite 20


Dynamics Mechanics

Laws of Collision / Air track 1.3.05-01

Principle:The volocities of two gliders, movingwithout friction on an air-cushiontrack, are measured before and aftercollision, for both elastic and inelas-tic collision.

1.3 In accordance with the meanvalue of the measured impulse ofthe first glider before the colli-sion, the theoretical values of theimpulses for the two gliders areentered for a range of massratios from 0 to 3. For purposesof comparison the measuringpoints (see 1.1) are plotted in thegraph.

1.4 In accordance with the meanvalue of the measured energy ofthe first glider before the colli-sion, the theoretical values of theenergy after the collision areplotted analogously to Task 1.3.In the process, the measured val-ues are compared with the theo-retical curves.

Elastic collision: calculated energies after the collision as functions of themass ratio of the gliders.

Tasks:1. Elastic collision1.1 The impulses of the two gliders

as well as their sum after thecollision. For comparison themean value of the impulses ofthe first glider is entered as ahorizontal line in the graph.

1.2 Their energies, in a manner anal-ogous to Task 1.1


� Conservation of momentum� Conservation of energy� Linear motion� Velocity� Elastic loss� Elastic collision

Air track rail 11202.17 1

Blower 13770.93 1


Glider f. air track 11202.02 2



Needle with plug 11202.06 2

Fork with plug 11202.08 1

Rubber bands f. fork w/plug, 10 pcs 11202.09 1

Plate with plug 11202.10 1

Starter system 11202.13 1

Magnet w. plug f. starter system 11202.14 1

Endholder for air track rail 11202.15 1




Timer 4-4 13605.99 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of Collision / Air track P2130501

2. Inelastic collision2.1 The impulse values are plotted as

in Task 1.1.

2.2 The energy values are plotted asin Task 1.2.

2.3 The theoretical and measuredimpulse values are compared asin Task 1.3.

2.4 As in Task 1.4, the theoretical anmeasured energy values arecompared. In order to clearlyillustrate the energy loss and itsdependence on the mass ratios,the theoretical functions of thetotal energy of both gliders andthe energy loss after the collisionare plotted.

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 21



Principle:The velocity of two gliders, movingwithout friction on an air-cushiontrack, are measured before and aftercollision, for both elastic and inelas-tic collision.

Tasks:1. Elastic collision

A glider whose mass always re-mains unchanged collides with asecond resting glider at a constantvelocity. A measurement series, inwhich the velocities of the firstglider before the collision and thevelocities of both gliders after itare to be measured, is conductedby varying mass of the restingglider.

Measuring parameters for velocity measurement

2. Inelastic collisionA glider, whose mass always re-mains unchanged, collides with aconstant velocitiy with a secondresting glider. A measurement se-ries with different masses of theresting glider is performed: thevelocities of the first glider beforethe collision and those of bothgliders, which have equal veloci-ties, after it are to be measured.



RS232 data cable 14602.00 1

Cobra3 Timer / Counter Software 14511.61 1

Air track, basic set 11202.77 1


Needle with plug 11202.06 1

Starter system, mechanical, with trigger 11202.13 1

Magnet with plug for starter system 11202.14 1

Plasticine 03935.03 1


Blower 13770.93 1

Pressure tube, l = 1,5 m 11205.01 1

Support rod, stainless steel, l = 500 mm 02032.00 2



Barrel base, -Pass- 02006.55 2




Power supply 9 V/120 mA 46005.93 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of collision with Cobra3 P2130511

Mechanics Dynamics


� Conservation of momentum� Conservation of energy� Linear motion� Velocity� Elastic loss

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 22


Dynamics Mechanics

Free fall 1.3.07-01

Principle:A sphere falling freely covers certaindistances. The falling time is meas-ured and evaluated from diagrams.The acceleration due to gravity canbe determined.

Height of fall as a function of falling time.

Tasks:1. To determine the functional rela-

tionship between height of falland falling time (h = h(t)=1/2 gt2).

2. To determine the acceleration dueto gravity.


� Linear motion due to constantacceleration

� Laws of falling bodies� Gravitational acceleration

Falling sphere apparatus 02502.88 1

consisting of:

Release unit 02502.00 1

Impact switch 02503.00 1

Digital counter, 4 decades 13600.93 1



Plate holder 02062.00 1



Support rod-PASS-, square, l = 1000 mm 02028.55 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedFree fall P2130701

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 23

Height of fall as a function of falling time.



Principle:The fall times t are measured for dif-ferent heights of fall h. h is repre-sented as the function of t or t2, sothe distance-time law of the free fallresults as

h = 1 · g · t2

Then the measured values are takento determine the acceleration due togravity g.

2

Tasks:Determination of:

– Distance time law for the free fall.

– Velocity-time law for the free fall.

– Precise measurement of the accel-eration due to gravity for the freefall.

Falling sphere apparatus 02502.88 1consisting of:Release unit 02502.00 1Impact switch 02503.00 1Cobra3 Basic Unit 12150.00 1Power supply, 12V– 12151.99 1RS 232 data cable 14602.00 1Cobra3 Timer/Counter Software 14511.61 1Tripod base -PASS- 02002.55 1Support rod -PASS-, l = 1000 mm 02028.55 1Right angle clamp -PASS- 02040.55 2Measuring tape, l = 2 m 09936.00 1Connecting cord, l = 750 mm, yellow 07362.02 1Connecting cord, l = 750 mm, blue 07362.04 1Connecting cord, l = 1500 mm, yellow 07364.02 1Connecting cord, l = 1500 mm, blue 07364.04 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedFree fall with Cobra3 P2130711

Mechanics Dynamics


� Linear motion due to constantacceleration

� Laws governing falling bodies� Acceleration due to gravity

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 24


Dynamics Mechanics

Determination of the gravitational constant / Computerized Cavendish balance 1.3.09-11

Principle:Two small lead spheres are positionedon a beam, which is freely suspendedon a thin metal wire. At the beginningthe large lead spheres are positionedsymmetrically opposite to the smallspheres in that way that the attractiveforces are eliminated. Thereafter, thelarge spheres are swung so that theyare close to the small spheres. As aconsequence of the gravitational at-tracting force the beam with the smallspheres now moves in a new equilibri-um position, where the attractiveforces are equivalent to the force ofthe torsion of the wire. The gravita-tional constant can be determinedfrom the new equilibrium position.

Output voltage of the free and damped oscillating Cavendish balance.

Tasks:1. Calibration of an angular detector.

2. Determination of the oscillationtime of a free and damped oscil-lating torsion pendulum.

3. Determination of the gravitationalconstant.

Cavendish balance,computerized 02540.00 1


Circular level 02122.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedDetermination of the gravitational constant /Computerized Cavendish balance P2130911


� Law of gravitation� Free, damped, forced and

torsional oscillations� Moment of inertia of spheres

and rods� Steiner’s theorem� Shear modulus

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 25


Mechanics Dynamics


Principle:A steel ball is fired by a spring at dif-ferent velocities and at differentangles to the horizontal. The rela-tionships between the range, theheight of projection, the angle of in-clination, and the firing velocity aredetermined.

Maximum range as a function of the angle of inclination � for different initialvelocity v0: Curve 1 v0 = 5.3 m/s

Curve 2 v0 = 4.1 m/sCurve 3 v0 = 3.1 m/s

Tasks:1. To determine the range as a func-

tion of the angle of inclination.

2. To determine the maximum heightof projection as a function of theangle of inclination.

3. To determine the (maximum)range as a function of the initialvelocity.


� Trajectory parabola� Motion involving uniform

acceleration� Ballistics

Ballistic pendulum 11229.10 1

Recording paper, 1 roll, 25 m 11221.01 1

Steel ball, d = 19 mm 02502.01 2

Two-tier platform support 02076.03 1



Speed measuring attachement 11229.30 1

Power supply 5 VDC/2.5 A 11079.99 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedProjectile motion P2131100

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 26


Dynamics Mechanics

Principle:A classic method of determining thevelocity of a projectile is to shoot theprojectile into a resting mass whichis large compared to the projectile’smass and hung as a pendulum. In theprocess, the projectile remains in thependulum mass and oscillates withit. This is an inelastic collision inwhich the momentum remainsunchanged. If the pendulum’smechanical data are known, one caninfer the velocity of the pendulum’smass (including the projectile’s mass)at the lowest point of thependulum’s oscillation from theamplitude of the pendulum’s oscilla-tion. The momentum of the twomasses in this phase of the oscilla-tion must thus be equal to theimpulse of the projectile before itstruck the pendulum. If one knowsthe masses of the pendulum and theprojectile, one can calculate theprojectile’s velocity.

In order to be able to use this meas-uring principle without danger, thefollowing set-up is used here: A steelball is shot at the mass of a pendu-lum with the aid of a spring catapult.The pendulum mass has a hollowspace in which the steel ball is held.

If, additionally, two light barriers anda time measuring device are avail-able, an independent, direct meas-urement of the initial velocity of theball can be made.

Experimental set-up with supplement for direct measurement of the initialvelocity of the ball.

Tasks:1. Measurement of the oscillation

amplitudes of the ballistic pendu-lum after capturing the steel ballfor the three possible tensionenergies of the throwing device.

2. Calculation of the initial velocitiesof the ball from the measuredoscillation amplitudes and themechanical data of the pendulumis performed using the approxima-tion formula (3).

3. Plotting of the velocity v of thesteel ball as a function of themaximum deflection � (0…90°) ofthe pendulum according to for-mula (3), taking into considerationthe special mechanical data of theexperiment.

4. Determination of the correctionfactor fcor for the utilised pendu-lum for the conversion of thevelocities determined by using theapproximation formula into thevalues obtained from the exacttheory. Correction of the velocityvalues from Tasks 2.

5. If the supplementary devices forthe direct measurement of theinitial velocity are available,measure the initial velocities cor-responding to the three tensionsteps of the throwing device byperforming 10 measurementseach with subsequent mean valuecalculation. Plot the measuredpoints in the diagram from Task 3.Give reasons for contingentsystematic deviations from thetheoretical curve.

Ballistic pendulum 11229.00 1

Steel ball, d = 19 mm 02502.01 2

Speed measuring attachement 11229.30 1

Power supply 5 VDC/2.5 A 11079.99 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedBallistic Pendulum P2131200


� Potential and kinetic energy� Rotational energy� Moment of inertia� Inelastic collision� Principle of conservation of

momentum� Angular momentum� Measurement of projectile

velocities

Ballistic Pendulum 1.3.12-00

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 27


Principle:A moment acts on a body which canbe rotated about a bearing withoutfriction. The moment of inertia isdetermined from the angular accel-eration.

Moment of inertia of a mass point as a function of the square of its distancefrom the axis of rotation.

Tasks:From the angular acceleration, themoment of inertia are determined asa function of the mass and of thedistance from the axis of rotation.

1. of a disc,

2. of a bar,

3. of a mass point.


� Angular velocity� Rotary motion� Moment� Moment of inertia of a disc� Moment of inertia of a bar� Moment of inertia of a mass

point

Turntable with angle scale 02417.02 1

Aperture plate for turntable 02417.05 1

Air bearing 02417.01 1

Inertia rod 02417.03 1

Holding device w. cable release 02417.04 1


Blower 13770.97 1


Light barrier with Counter 11207.30 1

Power supply 5 V DC/0.3 A 11076.99 1

Supporting blocks, set of 4 02070.00 1

Slotted weight, 1 g, natur. colour 03916.00 20




Silk thread, 200 m 02412.00 1





Bench clamp, -PASS- 02010.00 2

What you need:

Complete Equipment Set, Manual on CD-ROM includedMoment of inertia and angular acceleration P2131301


Mechanics Dynamics

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 28


Dynamics Mechanics

Moment of inertia and angular acceleration with Cobra3 1.3.13-11

Principle:If a constant torque is applied to abody that rotates without frictionaround a fixed axis, the changingangle of rotation increases propor-tionally to the square of the time andthe angular velocity proportional tothe time.

Potential energy and additionally the rotational energy.

Tasks:1. Measurement of the laws of angle

and angular velocity according totime for a uniform rotation move-ment.

2. Measurement of the laws of angleand angular velocity according totime for a uniformly acceleratedrotational movement.

3. Rotation angle � is proportional tothe time t required for the rotati-on:

4. Measurement of the laws of angleand angular velocity according totime for a uniformly acceleratedrotational movement.

Cobra3 Basic Unit 12150.00 1Power supply, 12 V- 12151.99 1RS232 cable 14602.00 1Translation/Rotation Software 14512.61 1Light barrier, compact 11207.20 1Blower 13770.97 1Pressure tube, l = 1,5 m 11205.01 1Air bearing 02417.01 1Turntable with angle scale 02417.02 2Holding device with cable release 02417.04 1Aperture plate for turntable 02417.05 1Slotted weight, 1 g, polished 03916.00 9Slotted weight, 10 g, black 02205.01 3Slotted weight, 50 g, silver bronze 02206.02 2Silk thread, l = 200 m 02412.00 1Weight holder, 1 g 02204.00 1Bench clamp -PASS- 02010.00 2Tripod -PASS- 02002.55 1Stand tube 02060.00 1Support rod, l = 250 mm 02031.00 1Measuring tape, l = 2 m 09936.00 1Circular level 02122.00 1Right-angle clamp 02043.00 1Connecting cord, l = 100 cm, red 07363.01 1Connecting cord, l = 100 cm, blue 07363.04 1Connecting cord, l = 100 cm, yellow 07363.02 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedMoment of inertia and angular accelerationwith Cobra3 P2131311


� Angular velocity� Rotation� Moment� Torque� Moment of inertia� Rotational energy

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 29


Principle:The angle of rotation and angularvelocity are measured as a functionof time on a body which is pivoted soas to rotate without friction andwhich is acted on by a moment. Theangular acceleration is determinedas a function of the moment.

3. the angular acceleration as afunction of time,

4. the angular acceleration as afunction of the lever arm.

Angle of rotation as a function of time with uniformly accelerated rotarymotion for m = 0.01 kg, r = 0.015 m.

Tasks:With uniformly accelerated rotarymotion, the following will be deter-mined:

1. the angle of rotation as a functionof time,

2. the angular velocity as a functionof time.


� Circular motion� Angular velocity� Angular acceleration� Moment of inertia� Newton’s laws� Rotation

Turntable with angle scale 02417.02 1

Aperture plate for turntable 02417.05 1

Holding device w. cable release 02417.04 1

Air bearing 02417.01 1



Blower 13770.93 1


Power supply 5V DC/0, 3 A 11076.99 1

PEK capacitor, 100 nF/250 V 39105.18 1

Adapter, BNC-plug/socket 4 mm 07542.26 1



Silk thread, l = 200 m 02412.00 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedMoment and angular momentum P2131500


Mechanics Dynamics

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 30


Dynamics Mechanics

Centrifugal force 1.3.16-01

Principle:A body with variable mass moves ona circular path with adjustable radiusand variable angular velocity. Thecentrifugal force of the body will bemeasured as a function of theseparameters.

Centrifugal force as a function of the angular velocity v.

Tasks:Determination of the centrifugalforce as a function

1. of the mass,

2. of the angular velocity,

3. of the distance from the axis ofrotation to the centre of gravity ofthe car.

Centrifugal force apparatus 11008.00 1

Car 11060.00 1


Laboratory motor, 220 V AC 11030.93 1

Gearing 30/1, for 11030.93 11029.00 1

Bearing unit 02845.00 1

Driving belt 03981.00 1

Support rod w. hole, 100 mm 02036.01 1


Spring balance holder 03065.20 1


Bosshead 02043.00 2


Fish line, l = 100 m 02090.00 1

Spring balance, transparent, 2 N 03065.03 1




Power supply 5 V DC/0, 3 A 11076.99 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedCentrifugal force P2131601


� Centripetal force� Rotary motion� Angular velocity� Apparent force

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 31


Principle:A body with variable mass moves ona circular path with adjustable radiusand variable angular velocity. Thecentrifugal force of the body will bemeasured as a function of these pa-rameters.

Typical evaluation of central force as a function of the square of angular ve-locity.

Tasks:Determination of the centrifugalforce as a function

1. of the mass,

2. of the angular velocity,

3. of the distance from the axis ofrotation to the centre of gravity ofthe car.


� Centrifugal force� Centripetal force� Rotary motion� Angular velocity� Apparent force


Power supply, 12V- 12151.99 1

RS232 cable 14602.00 1

Newton measuring module 12110.00 1

Newton sensor 12110.01 1

Cobra3 Force/Tesla Software 14515.61 1

Centrifugal force apparatus 11008.00 1

Car 11060.00 1



Gearing 30/1, for 11030.93 11029.00 1



Support rod w. hole, 100 mm 02036.00 1



Right angle clamp 02040.55 1


Fish line, l = 100m 02090.00 1






PC, Windows 95® or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedCentrifugal force with Cobra3 P2131611


Mechanics Dynamics

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 32


Dynamics Mechanics

Mechanical conservation of energy / Maxwell’s wheel 1.3.18-00

Principle:A disk, which can unroll with its axison two cords, moves in the gravita-tional field. Potential energy, energyof translation and energy of rotationare converted into one another andare determined as a function of time.

Energy of the Maxwell disk as afunction of time.1. Negative potential energy2. Energy of translation3. Energy of rotation

Tasks:The moment of inertia of theMaxwell disk is determined.

Using the Maxwell disk,

1. the potential energy,

2. the energy of translation,

3. the energy of rotation,

are determined as a function of time.

Support base -PASS- 02005.55 1Support rod-PASS-, square, l = 1000 mm 02028.55 3Right angle clamp -PASS- 02040.55 4Meter scale, demo, l = 1000 mm 03001.00 1Cursors, 1 pair 02201.00 1Maxwell wheel 02425.00 1Connecting cord, l = 1000 mm, red 07363.01 1Connecting cord, l = 1000 mm, blue 07363.04 1Light barrier with Counter 11207.30 1Holding device w. cable release 02417.04 1Plate holder 02062.00 1Adapter, BNC-plug/socket 4 mm 07542.26 1PEK capacitor, 100 nF/250 V 39105.18 1Power supply 5 V DC/0.3 A 11076.99 1Connecting cord, l = 1500 mm, red 07364.01 1Connecting cord, l = 1500 mm, blue 07364.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMechanical conservation of energy /Maxwell’s wheel P2131800


� Maxwell disk� Energy of translation� Energy of rotation� Potential energy� Moment of inertia� Angular velocity� Angular acceleration� Instantaneous velocity� Gyroscope

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 33


Principle:The momentum of inertia of thegyroscope is investigated by measur-ing the angular acceleration causedby torques of different known values.In this experiment, two of the axes ofthe gyroscope are fixed.

The relationship between the preces-sion frequency and the gyro-fre-quency of the gyroscope with 3 freeaxes is examined for torques of dif-ferent values applied to the axis ofrotation.

If the axis of rotation of the force-free gyroscope is slightly displaced, anutation is induced. The nutationfrequency will be investigated as afunction of gyro-frequency.

3. Investigation of the relationshipbetween precession and gyro-fre-quency and its dependence fromtorque.

4. Investigation of the relationshipbetween nutation frequency andgyro-frequency.

Determination of the momentum of inertia from the slope of straight line tR

-1 = f(tP).

Tasks:1. Determination of the momentum

of inertia of the gyroscope bymeasurement of the angularacceleration.

2. Determination of the momentumof inertia by measurement of thegyro-frequency and precessionfrequency.


� Momentum of inertia� Torque� Angular momentum� Precession� Nutation


Mechanics Dynamics

Gyroscope with 3 axes 02555.00 1



Additional gyro-disc w. counter-weight 02556.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of gyroscopes / 3-axis gyroscope P2131900

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 34


Dynamics Mechanics

Laws of gyroscopes / cardanic gyroscope 1.3.20-00

Principle:If the axis of rotation of the forcefreegyroscope is displaced slightly, a nu-tation is produced. The relationshipbetween precession frequency or nu-tation frequency and gyro-frequencyis examined for different moments ofinertia.

Additional weights are applied to agyroscope mounted on gimbals, socausing a precession.

Precession frequency as a function of the gyro frequency for different addi-tional masses.

Tasks:1. To determine the precession fre-

quency as a function of the torqueand the angular velocity of thegyroscope.

2. To determine the nutational fre-quency as a function of the an-gular velocity and the moment ofinertia.

Gyro, Magnus type, incl. Handb. 02550.00 1


Digital stroboscope 21809.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of gyroscopes / cardanic gyroscope P2132000


� Moment of inertia� Torque� Angular momentum� Nutation� Precession

1. m2 = 0.163 kg

2. m2 – m1 = 0.112 kg

3. m1 = 0.051 kg

Note:A detailed handbook (128 pages)containing additional experiments isincluded, free of charge, in theequipment.

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:49 Uhr Seite 35


Principle:A mass, considered as of point form,suspended on a thread and subjectedto the force of gravity, is deflectedfrom its position of rest. The periodof the oscillation thus produced ismeasured as a function of the threadlength and the angle of deflection.

Period of the pendulum as a function of the angle of deflection.

Tasks:1. For small deflections, the oscilla-

tion period is determined as afunction of the cord length.

2. The acceleration due to gravity isdetermined.

3. The oscillation period is deter-mined as a function of the deflec-tion.


� Duration of oscillation� Period� Amplitude� Harmonic oscillation


Power supply 5 V DC/0,3 A 11076.99 1

Steel ball with eyelet, d = 24.4 mm 02465.01 1

Steel ball with eyelet, d = 32 mm 02466.01 1



Fish line, l = 100 m 02090.00 1


Clamping pads on stem 02050.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedMathematical pendulum P2132100


Mechanics Dynamics

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 36


Dynamics Mechanics

Reversible pendulum 1.3.22-00

T2

S

1.50

1.56

1.42

1.38

1.34

1.30

X

X

X

X

X

X X XX

X

X

X

X

30 40 50 60

�'a �'min �'s �'cm

Principle:By means of a reversible pendulum,terrestrial gravitational accelerationg may be determined from the peri-od of oscillation of a physical pendu-lum, knowing neither the mass northe moment of inertia of the latter.

Period T2 as a function of the position of the axis of rotation of the physicalpendulum.

Tasks:1. Measurement of the period for

different axes of rotation.

2. Determination of terrestrial gravi-tational acceleration g.

Bearing bosshead 02805.00 2

Support rod, l = 750 mm 02023.01 1

Bolt with knife-edge 02049.00 2








What you need:

Complete Equipment Set, Manual on CD-ROM includedReversible pendulum P2132200


� Physical pendulum� Moment of inertia� Steiner’s law� Reduced length of pendulum� Reversible pendulum� Terrestrial gravitational

acceleration

LEP 1.1.00-01_1.3.28-11 12.10.2003 23:02 Uhr Seite 37


Principle:Investigate the oscillation behaviourof a pendulum (rod pendulum) byvarying the magnitude of the com-ponents of the acceleration of grav-ity which are decisive for the oscilla-tion period. The pendulum that is tobe used is constructed in such amanner that its oscillation plane canbe progressively rotated from a ver-tical orientation to a horizontal one.The angle F, by which the oscillationplane deviates from its normal ver-tical position, can be read from ascale.

Oscillation period of the pendulumas a function of the slope �. of theoscillation plane. The measuredpoints are plotted above the corre-sponding theoretical curve (solidline). Upper curve: L = 270 mm;lower curve: L = 141 mm.

Tasks:1. Measurement of the oscillation

period of the pendulum as a func-tion of the angle of inclination �of the oscillation plane for twodifferent pendulum lengths.

2. Graphical analysis of the meas-ured correlations and a compari-son with the theoretical curves,which have been standardisedwith the measured value at � = 0.

3. Calculation of the effective pen-dulum length l for the accelera-tion of gravity, which is assumedto be known. Comparison of thisvalue with the distance betweenthe pivot point of the pendulumand the centre of gravity of themobile pendulum weight.

4. On the moon’s surface the “lunaracceleration of gravity” gm is only16.6% of the earth’s accelerationof gravity g. Calculate the angle �and set it on the device such thatthe pendulum in the laboratoryoscillates with the same oscilla-tion period with which it wouldoscillate on the moon in a perpen-dicular position. Compare themeasured oscillation period withthe calculated one.


� Oscillation period� Harmonic oscillation� Mathematical pendulum� Physical pendulum� Decomposition of force� Moment of inertia

Variable g pendulum 02817.00 1

Holder for light barrier 02817.10 1


Timer 4-4 13605.99 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedPendulum oscillations /variable g pendulum P2132301


Mechanics Dynamics

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 38


Dynamics Mechanics

Pendulum oscillations with Cobra3 1.3.23-11

Principle:Earth’s gravitational acceleration g isdetermined for different lengths ofthe pendulum by means of the oscil-lating period. If the oscillating planeof the pendulum is not parallel to thegravitational field of the earth, onlyone component of the gravitationalforce acts on the pendulum move-ment.

Typical measurement result

Tasks:1. Determination of the oscillation

period of a thread pendulum as afunction of the pendulum length.

2. Determination of g.

3. Determination of the gravitation-al acceleration as a function ofthe inclination of the pendulumforce.

Cobra3 Basic Unit 12150.00 1Power supply, 12 V- 12151.99 1RS232 data cable 14602.00 1Cobra3 Translation/Rotation Software 14512.61 1Movement sensor with cable 12004.10 1Adapter, BNC-socket/4mm plug pair 07542.27 1Adapter, BNC-socket-plug, 4 mm 07542.20 1Silk thread, l = 200 m 02412.00 1Fish line, l = 20 m 02089.00 1Weight holder, 1 g 02407.00 1Pendulum ball with eyelet, d = 32 mm 02466.01 2Tripod, -PASS- 02002.55 1Support rod, -PASS-, l = 1000 mm 02028.55 1Stand tube 02060.00 1Plate holder, l = 0 ... 10 mm 02062.00 1Right-angle clamp, -PASS- 02040.55 2Bench clamp -PASS- 02010.00 1Semicircular scale with pointer 08218.00 1Circular level 02122.00 1Measuring tape, l = 2 m 09936.00 1Pendulum for movement sensor 12004.11 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedPendulum oscillations with Cobra3 P2132311


� Oscillation period� Harmonic oscillation� Mathematical pendulum� Physical pendulum� Variable g-pendulum� Decomposition of force� Gravitational force

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 39



Principle:Two equal gravity pendula with aparticular characteristic frequencyare coupled by a “soft” spiral spring.The amplitudes of both pendula arerecorded as a function of time forvarious vibrational modes and differ-ent coupling factors using a y/trecorder. The coupling factors aredetermined by different methods.

Tasks:1. To determine the spring constant

of the coupling spring.

2. To determine and to adjust thecharacteristic frequencies of theuncoupled pendula.

3. To determine the coupling factorsfor various coupling-lengths using

a) the apparatus constants

b) the angular frequencies for“inphase” and “in oppositephase” vibration

c) the angular frequencies of thebeat mode.

4. To check the linear relationbetween the square of thecoupling-lengths and

a) the particular frequencies ofthe beat mode

b) the square of the frequency for“in opposite phase” vibration.

5. To determine the pendulum’scharacteristic frequency from thevibrational modes with couplingand to compare this with thecharacteristic frequency of theuncoupled pendula.

Pendulum w. recorder connection 02816.00 2


Rod with hook 02051.00 1


Slotted weight,10 g, black 02205.01 5

Recorder, Yt, 2 channel 11415.95 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedCoupled Pendula P2132501

Mechanics Dynamics


� Spiral spring� Gravity pendulum� Spring constant� Torsional vibration� Torque� Beat� Angular velocity� Angular acceleration� Characteristic frequency

Amplitude curves of the vibrations ofcoupled pendula in the beat case forthree different coupling lengths l asa function of time.Speed of recorder: t = 10 s/Div.

l = 30 cm

l = 60 cm

l = 90 cm

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 40


Coupled Pendula with Cobra3 1.3.25-11

Dynamics Mechanics

Principle:Two equal gravity pendula with aparticular characteristic frequencyare coupled by a “soft” spiral spring.The amplitudes of both pendula arerecorded as a function of time forvarious vibrational modes and differ-ent coupling factors using a y/trecorder. The coupling factors aredetermined by different methods.

Tasks:1. To determine the spring constant

of the coupling spring.

2. To determine and to adjust thecharacteristic frequencies of theuncoupled pendula.

3. To determine the coupling factorsfor various coupling-lengths using

a) the apparatus constants

b) the angular frequencies for“inphase” and “in oppositephase” vibration

c) the angular frequencies of thebeat mode.

4. To check the linear relation be-tween the square of the coupling-lengths and

a) the particular frequencies ofthe beat mode

b) the square of the frequency for“in opposite phase” vibration.

5. To determine the pendulum’scharacteristic frequency from thevibrational modes with couplingand to compare this with thecharacteristic frequency of theuncoupled pendula.


� Spiral spring� Gravity pendulum� Spring constant� Torsional vibration� Torque� Beat� Angular velocity� Angular acceleration� Characteristic frequency

Pendulum w. recorder connection 02816.00 2Helical spring, 3 N/m 02220.00 1Rod with hook 02051.00 1Weight holder f. slotted weights 02204.00 1Slotted weight,10 g, black 02205.01 5Capacitor, 10 µF/35 V 39105.28 2Cobra3 Basic Unit 12150.00 1Power supply, 12 V 12151.99 1Cobra3 Universal writer software 14504.61 1RS 232 data cable 14602.00 1Power supply 0-12 V DC/6 V, 12 V AC 13505.93 1Bench clamp -PASS- 02010.00 2Support rod -PASS-, square, l = 630 mm 02027.55 2Right angle clamp -PASS- 02040.55 2Measuring tape, l = 2 m 09936.00 1Connecting cord, l = 500 mm, red 07361.01 2Connecting cord, l = 500 mm, blue 07361.04 2PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedCoupled Pendula with Cobra3 P2132511

l = 30 cm

l = 60 cm

l = 90 cm

Amplitude curves of the vibrations ofcoupled pendula in the beat case forthree different coupling lengths l (30 cm, 60 cm and 90 cm) as afunction of time.

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 41


Principle:The spring constant D is determinedfor different experimental set-upsfrom the oscillation period and thesuspended mass.

Typical measurement result

Tasks:1. Determination of the spring con-

stant D for different springs.

2. Determination of the spring con-stant for springs linked in parallel.

3. Determination of the spring con-stant for springs linked in series.


� Spring constant� Hooke’s Law oscillations� Limit of elasticity� Parallel springs� Serial springs� Use of an interface



RS232 cable 14602.00 1



Silk thread, l = 200 m 02412.00 1


Slotted weights, 10 g 02205.01 4

Slotted weights, 50 g 02206.01 7

Tripod -PASS- 02002.55 1

Support rod -PASS-, l = 1000 mm 02028.55 1

Stand tube 02060.00 1


Right-angle clamp -PASS- 02040.55 2

Helical spring d = 3 N/m 02220.03 2

Helical spring d = 20 N/m 02222.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedHarmonic oscillations of spiral springs –Springs linked in parallel and series P2132611


Mechanics Dynamics

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 42


Dynamics Mechanics

Forced Oscillations – Pohl’s pendulum 1.3.27-01

Principle:If an oscillating system is allowed toswing freely it is observed that thedecrease of successive maximumamplitudes is highly dependent onthe damping. If the oscillatingsystem is stimulated to swing by an

B. Forced oscillation

1. The resonance curves are to bedetermined and to be repre-sented graphically using thedamping values of A.

2. The resonance frequencies areto be determined and are to becompared with the resonancefrequency values found before-hand.

3. The phase shifting between thetorsion pendulum and the stim-ulating external torque is to beobserved for a small dampingvalue assuming that in one casethe stimulating frequency is farbelow the resonance frequencyand in the other case it is farabove it.

Resonance curves for different dampings.

Tasks:A. Free oscillation

1. To determine the oscillatingperiod and the characteristicfrequency of the undampedcase.

2. To determine the oscillatingperiods and the correspondingcharacteristic frequencies fordifferent damping values. Suc-cessive, unidirectional maxi-mum amplitudes are to be plot-ted as a function of time. Thecorresponding ratios of attenu-ation, the damping constantsand the logarithmic decrementsare to be calculated.

3. To realize the aperiodic caseand the creeping.

Torsion pendulum after Pohl 11214.00 1

Power supply, universal 13500.93 1

Bridge rectifier, 30 V AC/1 A DC 06031.10 1


Digital multimeter 07134.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedForced Oscillations – Pohl’s pendulum P2132701


� Angular frequency� Characteristic frequency� Resonance frequency� Torsion pendulum� Torsional vibration� Torque and Restoring torque� Damped/undamped free

oscillation� Forced oscillation� Ratio of attenuation/

decrement� Damping constant� Logarithmic decrement� Aperiodic case� Creeping

external periodic torque, we observethat in the steady state the ampli-tude is a function of the frequencyand the amplitude of the externalperiodic torque and of the damping.The characteristic frequencies of thefree oscillation as well as the reso-nance curves of the forced oscilla-tion for different damping values areto be determined.

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 43


Mechanics Dynamics

1.3.27-11 Forced Oscillations – Pohl’s pendulumDetermination of resonance frequencies by Fourier analysis

Principle:If an oscillating system is allowed toswing freely it is observed that thedecrease of successive maximumamplitudes is highly dependent onthe damping. If the oscillatingsystem is stimulated to swing by anexternal periodic torque, we observethat in the steady state the ampli-tude is a function of the frequencyand the amplitude of the externalperiodic torque and of the damping.The characteristic frequencies of the

rectional maximum amplitudes areto be plotted as a function of time.The corresponding ratios of attenua-tion, the damping constants and thelogarithmic decrements are to becalculated.

3. To realize the aperiodic case andthe creeping.

Tasks:A. Free oscillation1. To determine the oscillating peri-

od and the characteristic frequen-cy of the undamped case.

2. To determine the oscillating peri-ods and the corresponding char-acteristic frequencies for differentdamping values. Successive, unidi-


� Angular frequency� Characteristic frequency� Resonance frequency� Torsion pendulum� Torsional vibration� Torque� Testoring torque� Damped/undamped free

oscillation� Forced oscillation� Ratio of attenuation/

decrement� Damping constant� Logarithmic decrement� Aperiodic case� Creeping

Torsion pendulum after Pohl 11214.00 1


Bridge rectifier, 30 V AC/1 A DC 06031.10 1










Movement sensor with cable 12004.10 1

Adapter, BNC-socket/4mm plug pair 07542.27 1

Adapter, BNC-socket-plug, 4 mm 07542.20 1

Silk thread, l = 200 m 02412.00 1


Tripod base ”PASS” 02005.55 1

Support rod ”PASS”, 400 mm 02026.55 1

Support rod ”PASS”, 250 mm 02025.55 1

Right angle clamp ”PASS” 02040.55 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedForced Oscillations – Pohl’s pendulumDetermination of resonance frequencies by Fourier analysis P2132711 Recorded curve of the damped oscillation.

B. Forced oscillation1. The resonance curves are to be

determined and to be representedgraphically using the dampingvalues of A.

2. The resonance frequencies are tobe determined and are to be com-pared with the resonance fre-quency values found beforehand.

free oscillation as well as the reso-nance curves of the forced oscilla-tion for different damping values areto be determined.Therefore, the oscillations arerecorded with the Cobra3 systeminconnection with the movement sen-sor. The curves of the different oscil-lations are displayed and the neces-sary quantities for the determinationof the characteristic values can eas-ily becalculated.

3. The phase shifting between thetorsion pendulum and the stimu-lating external torque is to beobserved for a small dampingvalue assuming that in one casethe stimulating frequency is farbelow the resonance frequencyand in the other case it is farabove it.

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 44


Dynamics Mechanics

Moments of inertia of different bodies / Steiner’s theorem 1.3.28-01

Principle:The period of vibration of a circulardisc which performs torsional vibra-tions about various parallel axes, ismeasured. The moment of inertia ofthe disc is determined as a functionof the perpendicular distance of theaxis of rotation from the centre ofgravity.

Moment (torque) of a spiral spring as a function of the angle of rotation.

Tasks:1. Determination of the angular

restoring constant of the spiralspring.

2. Determination of the moment ofinertia of a circular disc as a func-tion of the perpendicular distanceof the axis of rotation from thecentre of gravity.

Rotation axle 02415.01 1

Disk, w. diametrical holes 02415.07 1






Rule, plastic, l = 200 mm 09937.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMoments of inertia of different bodies /Steiner’s theorem P2132801


� Rigid body� Moment of inertia� Centre of gravity� Axis of rotation� Torsional vibration� Spring constant� Angular restoring force

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 45


Mechanics Dynamics


Principle:The moment of inertia of a solid bodydepends on its mass distribution andthe axis of rotation. Steiner’s theo-rem elucidates this relationship.

Typical measuring result

Tasks:The moments of inertia of differentbodies are determined by oscillationmeasurements. Steiner’s theorem isverified.


� Rigid body� Moment of inertia� Centre of gravity� Axis of rotation� Torsional vibration� Spring constant� Angular restoring force



RS232 cable 14602.00 1

Translation/Rotation Software 14512.61 1


Angular oscillation apparatus 02415.88 1


Block battery, 9 V 07496.10 1

Silk thread, l = 200 m 02412.00 1


Slotted weight, 1 g 03916.00 3









What you need:

Complete Equipment Set, Manual on CD-ROM includedMoments of inertia of different bodies /Steiner’s theorem with Cobra3 P2132811

LEP 1.1.00-01_1.3.28-11 10.10.2003 22:50 Uhr Seite 46


Dynamics Mechanics

Torsional vibrations and torsion modulus 1.3.30-00

Principle:Bars of various materials will be ex-citing into torsional vibration. Therelationship between the vibrationperiod and the geometrical dimen-sions of the bars will be derived andthe specific shear modulus for thematerial determined.

Torque and deflection of a torsion bar.

Tasks:1. Static determination of the tor-

sion modulus of a bar.

2. Determination of the moment ofinertia of the rod and weightsfixed to the bar, from the vibrationperiod.

3. Determination of the dependenceof the vibration period on thelength and thickness of the bars.

4. Determination of the shear modu-lus of steel, copper, aluminiumand brass.

Torsion apparatus 02421.00 1Torsion rod, steel, l = 500 mm, d = 2mm 02421.01 1Torsion rod, Al, l = 500 mm, d = 2 mm 02421.02 1Torsion rod, Al, l = 400 mm, d = 2 mm 02421.03 1Torsion rod, Al, l = 300 mm, d = 2 mm 02421.04 1Torsion rod, Al, l = 500 mm, d = 3 mm 02421.05 1Torsion rod, Al, l = 500 mm, d = 4 mm 02421.06 1Torsion rod, brass, l = 500 mm, d = 2 mm 02421.07 1Torsion rod, Cu, l = 500 mm, d = 2 mm 02421.08 1Spring Balance 1 N 03060.01 1Spring balance 2, 5 N 03060.02 1Stopwatch, digital, 1/100 sec. 03071.01 1Sliding weight 02040.55 4Support base -PASS- 02005.55 1Support rod -PASS-, square, l = 250 mm 02025.55 1Support rod -PASS-, square, l = 630 mm 02027.55 1Right angle clamp -PASS- 02040.55 4

What you need:

Complete Equipment Set, Manual on CD-ROM includedTorsional vibrations and torsion modulus P2133000


� Shear modulus� Angular velocity� Torque� Moment of inertia� Angular restoring torque� G-modulus� Modulus of elasticity

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 47


Principle:Various bodies perform torsionalvibrations about axes through theircentres of gravity. The vibrationperiod is measured and the momentof inertia determined from this.

Moment of inertia of two equal masses, of 0.214 kg each, as a function of thedistance between them.

Tasks:The following will be determined:

1. The angular restoring moment ofthe spiral spring.

2. The moment of inertia

a) of a disc, two cylinder, a sphereand a bar,

b) of two point masses, as a func-tion of the perpendicular dis-tance to the axis of rotation.The centre of gravity lies in theaxis of rotation.


� Rigid body� Moment of inertia� Axis of rotation� Torsional vibration� Spring constant� Angular restoring moment� Moment of inertia of a

sphere� Moment of inertia of a disc� Moment of inertia of a

cylinder� Moment of inertia of a long

bar� Moment of inertia of 2 point

masses

Rotation axle 02415.01 1

Sphere 02415.02 1

Disk 02415.03 1

Hollow cylinder 02415.04 1

Solid cylinder 02415.05 1

Rod with movable masses 02415.06 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedMoment of inertia and torsional vibrations P2133100


Mechanics Dynamics

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 48


Dynamics Mechanics

The propagation of a periodically excited continuous transverse wave 1.3.32-00

Principle:The periodicity of connected station-ary oscillators is demonstrated onthe example of a continuous, har-monic transverse wave generated bya wave machine. The number ofoscillations carried out by differentoscillators within a certain time isdetermined and the velocity of prop-agation is measured. A relation be-tween frequency, wavelength andphase velocity is established. Theformation of standing waves isdemonstrated and studied.

3. For three different frequencies thecorresponding wavelengths are tobe measured and it is to be shownthat the product of frequency andwavelength is a constant.

4. The four lowest natural frequen-cies with two ends of the oscilla-tor system fixed are to be detect-ed.

5. The four lowest natural frequen-cies with one end of the oscillatorsystem fixed and the other onefree are to be detected.

The resonance frequencies measured with increasing speed of rotation.

Tasks:1. The frequency of the oscillators 1,

10, 20, 30 and 40 is to be deter-mined with the electronic counterof the light barrier and the stop-watch for a particular frequencyof excitation.

2. By means of a path-time mea-surement the phase velocity of atransverse wave is to be deter-mined.

Wave machine 11211.00 1

Power supply -2op-, 2�15 V/2 A 13520.93 1


Light barrier 11207.20 1


Gearing 30/1, for 11030.93 11029.00 1

Gearing 100/1, for 11030.93 11027.00 1

Stop watch, interruption type 03076.01 1

Screened cable, BNC, l = 1500 mm 07542.12 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedThe propagation of a periodically excitedcontinuous transverse wave P2133200


� Periodic motion� Frequency� Wavelength� Phase velocity� Standing waves� Natural frequency� Free and fixed end� Damping of waves

fk kf k �

Hz k

0.38 1 0.38 2L/1

0.74 2 0.37 2L/2

0.94 3 0.31 2L/3

1.43 4 0.36 2L/4

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 49


Principle:A quadrangular rubber rope is insert-ed through the demonstration motorand a linear polarised fixed wave isgenerated. With the help of a strob-oscope, the frequency and the wavelength are determined. Then thephase velocity of rope waves with afixed tensile stress is ascertained.Subsequently, the mathematicalrelationship between the phasevelocity of the rope and the tensileon the rope is examined.

The square of phase velocity depending upon the force F applied on the rope.

Tasks:1. With constant tensile stress, the

frequency f, which depends onthe wavelength � of the wavethat propagates itself along therope. The frequency is plotted as afunction of 1/�. From this graph,the phase velocity c is deter-mined.

2. The phase velocity c of the ropewaves, which depends on the ten-sile stress on the rope is to bemeasured. The quadrant of thephase velocity is plotted as afunction of tensile stress.


� Wavelength� Phase velocity� Group velocity� Wave equation� Harmonic wave

Grooved wheel, after Hoffmann 02860.00 1

Square section rubber strip, l = 10 m 03989.00 1


Gearing 10/1, for 11030.93 11028.00 1

Cotton cord, l = 10m 02091.00 1






Pulley, fixed, on rod, dia. 65 mm 02260.00 1

Spring balance 10 N 03060.03 1


Silk thread, 200 m 02412.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedPhase velocity of rope waves P2133300


Mechanics Dynamics

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 50


Mechanics of Liquids and Gaseous Bodies Mechanics

Density of liquids 1.4.01-00

Principle:The density of water and glycerol isdetermined as a function of temper-ature using the Mohr balance.

Density of water as a function of temperature.

Tasks:The density of water and glycerol ismeasured in 1 to 2° steps over atemperature range from 0 to 20°C,then in larger steps up to 50°C.

Mohr density balance 45017.00 1

Immersion thermostat A100 46994.93 1

Accessory set for A100 46994.02 1

Bath for thermostat, Makrolon 08487.02 1

Glycerol, 250 ml 30084.25 2

Water, distilled, 5 l 31246.81 1

Sodium chloride, 500 g 30155.50 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDensity of liquids P2140100


� Hydrogen bond� H2O anomaly� Volume expansion� Melting� Evaporation� Mohr balance

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 51


Principle:A vessel containing liquid is rotatedabout an axis. The liquid surfaceforms a paraboloid of rotation, theparameters of which will be deter-mined as a function of the angularvelocity.

Location of the lowest point � c � of the liquid as a function of the angularvelocity.

Tasks:On the rotating liquid surface, thefollowing are determined:

1. the shape,

2. the location of the lowest point asa function of the angular velocity,

3. the curvature.


� Angular velocity� Centrifugal force� Rotary motion� Paraboloid of rotation� Equilibrium

Rotating liquid cell 02536.01 1



Motor, with gearing, 12 VDC 11610.00 1

Power supply 0-12V DC/6 V, 12 V AC 13505.93 1





Methylene blue sol., alkal. 250 ml 31568.25 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedSurface of rotating liquids P2140200


Mechanics Mechanics of Liquids and Gaseous Bodies

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 52



Viscosity of Newtonian and non-Newtonian liquids (rotary viscometer) 1.4.03-00

Principle:The viscosity of liquids can be deter-mined with a rotation viscometer, inwhich a motor with variable rotationspeed drives a cylinder immersed inthe liquid to be investigated with aspiral spring. The viscosity of the liq-uid generates a moment of rotationat the cylinder which can be meas-ured with the aid of the torsion ofthe spiral spring and read on a scale.

Temperature dependence of the viscosity of castor oil.

Tasks:1. Determine the gradient of the ro-

tational velocity as a function ofthe torsional shearing stress fortwo Newtonian liquids (glycerine,liquid paraffin).

2. Investigate the temperature de-pendence of the viscosity of Cas-tor oil and glycerine.

3. Determine the flow curve for anon-Newtonian liquid (chocolate).

Rotary viscometer 18221.93 1Support base -PASS- 02005.55 1Support rod, stainl. steel, 500 mm 02032.00 1Right angle clamp 37697.00 1Magn. heating stirrer w. temp.con 35711.93 1Magn.stirring bar l = 30 mm, cyl. 46299.02 1Separator f. magnetic bars 35680.03 1Glass beaker, short, 600 ml 36015.00 3Glass beaker, tall, 250 ml 36004.00 2Glass rod, boro 3.3, l = 200 mm, d = 5 mm 40485.03 1Digital thermometer 07030.00 1Immersion probe NiCr-Ni, -50/1000°C 13615.03 1Glycerol, 250 ml 30084.25 2Liquid paraffin, 250 ml 30180.25 1Castor oil, 250 ml 31799.27 2Acetone, chem. pure, 250 ml 30004.25 3

What you need:

Complete Equipment Set, Manual on CD-ROM includedViscosity of Newtonian and non-Newtonianliquids (rotary viscometer) P2140300


� Shear stress� Velocity gradient� Internal friction� Viscosity� Plasticity

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 53


Principle:Due to internal friction among theirparticles, liquids and gases have dif-ferent viscosities. The viscosity, afunction of the substance’s structureand its temperature, can be experi-mentally determined, for example, bymeasuring the rate of fall of a ball ina tube filled with the liquid to be in-vestigated.

3. of methanol as a function of tem-perature.

From the temperature dependence ofthe viscosity, calculate the energybarriers for the displaceability ofwater and methanol.

Temperature dependence of the dynamic viscosity � of water (o) andmethanol (+), respectively.

Tasks:Measure the viscosity

1. of methanol-water mixtures ofvarious composition at a constanttemperature,

2. of water as a function of the tem-perature and


� Liquid� Newtonian liquid� Stokes law� Fluidity� Dynamic and kinematic

viscosity� Viscosity measurements

Falling ball viscometer 18220.00 1

Thermometer, 24...+51°C, f. 18220.00 18220.02 1




Retort stand, h = 750 mm 37694.00 1


Universal clamp with joint 37716.00 1

Pyknometer, calibrated, 25 ml 03023.00 1

Volumetric flask 100 ml, IGJ12/21 36548.00 9

Glass beaker, tall, 150 ml 36003.00 11

Glass beaker, short, 250 ml 36013.00 1

Pasteur pipettes, 250 pcs 36590.00 1

Rubber caps, 10 pcs 39275.03 1

Hose clip, d = 8-12 mm 40996.01 6

Rubber tubing, i.d. 7 mm 39282.00 6


Laboratory balance, data outp. 620 g 45023.93 1

Wash bottle, plastic, 500 ml 33931.00 2

Methanol, 500 ml 30142.50 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedViscosity measurements with the falling ballviscometer P2140400



LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 54



Surface tension by the ring method (Du Nouy method) 1.4.05-00

Principle:The force is measured on a ringshortly before a liquid film tearsusing a torsion meter. The surfacetension is calculated from the dia-meter of the ring and the tear-offforce.

Temperature dependency of surtace tension of olive oil.

Tasks:1. Determine the surface tension of

olive oil as a function of tempera-ture.

2. Determine the surface tension ofwater/methanol mixtures as func-tions of the mixture ratio.

Torsion dynamometer, 0.01 N 02416.00 1Surface tension measuring ring 17547.00 1Retort stand, h = 500 mm 37692.00 1Magn. heating stirrer w. temp.con 35711.93 1Support rod, l = 500 mm/M10 thread 02022.05 1Magn. stirring bar 15 mm, cyl. 46299.01 1Universal clamp 37715.00 2Right angle clamp 37697.00 2Right angle clamp -PASS- 02040.55 1Crystallising dish, boro 3.3, 1000 ml 46245.00 2Crystallising dish, boro 3.3, 560 ml 46244.00 2Lab thermometer, -10..+250°C 38065.00 1Silk thread, l = 200 m 02412.00 1Glass tubes, straight, l = 150 mm, 10 36701.64 1Stopcock, 1-way, straight, glass 36705.00 1Rubber tubing, i.d. 7 mm 39282.00 2Volumetric pipette, 10 ml 36578.00 1Volumetric pipette, 20 ml 36579.00 1Pipettor 36592.00 1Pipette dish 36589.00 1Graduated cylinder, 100 ml 36629.00 1Filter pump, plastic 02728.00 1Ethyl alcohol, absolute, 500 ml 30008.50 1Olive oil, pure, 100 ml 30177.10 5Water, distilled, 5 l 31246.81 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedSurface tension by the ring method(Du Nouy method) P2140500


� Surface energy� Interface� Surface tension� Adhesion� Critical point� Eötvös equation

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 55

1.4.06-11 Surface tension by the pull-out method with Cobra3

Principle:The force exerted on a measuringring shortly before the liquid film istorn away is determined with a forcemeter. The surface tension is calcu-lated from the diameter of the ringand the tearing force.

Typical measurement values

Tasks:Determination of the surface tensionof water and other liquids.


� Surface energy� Surface tension� Surface adhesion� Bounding surface

Surface tension measuring ring 17547.00 1


Power supply, 12 V– 12151.99 1

RS232 cable 14602.00 1

Cobra3 Force/Tesla software 14515.61 1

Measuring module Newton 12110.00 1

Newton sensor 12110.01 1




Lab jack, 160�130 mm 02074.00 1

Petri dish, d = 200 mm, glass 64796.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedSurface tension by the pull-out methodwith Cobra3 P2140611



LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 56



Barometric height formula 1.4.07-00

Principle:Glass or steel balls are accelerated bymeans of a vibrating plate, andthereby attain different velocities(temperature model). The particledensity of the balls is measured as afunction of the height and the vibra-tional frequency of the plate.

Number of steel balls (m = 0.034 g), as a function of the height h, which passthrough the volume element �V in 30 seconds (vibrational frequency 50 Hz).

Tasks:Measurement of the particle densityas a function of:

1. the height, at fixed frequency

2. the vibrational frequency of theexciting plate, at fixed height.

Kinetic gas theory apparatus 09060.00 1

Power supply var. 15 VAC/12 VDC/5 A 13530.93 1





Glass beads, d = 2 mm, 10000 pcs 09060.01 1

Steel balls, d = 2 mm, 1000 pcs 09060.02 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedBarometric height formula P2140700


� Kinetic gas theory� Pressure� Equation of state� Temperature� Gas constant

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:00 Uhr Seite 57


A) Objects of different cross-sectionand shape are placed in a laminarair stream. The drag is examinedas a function of the flow velocityand the geometry of the objects.

B) A rectangular plate or an aerofoilin a stream of air experiences abuoyant force (lift) and a resis-tance force (drag). These forces aredetermined in relation to area, rateof flow and angle of incidence.

Drag of an object as a function of its cross-sectional area A (q = 0.85 hPa).

B) Determination of the lift and thedrag of flat plates as a function of:

1. the plate area

2. the dynamic pressure

3. the angle of incidence (polar dia-gram)

4. Determination of the pressure dis-tribution over the aerofoil for var-ious angles of incidence.


� Resistance to pressure� Frictional resistance� Drag coefficient� Turbulent flow� Laminar flow� Reynolds number� Dynamic pressure� Bernoulli equation� Aerofoil� Induced resistance� Circulation� Angle of incidence� Polar diagram

Aerodynamic models, set of 14 02787.00 1

Aerofoil model 02788.00 1

Pitot tube, prandtl type 03094.00 1

Precision manometer 03091.00 1

Holder with bearing points 02411.00 1

Double shaft holder 02780.00 1



Vernier caliper 03010.00 1

Blower, mains voltage 220 V 02742.93 1

Rheostat, 500 �, 220 V 06111.93 1


Support rod -PASS-, sqare, l = 1000 mm 02028.55 1


Universal clamp 37715.01 1




Rod, pointed 02302.00 1

Silk thread, l = 200 m 02412.00 1

Rule, plastic, l = 200 mm 09937.01 1


Aerofoil model 02788.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedLift and drag (resistance to flow) P2140800



Tasks:A) Determination of the drag as a

function of:

1. the cross-section of differentbodies,

2. the flow velocity,

3. determination of the drag coeffi-cients cw for objects of variousshape.

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:09 Uhr Seite 58


Mechanical Vibration Acoustics Mechanics

Vibration of strings 1.5.01-00

Principle:A tensioned metal string is made tovibrate. The vibrations of the stringare optically scanned, the vibrationprocess observed on the oscilloscopeand the dependence of the frequen-cy on the string tension and stringlength and the density of the mate-rial are investigated.

2. To measure the frequency for var-ious types and cross-sections ofstring, at a fixed tension andstring length.

Fundamental frequency f as a function of string length l at a given tension-ing force F = 30 N.

Tasks:1. To measure the frequency of a

string (e.g. constantan, 0.4 mmdia.) as a function of the tension-ing force and the length of thestring.

String tensioning device, w. stem 03431.01 1Nickel wire, d = 0.3 mm, l = 100 m 06090.00 1Kanthal wire, d = 0.3 mm, l = 100 m 06092.00 1Constantan wire, d = 0.3 mm, l = 100 m 06101.00 1Constantan wire, d = 0.4 mm, l = 50 m 06102.00 1Copper wire, d = 0.4 mm, l = 50 m 06106.02 1Copper wire, d = 0.5 mm, l = 50 m 06106.03 1Barrel base -PASS- 02006.55 1Bench clamp -PASS- 02010.00 3Support rod -PASS-, square, l = 250 mm 02025.55 3Right angle clamp -PASS- 02040.55 3Rod with hook 02051.00 1Sign holder 02066.00 2Fish line, l = 100 m 02090.00 1Meter scale, demo, l = 1000 mm 03001.00 1Spring balance 100 N 03060.04 1Striking hammer, rubber 03429.00 1Photoelement f. opt. base plt. 08734.00 1Lampholder E10, housing g1 17049.00 1Lamp bulb 6 V/3 W, E10, 10 pcs 35673.03 1Distributor 06024.00 1Oscilloscope, 30 MHz, 2 channels 11459.95 1LF amplifier, 220 V 13625.93 1Digital counter, 4 decades 13600.93 1Plug with push-on sleeve 07542.04 1Adapter, BNC socket - 4 mm plug 07542.20 1Adapter, BNC-plug/socket 4 mm 07542.26 2Connector, T type, BNC 07542.21 1Adapter, BNC-socket/4 mm plug pair 07542.27 1Screened cable, BNC, l = 750 mm 07542.11 1Screened cable, BNC, l = 300 mm 07542.10 1Connecting cord, l = 750 mm, red 07362.01 1Connecting cord, l = 750 mm, blue 07362.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedVibrations of strings P2150100


� Natural vibration� Mass-spring system� Harmonic sound intervals

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 59


Principle:The speed of sound in air is deter-mined by measurements of soundtravel times.

Table 1

Tasks:Determination of the velocity ofsound in air.


� Linear relationship betweenthe propagation time ofsound and its respective path

� Longitudinal waves� Velocity of sound

What you need:

Complete Equipment Set, Manual on CD-ROM includedVelocity of sound in air with Cobra3 P2150311


Mechanics Mechanical Vibration Acoustics

v /(m/s)

338.448

338.438

338.753

337.230

337.258


Power supply, 12 V_ 12151.99 1



Microphone with amplifier 03543.00 1

Battery, 9 V, 6 F 22 DIN 40871 07496.10 1

Support rod with hole, l = 100 mm 02036.00 2

Support 09906.00 1





Connecting cord, l = 25 cm, 32 A, red 07360.01 1

Connecting cord, l = 25 cm, 32 A, blue 07360.04 1


LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 60



Acoustic Doppler effect 1.5.04-01

Principle:If a source of sound is in motion rel-ative to its medium of propagation,the frequency of the waves that itemits is displaced due to the Dopplereffect. With the superimposition of amoving and a stationary source ofsound which are emitting waves ofthe same frequency, beats occurwhose frequency is equal to theDoppler shift of the frequency of themoving source of sound. The Dopplershift of the frequency is measuredand compared with the theoreticalvalue for different velocities of thesound emitting source.

Beat frequency as a function of velocity VQ.

Tasks:1. The Doppler shift of the frequency

of the moving source of sound isto be determined by measuringthe beat frequency.

2. The measured values are to becompared with the calculatedones for velocities in the rangebetween 0.06 and 0.16 m/sec.

Measuring microphone 03542.00 1

Sound head 03524.00 2

Power frequency generator 1 MHz 13650.93 1

Yt recorder, 1 channel 11414.95 1

Car, motor driven 11061.00 1

Attachment for car 11061.02 1

Round cell, 1.5 V 07922.01 2







What you need:

Complete Equipment Set, Manual on CD-ROM includedAcoustic Doppler effect P2150401


� Propagation of sound waves� Superimposition of sound

waves� Doppler shift of frequency� Beat frequency

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 61


Principle:If a source of sound is in motion rel-ative to its medium of propagation,the frequency of the waves that areemitted is displaced due to theDoppler effect.

Table

Tasks:The frequency changes are measuredand analysed for different relativevelocities of source and observer.


� Propagation of sound waves� Doppler shift of frequency






Battery, 9 V, 6 F 22 DIN 40871 07496.10 1

Function generator 13652.93 1

Electrode holder 45284.01 1



Plug with socket and crosshole, 2 07206.01 1


Support rod, stainless steel, l = 600 mm 02037.00 1


Track, l = 900 mm 11606.00 1

Car, motor driven 11061.00 1

Attachment for car 11061.02 1

Round cell, 1.5 V, R 14 DIN 40865 (for car) 07922.01 2



Support 09906.00 1


Connecting cord, l = 25 cm, 32 A, red 07360.01 1

Connecting cord, l = 25 cm, 32 A, blue 07360.04 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedAcoustic Doppler effect with Cobra3 P2150411



Movement toward Movement away fromthe sound source the sound source

v /m/s 0.162 0.157

v /m/s 0.159 0.156

v /m/s 0.158 0.157

v /m/s 0.159 0.156

Mean/m/s 0.160 0.157

Meanfmeasured/Hz 16199 16184

fcalculated/Hz 16199.6 16184.5

v

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 62



Velocity of sound using Kundt’s tube 1.5.06-01

Principle:A metal rod is made to vibrate longi-tudinally by rubbing it with a cloth.The gas column in a glass tube iscaused to vibrate naturally as aresult of resonance, through theradiation of sound from a discattached to the end of the rod.

The ratio of the velocities of sound inthe gas and in the vibration genera-tor is determined by measuring thewavelength.

Positions of the vibration nodes as a function of the number of nodes.

Tasks:1. To measure the wavelength of sta-

tionary waves using a steel or abrass rod as the vibration genera-tor. The longitudinal velocity ofsound in the material of the vibra-tion generator is determined,given the velocity of sound in air.

2. To measure the wavelength forCO2, and to determine the soundvelocity in CO2 from the ratios ofthe wavelengths in air determinedin 1. above.

Charging strip 03474.01 1

Piston 03474.02 1

Glass tube, e.d. 38 mm, l = 640 mm 03918.00 1

Vibration generator, brass 03476.01 1

Vibration generator, steel 03476.02 1

Cork dust, 3 g 03477.00 1

Lycopodium powder, 10 g 02715.00 1

Thermometer -10...+30°C 05949.00 1




Reducing valve for CO2 / He 33481.00 1

Steel cylinder, CO2, 10 l, full 41761.00 1

Wrench for steel cylinders 40322.00 1

Glass tubes, straight, 80 mm, 10 36701.65 1

Rubber stopper, d = 38/31 mm, 1 hole 39260.01 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedVelocity of sound using Kundt’s tube P2150601


� Longitudinal waves� Sound velocity in gases and

solids� Frequency� Wavelength� Stationary waves� Natural vibrations

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 63


Principle:If a sound wave of a particular fre-quency is divided into two coherentcomponents (like, for example, lightwaves in an interferometer experi-ment), and if the path of one of thecomponent waves is altered, it ispossible to calculate the wavelengthof the sound wave and its frequencyfrom the interference phenomenarecorded with a microphone.

Resonance wavelength dependent on the displacement �d.

Tasks:1. Record of the extension of a

Quincke tube for given frequen-cies in the range 2000 Hz to 6000Hz.

2. Calculation of the frequenciesfrom the wavelengths determined,comparison with the given fre-quencies.


� Transverse and longitudinalwaves

� Wavelength� Amplitude� Frequency� Phase shift� Interference� Velocity of sound in air� Loudness� Weber-Fechner law

Interference tube, Quincke type 03482.00 1







Adapter, BNC-socket/4 mm plug pair 07542.27 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedWavelengths and frequencies with a Quincke tube P2150700



LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 64



Resonance frequencies of Helmholtz resonators with Cobra3 1.5.08-11

Principle:Acoustic cavity resonators posses acharacteristic frequency which is de-termined by their geometrical form.In this case the resonator is excitedto vibrations in its resonance fre-quency by background noise.

Time signal, spectrum and parameter settings for measurements on the empty1000 ml round-bottomed flask.

Tasks:Determination of different resonancefrequencies of a resonator dependingon the volume.




Cobra3 Frequency Analysis Software 14514.61 1


Flat cell battery, 9 V, 6 F 22 DIN 40871 07496.10 1

Glass tube, l = 300 mm, d = 12 mm 45126.01 1


Support rod, l = 50 cm, round 02032.00 1




Round-bottom flask, 1000 ml, narrow neck 36050.00 1

Round-bottom flask, 100 ml, narrow neck 36046.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedResonance frequencies of Helmholtz resonators with Cobra3 P2150811


� Cavity resonator� Resonance frequency� Acoustic resonant circuit

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 65


Principle:– Two acoustic sources emit waves

of the same frequency and if theirdistance is a multiple of the wave-length, an interference structurebecomes apparent in the spacewhere the waves are superim-posed.

– An acoustic wave impinges per-pendicularly onto a reflector, theincident and the reflected waveare superimposed to a stationarywave. In case of reflection, a pres-sure antinode will always occur atthe point of reflection.

– An acoustic wave impinges on asufficiently narrow slot, it is dif-fracted into the geometrical shad-ow spaces. The diffraction and theinterference pattern occurringbehind the slot can be explainedby means of the Huygens-Fresnelprinciple and confirm the wavecharacteristics of sound.

Measurement example, stationary waves.

Tasks:1. To measure the interference of

acoustic waves.

2. To analyze the reflection of acous-tic waves – stationary waves.

3. To measure the diffraction at aslot of acoustic waves.


� Interference� Reflection� Diffraction� Acoustic waves� Stationary waves� Huygens-Fresnel principle� Use of an interface



Flat cell battery, 9 V 07496.10 1

Screen, metal, 300�300 mm 08062.00 2







Meter scale, demo. l = 1000 mm 03001.00 1

Silk thread, l = 200 m 02412.00 1






Adapter, BNC socket - 4 mm plug 07542.20 1

PC Cobra data cable RS232, 2 m 12100.01 1



Cobra3 Force/Tesla Measurement Software 14515.61 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference of acoustic waves, stationary wavesand diffraction at a slot with Cobra3 P2150911



LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 66



Optical determination of velocity of sound in liquids 1.5.10-00

Principle:A stationary ultrasonic wave in aglass cell full of liquid is traversed bya divergent beam of light. The soundwavelength can be determined fromthe central projection of the soundfield on the basis of the refractiveindex which canges with the soundpressure.

Image of a screen.

Tasks:To determine the wavelength ofsound in liquids, and from this calu-cate the sound velocity, from thestructure of the centrally projectedimage.

Ultrasonic generator 11744.93 1

Laser, He-Ne 1.0 mW, 230 V AC 08181.93 1

Glass cell, 150�55�100 mm 03504.00 1

Lens holder 08012.00 1

Lens, mounted, f = +20 mm 08018.01 1

Screen, metal, 300�300 mm 08062.00 1

Optical profile-bench, l = 1000 mm 08282.00 1

Base f. opt. profile-bench, adjust. 08284.00 2

Slide mount f. opt. pr.-bench, h = 80 mm 08286.02 1


Swinging arm 08256.00 1

Table top on rod, 18.5�11 cm 08060.00 1

Thermometer -10...+30 °C 05949.00 1


Support rod, l = 250 mm 02021.00 1


Glycerol, 250 ml 30084.25 3


What you need:

Complete Equipment Set, Manual on CD-ROM includedOptical determination of velocityof sound in liquids P2151000


� Ultrasonics� Sound velocity� Frequency� Wavelength� Sound pressure� Stationary waves

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 67


Principle:The sound waves transmitted to aliquid by the ultrasonic generator arepicked up by a piezoelectric ultra-sonic pick-up and the signal fromtransmitter and receiver comparedon an oscilloscope.

The wavelength is determined andthe phase velocity calculated fromthe relative phase position of thesignals. The group velocity is deter-mined from measurements of thesound pulse delay time.

2.1. To determine the oscilloscope’scoefficient of sweep with the aidof the ultrasonic frequency.

2.2. With the generator in the pulsedmode, to record the delay timeof the sound pulses as a functionof the distance between a gen-erator and the pick-up, and todetermine the group velocity.

Detector displacement �l as a function of the number n of wavelengths cov-ered, for water, glycerol and sodium chloride solution (temperature � = 25°C).

Tasks:The signals from the ultrasonic gen-erator and the ultrasonic pick-up arerecorded on the oscilloscope.

1. To measure the relative phaseposition of the signal from theultrasonic pick-up as a function ofits distance from the ultrasonicgenerator (which is in the sinemode), and to determine theultrasonic wavelength and thephase velocity when the frequen-cy is known.


� Longitudinal waves� Velocity of sound in liquids� Wavelength� Frequency� Piezoelectric effect� Piezoelectric ultrasonics

transformer

Ultrasonic pickup 11744.00 1


Glass cell, 150�55�100 mm 03504.00 1

Insulating support 07924.00 1

Optical profile bench l = 60 cm 08283.00 1




Table top on rod 08060.00 1



Support rod, stainl.steel, 500 mm 02032.00 1


Oscilloscope, 30 MHz, 2 channels 11459.95 1




Thermometer -10...+30 °C 05949.00 1

Glycerol, 250 ml 30084.25 3



What you need:

Complete Equipment Set, Manual on CD-ROM includedPhase and group velocity of ultrasonicsin liquids P2151100



LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 68



Temperature dependence of the Velocity of sound in liquids 1.5.12-00

Principle:Sound waves are radiated into a liq-uid by an ultrasonic transmitter anddetected with a piezoelectric trans-ducer. The wavelength of the soundis found by comparing the phase ofthe detector signal for differentsound paths and, when the frequen-cy is known, the velocity of sound asa function of the temperature of theliquid is determined.

termined when the ultrasonic fre-quency is known. The measurementis made for water and glycerol as thetemperatures of the liquids arechanged step-by-step.

Velocity of sound in water as a function of the temperature.

Tasks:The wavelength is found from thephase position of the sound pickupsignal relative to the generator sig-nal as a function of the sound pathand the velocity of the sound is de-

Ultrasonic pickup 11744.00 1


Sliding device, horizontal 08713.00 1









Lab thermometer, -10..+100°C 38056.00 1


Support rod, l = 100 mm 02020.00 2





Glycerol, 250 ml 30084.25 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedTemperature dependence of the Velocityof sound in liquids P2151200


� Wavelength� Frequency� Velocity of sound in liquids� Compressibility� Density� Ultrasonics� Piezoelectric effect� Piezoelectric ultrasonic

transducer

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:04 Uhr Seite 69



Principle:An ultrasonic wave is subjected tohard surface reflection from a metalplate. The reflected wave superim-poses on the incident wave, coinci-dent in phase and amplitude, to forma standing wave. The intensity of thiswave along the direction of propaga-tion is measured using a movable ul-trasonic receiver.

The change in the sound pressure intensity in the direction of propagation asa function of the distance.

Tasks:1. Determine the intensity of a

standing ultrasonic wave by mov-ing an ultrasonic receiver alongthe direction of propagation.

2. Plot a graph of the measuredvalues against the distance.

3. Determine the wavelength of theultrasonic wave.

Ultrasonic unit 13900.00 1

Power supply f. ultrasonic unit, 5 VDC, 12 W 13900.99 1

Ultrasonic transmitter on stem 13901.00 1

Ultrasonic receiver on stem 13902.00 1


Optical profile-bench, l = 60 cm 08283.00 1


Slide mount f. opt. profile-bench, h = 80 mm 08286.02 1




Screen metal, 30�30 cm 08062.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedStationary ultrasonic waves, determinationof wavelength P2151301



� Longitudinal waves � Superposition of waves� Reflection of longitudinal

waves� Stationary longitudinal waves

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:05 Uhr Seite 70


Absorption of ultrasonic in air 1.5.14-01


Principle:Sound needs a material medium withwhich it can enter into reciprocal ac-tion for its propagation, whereby aloss of energy occurs. The amplitude,and so also the intensity, decreasesalong the propagation path.

The change in sound pressure intensity as a function of the distance from thesource of sound.

Tasks:1. Move an ultrasonic receiver along

the direction of propagation of asound wave to measure the soundintensity as a function of the dis-tance from the source of thesound.

2. Plot linear and logarithmic graphsof the values for amplitudeagainst the distance.

3. Confirm the law of absorption anddetermine the absorption coeffi-cient.


� Longitudinal waves � Propagation of sound waves� Absorption coefficient of

ultrasonic waves� Law of absorption






Optical profile-bench, l = 150 cm 08281.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedAbsorption of ultrasonic in air P2151401

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:05 Uhr Seite 71



Principle:A plane ultrasonic wave is subjectedto diffraction at single slits of vari-ous widths and at various doubleslits. The intensity of the diffractedand interfering partial waves are au-tomatically recorded using a motor-driven, swivel ultrasound detectorand an interface system.

The angular distribution of the intensity of a plane ultrasonic wave diffract-ed at a slit.

Tasks:1. Record the intensity of an ultra-

sonic wave diffracted by varioussingle slits and double slits as afunction of the diffraction angle.

2. Determine the angular positionsof the maximum and minimumvalues and compare them with thetheoretical values.

Goniometer with reflecting mirror 13903.00 1

Power supply for goniometer 13903.99 1





Object holder f. ultrasonic 13904.00 1

Diffraction objects f. ultrasonic 13905.00 1



RS 232 data cable 14602.00 1


Software Cobra3 universal recorder 14504.61 1

Connecting cord, l = 50 cm , yellow 07361.02 4


What you need:

Complete Equipment Set, Manual on CD-ROM includedUltrasonic diffraction at different singleand double slit systems with Cobra3 P2151511



� Huygens principle� Longitudinal waves � Interference� Fraunhofer and Fresnel

diffraction

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:05 Uhr Seite 72


Ultrasonic diffraction at different multiple slit systems with Cobra3 1.5.16-11


Principle:A plane ultrasonic wave is subjectedto diffraction at various multipleslits. The intensity of the diffractedand interfering partial waves are au-tomatically recorded using a motor-driven, swivel ultrasound detectorand an interface system.

The angular distribution of the intensity of a plane ultrasonic wave diffract-ed by a fourfold slit.

Tasks:1. Determine the angular distribu-

tion of a plane ultrasonic wavediffracted by various multiple slits.

2. Determine the angular positionsof the maximum and mininumvalues and compare them withthe theoretical values.


� Huygens principle� Longitudinal waves � Interference� Fraunhofer and Fresnel

diffraction







Object holder f. ultrasonic 13904.00 1

Diffraction objects f. ultrasonic 13905.00 1



RS 232 data cable 14602.00 1

Measuring tape, l = 2m 09936.00 1


Connecting cord, l = 50cm , yellow 07361.02 4


What you need:

Complete Equipment Set, Manual on CD-ROM includedUltrasonic diffraction at different multipleslit systems with Cobra3 P2151611

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:05 Uhr Seite 73


1.5.17-11 Diffraction of ultrasonic waves at a pin hole and a circular obstacle with Cobra3

Principle:A plane ultrasonic wave is subjectedto diffraction by a pin-hole obstacleand a complementary circular obsta-cle. The intensity distribution of thediffracted and interfering partialwaves are automatically recordedusing a motor-driven, swivel detec-tor and an interface system.

The angular distribution of the intensity of a plane ultrasonic wave diffract-ed by a pin-hole obstacle.


tion of an ultrasonic wavediffracted by a pin-hole and circu-lar obstacle.

2. Compare the angular positions ofthe minimum intensities with thetheoretical values.







Object holder for goniometer 13904.00 1

Pin hole and circular obstacle f. ultrasonic 13906.00 1



RS 232 data cable 14602.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction of ultrasonic waves at a pin holeand a circular obstacle with Cobra3 P2151711



� Huygens principle� Longitudinal waves� Interference� Fraunhofer and Fresnel

diffraction� Fresnel’s zone construction� Poisson’s spot� Babinet’s theorem� Bessel function

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:05 Uhr Seite 74


Ultrasonic diffraction at Fresnel lenses / Fresnel zone contruction 1.5.18-01


Principle:A plane ultrasonic wave strikes aFresnel zone plate. The sound inten-sity is determined as a function ofthe distance, using an ultrasonicdetector that can be moved in thedirection of the zone plate axis.

Graph of the intensity of the ultrasound as a function of the distance from aFresnel zone plate( curve a ); curve b without zone plate.

Tasks:1. Determine and plot a graph of the

intensity of the ultrasound behindFresnel zone plates as a functionof the distance from the plate.

2. Carry out the same measurementseries without plates.

3. Determine the focal points of thezone plates and compare the val-ues found with those theoreticallyexpected.


� Huygens principle� Longitudinal waves� Interference� Fraunhofer and Fresnel

diffraction� Fresnel’s zone construction� Zone plates





Fresnel zone plates f. ultrasonic 13907.00 1


Optical profile bench, l = 150 cm 08281.00 1

Base f. optical profile bench 08284.00 2

Slide mount f. optical profile bench, h = 80 mm 08286.00 3



Connecting cord, l = 50cm , red 07361.01 1

Connecting cord, l = 50cm , blue 07361.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedUltrasonic diffraction at Fresnel lenses /Fresnel zone contruction P2151801

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:05 Uhr Seite 75


1.5.19-11 Interference by two identical ultrasonic transmitters with Cobra3

Principle:Ultrasonic waves of the same fre-quency, amplitude and direction ofpropagation are generated by twosources of sound positioned parallelto each other. The sources can vi-brate both in-phase and out-of-phase. The angular distribution ofthe intensity of the waves, which in-terfere with each other, is automati-cally recorded using a motor-driven,swivel ultrasound detector and aninterface system.

Angular distribution of the intensity of two interfering ultrasonic waves hav-ing the same phase, amplitude, frequency and direction of propagation.


tion of two sources of ultrasoundvibrating in-phase.

2. Determine the angular positionsof the interference minima andcompare the values found withthose theoretically expected.

3. Repeat the measurements withthe two sources of ultrasound vi-brating out-of-phase.

Goniometer with reflector 13903.00 1






Cobra3 basic unit 12150.00 1


RS 232 data cable 14602.00 1

Barrel base PASS 02006.55 2



Connecting cord, l = 50 cm , yellow 07361.01 4


What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference by two indentical ultrasonictransmitters with Cobra3 P2151911



� Huygens principle� Longitudinal waves� Interference

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:05 Uhr Seite 76


Handbooks Mechanics

1 Forces

MT 1.1 (12516)Mass and weight

MT 1.2 (12517)Extension of a rubber band and helical spring

MT 1.3 (12518)Hooke’s law

MT 1.4 (12519)Making and calibrating adynamometer

MT 1.5 (12520)Bending a leaf spring

MT 1.6 (12521)Force and counterforce

MT 1.7 (12522)Composition of forces having the same line of application

MT 1.8 (12523)Composition of non-parallel forces

MT 1.9 (12524)Resolution of a force into two non-parallel forces

MT 1.10 (12525)Resolution of forces on an inclinedplane

MT 1.11 (12526)Resolution of forces on a crane

MT 1.12 (12527)Restoring force on a displaced pendulum

MT 1.13 (12528)Determination of the centre ofgravity of an irregular plate

MT 1.14 (12529)Frictional force

MT 1.15 (12530)Determination of the coefficient offriction on an inclined plane

2 Simple machines

MT 2.1 (12531)Double-sided lever

MT 2.2 (12532)One-sided lever

MT 2.3 (12533)Double-sided lever and more thantwo forces

MT 2.4 (12534)Reaction at the supports

MT 2.5 (12535)Moment of rotation (torque)

MT 2.6 (12536)Beam balance

MT 2.7 (12537)Sliding weight balance

MT 2.8 (12538)Fixed pulley

MT 2.9 (12539)Free pulley

MT 2.10 (12540)Block and tackle

MT 2.11 (12541)Step wheel

MT 2.12 (12542)Toothed-gearing

MT 2.13 (12543)Belt drives

3 Oscillations

MT 3.1 (12544)Thread pendulum

MT 3.2 (12545)Spring pendulum

MT 3.3 (12546)Physical pendulum(reversible pendulum)

DEMONSTRATION EXPERIMENTSPHYSICS


0115

2.02

Winfried RösslerGeorg Schollmeyer

The use of the demonstration board for physics offers the following advantages for the lecturer:● Minimal preparation time

● Lucid and simple set-up

● Labelling of the experiment directly on the board

● Magnet-held arrows, linear and angular scales

● Stable storage box

● Both sides of board can be used for mechanics and optics

● Galvanised sheet steel board in aluminium profile frame

● Mechanics side: lacquered

● Optic side: white foil with lined grid


Physics Demonstration Experiments – Magnet Board Mechanics 1 • No. 01152.02 • 31 described ExperimentsPlease ask for a complete equipment list Ref. No. 21701

Fixed pulley (MT 2.8)

Resolution of forces on an inclined plane (MT 1.10)

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:05 Uhr Seite 77


Mechanics Handbooks

4 Movement

MT 4.1 (12960)Uniform rectilinear movement

MT 4.2 (12961)Uniform accelerated rectilinearmovement

MT 4.3 (12962)Horizontal and sloping trajectories

MT 4.4 (12963)Newton’s basic principle

5 Forms of Mechanical Energy

MT 5.1 (12964)Energy transformation duringupward and downward runs

MT 5.2 (12965)Kinetic energy

MT 5.3 (12966)Energy of refraction

6 Mechanics of Fluids and Gases

MT 6.1 (12967)U-tube manometer

MT 6.2 (12968)Hydrostatic pressure

MT 5.3 (12969)Communicating vessels

MT 6.4 (12970)Hydraulic press

MT 6.5 (12971)Artesian well

MT 6.6 (12972)Archimedes principle

MT 6.7 (12973)Density determination by measuringbuoyancy

MT 6.8 (12974)Discharge velocity of a vessel

MT 6.9 (12975)Pressure in flowing fluids

MT 6.10 (12976)Pressure in gases

MT 6.11 (12977)Boyle and Mariotte’s law



0115

2.02

Winfried RösslerGeorg Schollmeyer

The use of the demonstration board for physics offers the following advantagesfor the lecturer:● Minimal preparation time

● Lucid and simple set-up

● Labelling of the experiment directly on the board

● Magnet-held arrows, linear and angular scales

● Stable storage box

● Both sides of board can be used for mechanics and optics

● Galvanised sheet steel board in aluminium profile frame

● Mechanics side: lacquered

● Optic side: white foil with lined grid


Horizontal and sloping trajectories (MT 4.3)

Energy transformation during upward and downward runs (MT 5.1)

Physics Demonstration Experiments – Magnet Board Mechanics 2 • No. 01153.02 • 18 described ExperimentsPlease ask for a complete equipment list Ref. No. 21702

LEP 1.3.30-00_1.5.19-00 12.10.2003 10:05 Uhr Seite 78

2Optics

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 79


Contents

2.1 Geometrical Optics

2.1.01-00 Measuring the velocity of light


2.1.03-00 Dispersion and resolving power of the prism and grating spectroscope

2.2 Interference


2.2.02-00 Newton’s rings


2.2.04-00 Fresnel’s zone construction / zone plate


2.2.06-00 Coherence and width of spectral lines with Michelson interferometer


2.3 Diffraction

2.3.01-00 Diffraction at a slit and Heisenberg’s uncertainty principle


2.3.03-00 Intensity of diffractions due to pin hole diaphragms and circular obstacles

2.3.04-00 Diffraction intensity of multiple slits and grids

2.3.05-00 Determination of the diffraction intensity at slit and double slit systems


2.4 Photometry

2.4.02-01 Photometric law of distance


2.4.04-00 Lambert’s law

Optics

2.5 Polarisation


2.5.02-00 Polarimetry


2.5.04-00 Malus’ law

2.6 Applied Optics


2.6.02-00 Kerr effect


2.6.04-00 CO2-laser


2.6.07-00 Helium Neon Laser


2.6.09-00 Nd-YAG laser


2.6.11-00 Fourier optics – 2f Arrangement


2.7 Handbooks

Advanced Optics and Laser Physics


2LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 80


Measuring the velocity of light 2.1.01-00

Geometrical Optics Optics

Principle:The intensity of the light is modulat-ed and the phase relationship of thetransmitter and receiver signal com-pared. The velocity of light is calcu-lated from the relationship betweenthe changes in the phase and thelight path.

Measuring the velocity of light in other media.

Tasks:1. To determine the velocity of light

in air.

2. To determine the velocity of lightin water and synthetic resin andto calculate the refractive indices.


� Refractive index� Wavelength� Frequency� Phase� Modulation� Electric field constant� Magnetic field constant

Light velocity measuring app. 11224.93 1



Block, synthetic resin 06870.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMeasuring the velocity of light P2210100

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 81



Principle:The focal lengths of unknown lensesare determined by measuring thedistances of image and object and byBessel’s method. Simple opticalinstruments are then constructedwith these lenses.

Path of a ray in Galileo telescope.

Tasks:1. To determine the focal length of

two unknown convex lenses bymeasuring the distances of imageand object.

2. To determine the focal length of aconvex lens and of a combinationof a convex and a concave lensusing Bessel’s method.

3. To construct the following opticalinstruments:1. Slide projector; image scale to

be determined2. Microscope; magnification to

be determined3. Kepler-type telescope4. Galileo’s telescope

(opera glasses).

Lens, mounted, f = +20 mm 08018.01 1

Lens, mounted, f = +50 mm 08020.01 1

Lens, mounted, f = +100 mm 08021.01 1

Lens, mounted, f = +300 mm 08023.01 1

Lens, mounted, f = –50 mm 08026.01 1

Lens, mounted, f = –200 mm 08028.01 1

Screen, translucent, 250�250 mm 08064.00 1

Screen, with arrow slit 08133.01 1

Ground glass screen, 50�50�2 mm 08136.01 1

Double condenser, f = 60 mm 08137.00 1

Stage micrometer, 1 mm - 100 div. 62171.19 1

Dog flea, Ctenocephalus, mip 87337.10 1

Slide -Emperor Maximilian- 82140.00 1


Base f. opt.profile-bench, adjust. 08284.00 2

Slide mount f. opt.pr.-bench, h = 30 mm 08286.01 5

Slide mount f. opt.pr.-bench, h = 80 mm 08286.02 1

Diaphragm holder 08040.00 2


Condenser holder 08015.00 1


Experiment lamp 5, with stem 11601.10 1



Rule, plastic, l = 200 mm 09937.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedLaws of lenses and optical instruments P2210200

Optics Geometrical Optics


� Law of lenses� Magnification� Focal length� Object distance� Telescope� Microscope� Path of a ray� Convex lens� Concave lens� Real image� Virtual image

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 82


Dispersion and resolving power of the prism and grating spectroscope 2.1.03-00

Geometrical Optics Optics

Principle:The refractive indices of liquids,crown glass and flint glass are deter-mined as a function of the wave-length by refraction of light throughthe prism at minimum deviation. Theresolving power of the glass prisms isdetermined from the dispersioncurve.

Tasks:1. To adjust the spectrometer-gonio-

meter.

2. To determine the refractive indexof various liquids in a hollow prism.

3. To determine the refractive indexof various glass prism.

4. To determine the wavelengths ofthe mercury spectral lines.

5. To demonstrate the relationshipbetween refractive index andwavelength (dispersion curve).

6. To calculate the resolving powerof the glass prisms from the slopeof the dispersion curves.

Dispersion curves of various substances.

7. Determination of the grating con-stant of a Rowland grating basedon the diffraction angle (up to thethird order) of the high intensityspectral lines of mercury.

8. Determination of the angular dis-persion of a grating.

9. Determination of the resolvingpower required to separate thedifferent Hg-Lines. Comparisonwith theory.


� Maxwell relationship� Dispersion� Polarizability� Refractive index� Prism� Rowland grating� Spectrometer-goniometer

Spectrometer/goniom. w. vernier 35635.02 1

Lamp holder, pico 9, f. spectr. lamps 08119.00 1

Spectral lamp Hg 100, pico 9 base 08120.14 1

Power supply for spectral lamps 13662.93 1

Prism, 60 degrees, h = 30 mm, crown 08231.00 1

Hollow prism 08240.00 1

Glycerol, 250 ml 30084.25 1

Methanol, 500 ml 30142.50 1

Cyclohexene for synth., 500 ml 31236.50 1




Diffraction grating, 600 lines/mm 08546.00 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedDispersion and resolving power of the prism and grating spectroscope P2210300

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 83


Principle:By dividing up the wave-front of abeam of light at the Fresnel mirrorand the Fresnel biprism, interferenceis produced. The wavelength is de-termined from the interference pat-terns.

Geometrical arrangement, using the Fresnel mirror.

Tasks:Determination of the wavelength oflight by interference

1. with Fresnel mirror,

2. with Fresnel biprism.


� Wavelength� Phase� Fresnel biprism� Fresnel mirror� Virtual light source

Fresnel biprism 08556.00 1

Prism table with holder 08254.00 1

Fresnel mirror 08560.00 1

Lens, mounted, f = +20 mm 08018.01 1

Lens, mounted, f = +300 mm, achrom. 08025.01 1







Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1

Measuring tape, h = 2 m 09936.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference of light P2220100


Optics Interference

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 84


Interference Optics

Newton’s rings 2.2.02-00

Principle:In a Newton’s rings apparatus,monochromatic light interferes inthe thin film of air between theslightly convex lens and a plane glassplate. The wavelengths are deter-mined from the radii of the interfer-ence rings.

Radius of the interference rings as a function of the order number for variouswavelengths.

Tasks:Using the Newton’s rings apparatus,to measure the diameter of the ringsat different wavelengths and:

1. to determine the wavelengths fora given radius of curvature of thelens

2. to determine the radius of curva-ture at given wavelengths.

Newton rings apparatus 08550.00 1

Lens, mounted, f = +50 mm 08020.01 1

Interference filters, set of 3 08461.00 1

Screen, translucent, 250�250 mm 08064.00 1

Lamp, f. 50 W Hg high press. lamp 08144.00 1

Power supply for Hg CS/50 W lamp 13661.93 1



Condenser holder 08015.00 1





Rule, plastic, l = 200 mm 09937.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedNewton’s rings P2220200


� Coherent light� Phase relationship� Path difference� Interference in thin films� Newton’s ring apparatus

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 85


Principle:Monochromatic light falls on a planeparallel mica plate. The light rays,reflected at the front surface as wellas at the rear surface, will interfereto form a pattern of concentric rings.The radii of the rings depend on thegeometry of the experimental set-up, the thickness of the mica plateand the wavelength of the light.

Interference order m as a function of sin2� for Na-light.

Tasks:The experiment will be performedwith the light of a Na-lamp and withthe light of different wavelengths ofa Hg-vapour tube.

1. The thickness of the mica plate isdetermined from the radii of theinterference rings and the wave-length of the Na-lamp.

2. The different wavelengths of theHg-vapour tube are determinedfrom the radii of the interferencerings and the thickness of themica plate.


� Interference of equalinclination

� Interference of thin layers� Plane parallel plate� Refraction� Reflection� Optical path difference

Mica plate 08558.00 1

Colour filter, 440 nm 08411.00 1




Spectral lamp Na, pico 9 base 08120.07 1



Plate holder with tension spring 08288.00 2

Screen, metal, 300�300 mm 08062.00 2



Base f.opt.profile-bench, adjust. 08284.00 2




What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference at a mica plate according to Pohl P2220300


Optics Interference

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 86


Interference Optics

Fresnel’s zone construction / zone plate 2.2.04-00

Principle:A zone plate is illuminated with par-allel laser light. The focal points ofseveral orders of the zone plate areprojected on a ground glass screen.

Geometry of the zone plate.

Tasks:1. The laser beam must be widened

so that the zone plate is well illu-minated. It must be assured thatthe laser light beam runs parallelover several meters.

2. The focal points of several ordersof the zone plate are projected ona ground glass screen. The focallengths to be determined are plot-ted against the reciprocal value oftheir order.

3. The radii of the zone plate are cal-culated.

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1

Zone plate, after fresnel 08577.03 1


Lens, mounted, f= +20 mm 08018.01 1

Lens, mounted, f= +50 mm 08020.01 1

Lens, mounted, f= +100 mm 08021.01 1

Lens, mounted, f= –50 mm 08026.01 1

Object holder, 5�5 cm 08041.00 2

Ground glass screen, 50�50�2 mm 08136.01 1

Polarising filter, 50�50 mm 08613.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedFresnel’s zone construction / zone plate P2220400


� Huygens-Fresnel principle� Fresnel and Fraunhofer

diffraction� Interference� Coherence� Fresnel’s zone construction� Zone plates

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 87


Principle:In the Michelson arrangement inter-ference will occur by the use of 2mirrors. The wavelength is deter-mined by displacing one mirror usingthe micrometer screw.

Formation of circles on interference.

Tasks:Determination of the wavelength ofthe light of the used laser.


� Interference� Wavelength� Refractive index� Velocity of light� Phase� Virtual light source

Michelson interferometer 08557.00 1

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1


Lens, mounted, f = +20 mm 08018.01 1





Screen, metal, 300�300 mm 08062.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedMichelson interferometer P2220500


Optics Interference

ADVANCED OPTICSAND LASER PHYSICS

You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 115)

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 88


Interference Optics

Coherence and width of spectral lines with Michelson interferometer 2.2.06-00

Principle:The wavelengths and the corre-sponding lengths of coherence of thegreen spectral lines of an extremehigh pressure Hg vapour lamp aredetermined by means of a Michelsoninterferometer.

Different double slit combinationsare illuminated to verify the coher-ence conditions of non punctuallight sources. An illuminated auxil-iary adjustable slit acts as a nonpunctual light source.

Beam path in Michelson’s interferometer.

Tasks:1. Determination of the wavelength

of the green Hg spectral line aswell as of its coherence length.

2. The values determined in 1. areused to calculate the coherencetime and the half width value ofthe spectral line.

3. Verification of the coherence con-dition for non punctual lightsources.

Michelson Interferometer 08557.00 1

High pressure mercury vapour lamp CS 50 W 08144.00 1

Power supply for Hg-CS/50 W Lamp 13661.93 1

Optical profile bench, l = 100cm 08282.00 1

Base for optical profile bench 08284.00 2

Slide mount, h = 30 mm 08286.01 5


Object holder 50�50 mm 08041.00 1

Swingin arm 08256.00 1



Mounted lens f = 20 mm 08018.01 1

Mounted lens f = 200 mm 08024.01 1

Iris diaphragm 08045.00 1

Coloured filter, green, 525 nm 08414.00 1

Ground-glass screen 50�50 mm 08136.01 1

Diaphragm holder, attachable 11604.09 1

Measuring magnifier 09831.00 1

Slit, adjustable up to 1 mm 11604.07 1

Diaphragm with 4 double slits 08523.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedCoherence and width of spectral lineswith Michelson interferometer P2220600


� Fraunhofer and Fresnel diffraction

� Interference� Spatial and time coherence� Coherence conditions� Coherence length for non

punctual light sources� Coherence time� Spectral lines (shape and half

width value)� Broadening of lines due to

Doppler effect and pressurebroadening

� Michelson interferometer� Magnification

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:54 Uhr Seite 89


Principle:A measurement cuvette set in thebeam path of a Michelson interfe-rometer can be evacuated or filledwith CO2. The refraction indexes ofair or CO2 are determined throughthe assessed modification of theinterference pattern.

Number N of minima changes as a function of air pressure in the measuringcuvette.


� Interference� Wavelength� Phase� Refraction index� Light velocity� Virtual light source

Michelson interferometer 08557.00 1

Laser, He-Ne 1.0 mw, 220 V AC 08181.93 1

Glass cell for Faraday effect 08625.00 1

Manual vacuum pump 08745.10 1







Lens, mounted, f = +20 mm 08018.01 1

Digital manometer 03106.00 1

Compressed gas, CO2, 21 g 41772.06 1

Fine control valve 33499.00 1




Screen, metal, 300�300 mm 08062.00 1

Tubing adaptor, ID 3-6/7-11 mm 47517.01 1

Tubing connect., Y-shape, ID 8-9 mm 47518.03 1

PVC tubing, i.d. 7 mm 03985.00 1

Silicon tube int. diam. 3 mm 39292.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedRefraction index of air and CO2with Michelson interferometer P2220700


Optics Interference


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 115)

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 90


Diffraction Optics

Diffraction at a slit and Heisenberg’s uncertainty principle 2.3.01-00

Principle:The distribution of intensity in theFraunhofer diffraction pattern of aslit is measured. The results are eval-uated both from the wave patternviewpoint, by comparison withKirchhoff’s diffraction formula, andfrom the quantum mechanics stand-point to confirm Heisenberg’s uncer-tainty principle.

Tasks:1. To measure the intensity distri-

bution of the Fraunhofer diffrac-tion pattern of a single slit (e. g.0.1 mm).The heights of the maxima andthe positions of the maxima andminima are calculated accordingto Kirchhoff’s diffraction formulaand compared with the measuredvalues.

Intensity in the diffraction pattern of a 0.1 mm wide slit at a distance of 1140 mm. The photocurrent is plotted as a function of the position.

2. To calculate the uncertainty ofmomentum from the diffractionpatterns of single slits of differingwidths and to confirm Heisen-berg’s uncertainty principle.

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1

Diaphragm, 3 single slits 08522.00 1

Diaphragm, 4 double slits 08523.00 1

Diaphragm, 4 multiple slits 08526.00 1


Photoelement f. opt. base plt. 08734.00 1

Slide device, horizontal 08713.03 1

PEK carbon resistor 1 W 5% 2.2 k� 39104.23 1

Multi-range meter A 07028.01 1

Universal measuring amplifier 13626.93 1



Slide mount f. opt. pr.-bench 08286.00 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction at a slit and Heisenberg’suncertainly principle P2230100


� Diffraction� Diffraction uncertainty� Kirchhoff’s diffraction formula� Measurement accuracy� Uncertainty of location� Uncertainty of momentum� Wave-particle dualism� De Broglie relationship

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 91


Principle:Monochromatic light is incident on aslit or an edge. The intensity distribu-tion of the diffraction pattern isdetermined.

Intensity distribution on diffraction at the slit, as a function of the positionalong a straight line parallel to the plane of the slit, standardised on theintensity without the slit.

Tasks:1. Measurement of the width of a

given slit.

2. Measurement of the intensity dis-tribution of the diffraction patternof the slit and

3. of the edge.


� Intensity� Fresnel integrals� Fraunhofer diffraction

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1

Photoelement for opt. base plate 08734.00 1



Lens, mounted, f = -50 mm 08026.01 1

Slit, adjustable 08049.00 1

Screen, metal, 300�300 mm 08062.00 1

Diaphragm with slit 09816.02 1



Meter scale, demo. l = 1000 mm 03001.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction of light at a slit and an edge P2230200


Optics Diffraction


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 115)

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 92


Diffraction Optics

Intensity of diffractions due to pin hole diaphragms and circular obstacles 2.3.03-00

Principle:Pin hole diaphragms and circularobstacles are illuminated with laserlight. The resulting intensity distribu-tions due to diffraction are measuredby means of a photo diode.

Tasks:1. The complete intensity distribu-

tion of the diffraction pattern of apin hole diaphragm (D1 = 0.25mm) is determined by means of asliding photo diode. The diffrac-tion peak intensities are comparedwith the theoretical values. Thediameter of the pin hole dia-phragm is determined from thediffraction angles of peaks andminima.

2. The positions and intensities ofminima and peaks of a second pinhole diaphragm (D2 = 0.5 mm) are

Diffracted intensity I vs position x of the photodiode, using a diaphragm withD1 = 0.25 mm.

determined. The diffraction peakintensities are compared with thetheoretical values. The diameter ofthe pin hole diaphragm is deter-mined.

3. The positions of minima and peaksof the diffraction patterns of twocomplementary circular obstacles(D*1 = 0.25 mm and D*2 = 0.5mm) are determined. Results arediscussed in terms of Babinet’sTheorem.

Laser, He-Ne 1.0 mw, 220V AC 08181.93 1








Screen, metal, 300�300 mm 08062.00 1

Screen, with diffracting elements 08577.02 1



PEK carbon resistor, 1 W, 5%, 2.2 k� 39104.23 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedIntensity of diffractions due to pin holediaphragms and circular obstacles P2230300


� Huygens principle� Interference� Fraunhofer and Fresnel

diffraction� Fresnel’s zone construction� Coherence� Laser� Airy disk� Airy ring� Poisson’s spot� Babinet’s theorem� Bessel function� Resolution of optical

instruments

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 93

2.3.04-00 Diffraction intensity of multiple slits and grids

Principle:Multiple slits which all have thesame width and the same distanceamong each other, as well as trans-mission grids with different grid con-stants, are submitted to laser light.The corresponding diffraction pat-terns are measured according totheir position and intensity, bymeans of a photo diode which can beshifted.

Tasks:1. The position of the first intensity

minimum due to a single slit isdetermined, and the value is usedto calculate the width of the slit.

2. The intensity distribution of thediffraction patterns of a three-fold, fourfold and even a fivefoldslit, where the slits all have thesame widths and the same dis-tance among each other, is to be

Diffraction intensity I as a function of the position x for a threefold slit, b1 = 0.1 mm and g = 0.25 mm. Distance between threefold slit and photo-cell: L = 107 cm. For comparison, the intensity distribution of a single slit, b = 0.1 mm, is entered as a dotted line.

determined. The intensity relationsof the central peaks are to beassessed.

3. For transmission grids with differ-ent lattice constants, the positionof the peaks of several orders ofdiffraction is to be determined,and the found value used to cal-culate the wavelength of the laserlight.


� Huygens principle� Interference� Fraunhofer und Fresnel

diffraction� Coherence� Laser

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1









Lens, mounted, f = +20 mm 08018.01 1

Lens, mounted, f = +100 mm 08021.01 1


Diaphragm, 3 single slits 08522.00 1

Diaphragm, 4 multiple slits 08526.00 1






PEK carbon resistor 1 W 5%, 2.2 k� 39104.23 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction intensityof multiple slits and grids P2230400


Optics Diffraction

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 94


Diffraction Optics

Determination of the diffraction intensity at slit and double slit systems 2.3.05-00

Principle:Slit and double slit systems are illu-minated with laser light. The corre-sponding diffraction patterns aremeasured by means of a photodiodewhich can be shifted, as a functionof location and intensity.

Tasks:1. Determination of the intensity

distribution of the diffraction pat-terns due to two slits of differentwidths.The corresponding width of theslit is determined by means of therelative positions of intensity val-ues of the extremes. Furthermore,intensity relations of the peaks areevaluated.

Diffraction intensity I as a function of location x for the single slit b1 = 0.1 mm and b2 = 0.2 mm.The x axis of the graph for b1 = 0.1 mm is shifted upwards. The intensity ofthe areas next to the central peak is represented enlarged by a factor of 10.(Distance between slit and photodiode L = 107 cm; � = 632.8 nm).

2. Determination of location andintensity of the extreme values ofthe diffraction patterns due totwo double slits with the samewidths, but different distancesbetween the slits. Widths of slitsand distances between the slitsmust be determined as well as theintensity relations of the peaks.

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1Universal measuring amplifier 13626.93 1Optical profile bench l = 150 cm 08281.00 1Base f.opt.profile-bench, adjust. 08284.00 2Slide mount f. opt. pr.-bench, h = 80 mm 08286.02 4Slide device, horizontal 08713.00 1Slide mount f. opt. pr.-bench 08286.00 1Lens holder 08012.00 2Object holder, 5�5 cm 08041.00 1Lens, mounted, f = +20 mm 08018.01 1Lens, mounted, f = +100 mm 08021.01 1Photoelement f. opt. base plt. 08734.00 1Diaphragm, 3 single slits 08522.00 1Diaphragm, 4 double slits 08523.00 1PEK carbon resistor 1 W 5% 2.2 k� 39104.23 1Multi-range meter A 07028.01 1Connecting cord, l = 750 mm, red 07362.01 1Connecting cord, l = 750 mm, blue 07362.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedDetermination of diffraction intensityat slit and double slit systems P2230500


� Huygens principle� Interference� Fraunhofer and Fresnel

diffraction� Coherence� Laser


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 115)

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 95


Principle:An aperture consisting of a single slitand a complementary strip (wire) isilluminated with a laser beam. Thecorresponding diffraction patternsare measured according to positionand intensity with a photocell whichcan be shifted.

Tasks:1. Determination of the intensity

distribution of the diffraction pat-terns due to a slit and comple-mentary strip (wire).

2. Determination of the intensityrelations of the diffraction patternpeaks for the single slit.

Diffraction intensity I as a function of the position x for single slit a) andstrip b). Width of the diffracting object b = 0.2 mm.The intensities in the areas next to the central peak are represented extend-ed by a factor of 10. (Distance between diffracting object and photocellL=120cm; Wavelength of the laser light � = 632.8 nm)

3. Babinet’s theorem is discussedusing the diffraction patterns ofthe slit and the complimentarystrip.


� Huygens’ principle� Interference� Fraunhofer und Fresnel

diffraction� Babinet’s theorem� Poissons’ spot� Coherence� Laser

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1










PEK carbon resistor 1 W 5 % 2.2 k� 39104.23 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction intensity through a slit and a wire – Babinet’s theorem 22306-00


Optics Diffraction


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 115)

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 96


Photometry Optics

Photometric law of distance 2.4.02-01

Principle:The luminous intensity emitted by apunctual source is determined as afunction of distance.

Illuminance as a function of the reciprocal values of the square of the dis-tances.

Tasks:1. The luminous intensity emitted by

a punctual source is determined asa function of distance from thesource.

2. The photometric law of distance isverified by plotting illuminance asa function of the reciprocal valueof the square of the distance.


� Luminous flux� Quantity of light� Luminous intensity� Illuminance� Luminance

Lux meter, hand-held 07137.00 1

Luxmeter probe 12107.01 1




Slide mount f. opt. pr.-bench, h= 80 mm 08286.02 1

Lamp holder E 14, on stem 06175.00 1

Filament lamp 6 V/5 A, E14 06158.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedPhotometric law of distance P2240201

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 97



Principle:The luminous intensity emitted by apunctual source is determined as afunction of distance.

Experimental objective:The luminous intensity is a functionof the distance of the light sensorfrom the light source. The law forpoint light sources on which this isbased should be determined.

Luminous intensity as a function of the square of the reciprocal of the dis-tance (lamp – diode)

Tasks:1. The luminous intensity emitted by

a punctual source is determined asa function of distance from thesource.

2. The photometric law of distance isverified by plotting illuminance asa function of the reciprocal valueof the square of the distance.




Cobra3 Force/Tesla Measurement Software 14515.61 1

Power supply, 0...12 V 13505.93 1


Distributor 06024.00 1



Meter scale, l = 1000 mm 03001.00 1

PEK photodiode, 33f2 39119.01 1

Film resistor, 470 �, G1 39104.15 1

Incandescent lamp, 6 V/5 A, E 14 06158.00 1

Lamp holder E14, on stem 06175.00 1

Connecting cord, 32 A, l = 50 cm, red 07361.01 1

Connecting cord, 32 A, l = 50 cm, blue 07361.04 1



Adapter, BNC-socket / 4mm plug 07542.20 1



Silk thread, l = 200 m 02412.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedPhotometric law of distance with Cobra3 P2240211

Optics Photometry


� Luminous flux� Quantity of light� Luminous intensity� Illuminance� Luminance

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 98


Photometry Optics

Lambert’s law 2.4.04-00

Principle:Visible light impinges on a diffuselyreflecting surface. The luminance ofthis surface is determined as a func-tion of the angle of observation.

Illuminance as a function of cos �.

Tasks:1. The luminous flux emitted reflect-

ed by a diffusely reflecting surfaceis to be determined as a functionof the angle of observation.

2. Lambert’s law (cos-law) is to beverified using the graph of themeasurement values.

Housing for experiment lamp 08129.01 1

Halogen lamp, 12 V/50 W 08129.06 1

Holder G 6.35 f. 50/100 W halo.lamp 08129.04 1



Lens, mounted, f = +200 mm 08024.01 1

Zinc sulfide screen 08450.00 1





Support rod, stainl.steel, l = 100 mm 02030.00 1



Articulated radial holder 02053.01 1

Graduated disk, f. demonstration 02053.02 1



Lux meter, hand-held 07137.00 1

Measuring module lux 12107.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedLambert’s law P2240400


� Luminous flux� Light quantity� Light intensity� Illuminance� Luminance

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 99


Principle:Monochromatic light falls on a micaplate perpendicular to its optic axis.At the appropriate plate thickness(�/4, or quarter-wave plate) there isa 90 ° phase shift between the ordi-nary and the extraordinary ray whenthe light emerges from the crystal.The polarisation of the emergentlight is investigated at differentangles between the optic axis of the�/4 plate and the direction of pola-risation of the incident light.

Tasks:1. To measure the intensity of plane-

polarised light as a function of theposition of the analyser.

2. To measure the light intensitybehind the analyser as a functionof the angle between the opticaxis of the �/4 plate and that ofthe analyser.

Intensity distribution of polarised light as a function of the direction of trans-mission of the analyser: with �/4 plate at various angular settings.

3. To perform experiment 2. with two�/4 plates one behind the other.


� Plane� Circularly and elliptically

polarised light� Polariser� Analyzer� Plane of polarisation� Double refraction� Optic axis� Ordinary and extraordinary

ray



Lens, mounted, f = +100 mm 08021.01 1


Iris diaphragm 08045.00 1


Lamp, f. 50 W Hg high press. lamp 08144.00 1

Power supply for Hg CS/50 W lamp 13661.93 1

Interference filter, yellow, 578 nm 08461.01 1

Polarising filter, on stem 08610.00 2

Optical profile-bench, l = 1000mm 08282.00 1



Slide mount f. opt. pr.-bench, h = 80 cm 08286.02 1

Polarization specimen, mica 08664.00 2

PEK carbon resistor 1 W 5% 2,2 K� 39104.23 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedPolarisation by quarterwave plates P2150100


Optics Photometry

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 100


Polarisation Optics

Polarimetry 2.5.02-00

Principle:The rotation of the plane of polarisa-tion through a sugar solution meas-ured with a half-shade penumbrapolarimeter and the reaction rateconstant for the inversion of canesugar determined.

Semi-logarithmic plot of the measured values from cane sugar inversion.

Tasks:1. To determine the specific rotation

of cane sugar (sucrose) and lac-tose by measuring the rotation ofvarious solutions of known con-centration.

2. To determine the reaction rateconstant when cane sugar istransformed into invert sugar.

Half-shade polarimeter, 220 V AC 08628.93 1





Crucible tongs, 200 mm, stainl. steel 33600.00 1

Beaker, 250 ml, low form, plastic 36013.01 2

Graduated cylinder, 100 ml, plastic 36629.01 2

Graduated vessel, 1 l, w. handle 36640.00 1

Funnel, plastic, dia 90 mm 36891.00 1

Spoon, w. spatula end, 18 cm, plastic 38833.00 1

Glass rod, boro 3.3, l = 300 mm, d = 8 mm 40485.06 1

Pipette, with rubber bulb, long 64821.00 1

D (+)-Sucrose, 100 g 30210.10 1

Hydrochloric acid 1.19, 2500 ml 30214.79 1


D(+)-Lactose, powder, 100 g 31577.10 1

Balance LG 311, 4 beams 44007.31 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedPolarimetry P2250200


� Half-shade principle� Optical rotatory power� Optical activity� Saccharimetry� Specific rotation� Reaction rate� Weber-Fechner law

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:55 Uhr Seite 101


0.8

0.6

0.4

0.2

20° 40° 60° 80°

EXP.

THEOR.

�

�

�

�

''

� �p

Principle:Plane-polarized light is reflected at aglas surface. Both the rotation of theplane of polarization and the inten-sity of the reflected light are to bedetermined and compared withFrewsnel’s formulae for reflection.

Tasks:1. The reflection coefficients for light

polarized perpendicular and par-allel to the plane of incidence areto be determined as a function ofthe angle of incidence and polttedgraphically.

2. The refractive index of the flintglass prism is to be found.

3. The reflection coefficients are tobe calculated using Fresnel’s for-mulae and compared with themeasured curves.

Measured and calculated curves for�r" and �r� as a function of the angle of

incidence.

4. The reflection factor for the flintglass prism is to be calculated.

5. The rotation of the polarizationplane for plane polarized lightwhen reflected is to be deter-mined as a function of the angleof incidence and presented graph-ically. It is then to be comparedwith values calculated using Fres-nel’s formulae.


� Electromagnetic theory oflight

� Reflection coefficient� Reflection factor� Brewster’s law� Law of refraction� Polarization� Polarization level

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1

Polarising filter, on stem 08610.00 2

Prism, 60 degrees, h = 36.4 mm, flint 08237.00 1

Prism table with holder 08254.00 1


Protractor scale with pointer 08218.00 1




H-base -PASS- 02009.55 2





Multirange meter with amplifier 07034.00 1

Dry cell, 1.5 V 11620.34 6

What you need:

Complete Equipment Set, Manual on CD-ROM includedFresnel’s equations – theory of reflection P2250300


Optics Polarisation


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 115)

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 102


Polarisation Optics

Malus’ law 2.5.04-00

Principle:Linear polarized light passes througha polarization filter.

Transmitted light intensity is deter-mined as a function of the angularposition of the polarization filter.

Corrected photo cell current as a function of the angular position � of the po-larization plane of the analyzer.

Tasks:1. The plane of polarization of a lin-

ear polarized laser beam is to bedetermined.

2. The intensity of the light transmit-ted by the polarization filter is tobe determined as a function of theangular position of the filter.

3. Malus’ law must be verified.

Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1


Base for optical profile bench, adjustable 08284.00 2


Polarising filter on stem 08610.00 1

Photoelement f. opt. base plate 08734.00 1


PEK carbon resistor 1 W, 5%, 2,2 k� 39104.23 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMalu’s law P2250400


� Electric theory of light� Polarization� Polarizer� Analyzer� Brewster's law� Malus' law


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 115)

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 103


Principle:The angle of rotation of the polarisa-tion-plane of plane polarized lightthrough a flint glass rod is found tobe a linear function of the product ofthe mean flux-densitiy and thelength of the optical medium. Thefactor of proportionally, calledVerdet’s constant, is investigated asa function of the wavelength and theoptical medium.

Tasks:1. To determine the magnetic flux-

densitiy between the pole piecesusing the axial Hall probe of theteslameter for different coil cur-rents. The mean flux-density iscalculated by numerical integra-tion and the ratio maximum flux-density over mean flux-density es-tablished.

2. To measure the maximum flux-density as a function of the coilcurrent and to establish the rela-tionship between mean flux-den-sity and coil current anticipatingthat the ratio found under 1. re-mains constant.

Verdet’s constant as a function of the wavelength+ measured values --- theoretical values.

3. To determine the angle of rotationas a function of the mean flux-density using different colour fil-ters. To calculate the correspond-ing Verdet’s constant in each case.

4. To evaluate Verdet’s constant as afunction of the wavelength.


� Electromagnetic fieldinteraction

� Electron oscillation� Electromagnetism� Polarization� Verdet’s constant� Hall effect

Glass rod for Faraday effect 06496.00 1Coil, 600 turns 06514.01 2Pole pieces, drilled, 1 pair 06495.00 1Iron core, U-shaped, laminated 06501.00 1Housing for experiment lamp 08129.01 1Halogen lamp, 12 V/50 W 08129.06 1Holder G 6.35 f. 50/100 W halo.lamp 08129.04 1Double condenser, f = 60 mm 08137.00 1Var.transformer, 25 VAC/20 VDC, 12A 13531.93 1Voltmeter 5/15 V DC 07037.00 1Commutator switch 06034.03 1Teslameter, digital 13610.93 1Hall probe, axial 13610.01 1Lens, mounted, f = +150 mm 08022.01 1Lens holder 08012.00 1Table top on rod, 18.5�11 cm 08060.00 1Object holder, 5�5 cm 08041.00 1Colour filter, 440 nm 08411.00 1Colour filter, 505 nm 08413.00 1Colour filter, 525 nm 08414.00 1Colour filter, 580 nm 08415.00 1Colour filter, 595 nm 08416.00 1Polarizing filter with vernier 08611.00 2Screen, translucent, 250�250 mm 08064.00 1Optical profile-bench, l = 1000 mm 08282.00 1Base f. opt. profile-bench, adjust. 08284.00 2Slide mount f. opt. pr.-bench, h = 30 mm 08286.01 2Slide mount f. opt. pr.-bench, h = 80 mm 08286.02 5Universal clamp 37715.00 1Connecting cord, l = 750 mm, red 07362.01 3Connecting cord, l = 750 mm, blue 07362.04 3

What you need:

Complete Equipment Set, Manual on CD-ROM includedFaraday effect P2260100


Optics Applied Optics

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 104


Applied Optics Optics

Kerr effect 2.6.02-00

Principle:Monochromatic, vertically polarizedlight impinges on a PLZT element(lead-lanthanum-zirconium-titani-um compount) which is set in itsholder at 45 ° to the vertical.

An electric field is applied to thePLZT element and causes it tobecome birefractive. The phase-shiftbetween the normal and the extraor-dinary light beam behind the PLZTelement is recorded as a function ofthe applied voltage and it is shownthat the phase-shift is proportionalto the square of the electric fieldstrength respectively of the voltageapplied. From the constant of pro-

portionality the Kerr constant is cal-culated for the PLZT element.

The Kerr effect has usually beendemonstrated with nitrobenzene inthe past. Since nitrobenzene is verytoxic and needs high voltages ofsome kV the PLZT element whichonly needs some hundred volts rep-resents an attractive alternative.

Relative luminous intensity behind the analyser as a function of the volt-age U applied to the PLZT element and the phase-shift � between normaland extraordinary beam.

II0

Tasks:1. The phase-shift between the nor-

mal and the extra-ordinary lightbeam is to be recorded for differ-ent voltages applied to the PLZT-element respectively for differentelectric field strengs.The half-wave voltage U is to be deter-mined.

2. By plotting the square of theapplied voltage versus the phaseshift between normal and extraor-dinary beam it is to be shown thatthe relation between the twoquantities is approximately linear.From the slope of the straight linethe Kerr constant is to be calcu-lated.

(l2)

Kerr cell, PLZT-element 08641.00 1High voltage supply unit, 0-10 kV 13670.93 1Laser, He-Ne 1.0 mW, 220 V AC 08181.93 1Polarising filter, on stem 08610.00 2Optical profile bench l = 60 cm 08283.00 1Base f.opt.profile-bench, adjust. 08284.00 2Slide mount f.opt.pr.-bench, h = 30 mm 08286.01 5Photoelement f. opt. base plt. 08734.00 1Universal measuring amplifier 13626.93 1Digital multimeter 07134.00 2Screened cable, BNC, l = 750 mm 07542.11 1Adapter, BNC-socket/4 mm plug pair 07542.27 1Connecting cord, l = 750 mm, red 07362.01 3Connecting cord, l = 750 mm, blue 07362.04 2

OPTION for electro-optical modulatorPower frequency generator 1MHz 13650.93 1

Loudspeaker, 8 �/5 k� 13765.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedKerr effect P2260200


� Polarization of light� Birefraction� Optical anisotropy� Modulation of light� Electro-optical modulator� PLZT-element


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 115)

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 105


Principle:In contrast to normal photography ahologram can store information aboutthe three-dimensionality of an object.To capture the three-dimensionalityof an object, the film stores not onlythe amplitude but also the phase ofthe light rays. To achieve this, a co-herent light beam (laser light) is splitinto an object and a reference beamby being passed through a beam split-ter. These beams interfere in the planeof the holographic film. The hologramis reconstructed with the referencebeam which was also used to recordthe hologram.

Setup for recording and reconstruction of a transmission hologram.

Tasks:1. Capture the holographic image of

an object.

2. Perform the development andbleaching of this phase hologram.

3. Reconstruct the transmissionhologram (reconstruction beam isthe reference beam during imagecapture).


� Object beam� Reference beam� Real and virtual image� Phase holograms� Amplitude holograms� Interference� Diffraction� Coherence� Developing of film

Complete Equipment Set, Manual on CD-ROM includedRecording and reconstruction of holograms P2260300



Optical base plate in exp. case 08700.01 1

He/Ne Laser, 5 mW with holder 08701.00 1

Power supply f. laser head 5 mW 08702.93 1

Magnetic foot f. opt. base plt. 08710.00 6

Holder f. diaphr./beam splitter 08719.00 2


xy shifting device 08714.00 2

Adapter ring device 08714.01 1

Achromatic objective 20� N.A. 0.45 62174.20 1

Pin hole 30 micron 08743.00 1

Adjusting support 35�35 mm 08711.00 2

Surface mirror 30�30 mm 08711.01 2

Surface mirror, large, d = 80 mm 08712.00 1

Beam splitter 1/1, non polarizing 08741.00 1

Object for holography 08749.00 1

Holographic plates, 20 pieces* 08746.00 1

Darkroom equipment for holography 08747.88 1

consisting of:

Plastic trays, 4 pcs. • Laboratory gloves, medium, 100 pcs. • Tray

thermometer, offset, +40°C • Roller squeegee • Clamps, 2 pcs. • Film

tongs, 2 pcs. • Darkroom lamp with green filter • Light bulb 230 V/15 W •

Funnel • Narrow-necked bottles, 4 pcs.

Set of photographic chemicals 08746.88 1

consisting of: Holographic developer • Stop bath • Wetting agent •

Laminate • Paint

Bleaching chemicals:

Potassium dichromate, 250 g 30102.25 1

Sulphuric acid, 95-98%, 500 ml 30219.50 1

What you need:

*Alternative:

Holographic sheet film 08746.01 1

Glass plate, 120�120�2 mm 64819.00 2

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 106



CO2-laser 2.6.04-00

Principle:Among molecular laser, the CO2-laseris of greatest practical importance.The high level of efficiency with whichlaser radiation can be generated incontinuous wave (cw) and pulse oper-ation is its most fascinating feature.The experimental equipment set is anopen CO2-didactic laser system ofmax. 8 W power output. Since it is an“open” system, all components of thesystem can be handled individuallyand the influence of each procedureon the output power can be studied.One very primary and essential targetin learning is the alignment of theCO2-laser by means of a He/Ne-laser.

Tasks:1. Align the CO2-laser and optimize

its power output.

2. Check the influence of the Brew-ster windows position on thepower output.

3. Determine the power output as afunction of the electric powerinput and gasflow.

4. Evaluate the efficiency as a func-tion of the electric power inputand gasflow.

Laser power as a function of the angle of inclination of the brewster windownormal N.

5. If the gas-mixing unit is suppliedthe influence of the differentcomponents of the laser gas (CO2,He, N2) to the output efficiency ofthe CO2-laser are analyzed.

6. Measurement of temperaturesdifferences for the laser gas(imput / output) for study of con-version efficiency.

CO2-laser tube, detachable, typ 5 W 08596.00 1Module box for CO2-laser tube 08597.00 1Set of laser mirrors, ZnSe and Si 08598.00 1Opt.bench on steel rail l 1,3 m 08599.00 1HV-power supply 5 kV/50 mA DC 08600.93 1Ballast resistor unit incl. 3 HV cables 08601.00 1Cooling water unit, portable 08602.93 1Vacuum pump, two-stage 02751.93 1Gas filter/buffer unit 08605.00 1He/Ne-laser/adjusting device 08607.93 1Diaphragm f.adj. CO2-laser 08608.00 2Screen translucent, 250�250 mm 08064.00 1Right angle clamp –PASS- 02040,55 1Powermeter 30 mW/10 Watt 08579.93 1Support for power probe 08580.00 1Protecting glasses, 10.6 micro-m 08581.00 1Cleaning set for laser 08582.00 1ZnSe biconvex lens, d = 24 mm, f = 150 mm 08609.00 1Digit.thermom.,NiCr-Ni 08583.00 1HV-isolated temperature probe 08584.00 1Control panel w. support, 1 gas* 08606.00 1Press.contr.valve 200/3bar* 08604.00 1Laser gas in bottle, 50 l/200 bar* 08603.00 1

*Alternative:Laser gas mixing unit, 3 gases 08606.88 1He-, N2- and CO2-gas

Option:Experiment set for laser beam analysis 08610.10 1

1. estimation of wavelength by diffraction grating and2. distribution of power by diaphragm

IR conversion plate for observation of CO2-laserinfrared radiation 08611.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedCO2-laser P2260400


� Molecular vibration� Exitation of molecular

vibration� Electric discharge� Spontaneous emission� Vibration niveau� Rotation niveau� Inversion� Induced emission� Spectrum of emission� Polarization� Brewster angle� Optical resonator

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 107


Principle:Small particles in a current passthrough the LDA measuring volumeand scatter the light whose frequen-cy is shifted by the Doppler effectdue to the particle movement.

The frequency change of the scat-tered light is detected and convertedinto a particle or flow velocity.

Measurement of the signal spectrum with a signal peak


� Interference� Doppler effect� Scattering of light by small

particles (Mie scattering)� High- and low-pass filters� Sampling theorem� Spectral power density� Turbulence



Tasks:1. Measurement of the light-fre-

quency change of individual lightbeams which are reflected bymoving particles.

2. Determination of the flow veloci-ties.

Optical base plate with rubber feet 08700.00 1He/Ne Laser, 5 mW with holder 08701.00 1Power supply f. laser head 5 mW 08702.93 1Adjusting support 35�35 mm 08711.00 2Surface mirror 30�30 mm 08711.01 2Magnetic foot f. opt.base plt. 08710.00 8Holder f. diaphr./beam splitter 08719.00 1Lens, mounted, f = +100 mm 08021.01 1Lens, mounted, f = +50 mm 08020.01 1Lens, mounted, f = +20 mm 08018.01 1Iris diaphragm 08045.00 1Beam splitter 1/1, non polarizing 08741.00 1Si-Photodetector with Amplifier 08735.00 1Control Unit f. Si-Photodetector 08735.99 1Adapter, BNC-socket/4 mm plug pair 07542.27 1Screened cable, BNC, l = 750 mm 07542.11 1Prism table w.holder f. opt. b. plt. 08725.00 1Lensholder f. optical base plate 08723.00 3Screen, white, 150�150 mm 09826.00 1xy shifting device 08714.00 1Pin hole 30 micron 08743.00 1LDA-Accessory-Set 08740.00 1Support rod -PASS-, square, l = 630 mm 02027.55 2Right angle clamp -PASS- 02040.55 2Universal clamp 37715.00 2Support base -PASS- 02005.55 1Aspirator bottle, clear gl. 1000 ml 34175.00 2Pinchcock, width 10 mm 43631.10 3Glass tubes, straight, 80 mm, 10 36701.65 1Rubber stopper, d = 32/26 mm, 1 hole 39258.01 2Rubber stopper, d = 22/17 mm, 1 hole 39255.01 2Measuring tape, l = 2 m 09936.00 1Spatula, double blade, 150 mm 33460.00 1Glass beaker, short, 150 ml 36012.00 1Cobra3 Basic Unit 12150.00 1

What you need:

Power supply 12 V/2 A 12151.99 1RS232 data cable 14602.00 1Software Cobra3 Fourieranalyse 14514.61 1PC, Windows® 95 or higher

Complete Equipment Set, Manual on CD-ROM includedLDA – Laser Doppler Anemometrywith Cobra3 P2260511

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 108



Helium Neon Laser 2.6.07-00

Principle:The difference between spontaneousand stimulated emission of light isdemonstrated. The beam propagationwithin the resonator cavity of a He-Ne laser and its divergence are deter-mined, its stability criterion ischecked and the relative outputpower of the laser is measured as afunction of the tube’s position insidethe resonator and of the tube current.

The following items can be realizedwith advanced set 08656.02.By means of a birefringent tuner anda Littrow prism different wave-lengths can be selected and quanti-tatively determined if a monochro-mator is available.Finally you can demonstrate the ex-istence of longitudinal modes andthe gain profile of the He-Ne laserprovided an analysing Fabry Perotsystem is at your disposal.

Tasks:1. Set up the He-Ne laser. Adjust the

resonator mirrors by use of thepilot laser. (left mirror: VIS, HR,plane ; right mirror: VIS, HR, R =700 mm)

2. Check on the stability condition ofa hemispherical resonator.

Relative output power as a function of mirror spacing.

Exp.Set HeNe-Laser, basic set 08656.01 1

Exp.Set HeNe-Laser, advanced optics 08656.02 1

Optical bench on carrier rail 08599.01 1

Diaphragm for adjustment of laser 08608.00 2

Photoelement, silicon 08734.00 1


Screen, white, 150�150 mm 09826.00 1

Danger sign -LASER- 06542.00 1

Barrel base –PASS- 02006.55 1



Option:

Exp.Set HeNe-Laser, advanced set 08656.02 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedHelium Neon Laser P2260700


� Spontaneous and stimulatedlight emission

� Inversion� Collision of second type� Gas discharge tube� Resonator cavity� Transverse and longitudinal

resonator modes� Birefringence� Brewster angle� Littrow prism� Fabry Perot Etalon

Helium Neon Laser, advanced set P2260705

3. Measure the integral relative out-put power as a function of thelaser tube’s position within thehemispherical resonator.

4. Measure the beam diameter with-in the hemispherical resonatorright and left of the laser tube.

5. Determine the divergence of thelaser beam.

6. Measure the integral relative out-put power as a function of thetube current.

The He-Ne laser can be tuned usinga BFT or a LTP. Longitudinal modescan be observed by use of a FabryPerot Etalon of low finesse. Remark:These points can only be coveredquantitatively if a monochromatorand an analysing Fabry Perot systemare available.


You can find more

advanced optics

in this brochure

Order No. 00117.02

(see page 115)

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 109


10 20 30 40 50 60

Prel

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

812,9 nm

817,3 nm

808,4 nm

804,4 nm

T°C

Principle:The visible light of a semiconductordiode laser is used to excite theneodymium atoms within a Nd-YAG(Neodymium-Yttrium AluminiumGarnet) rod. The power output of thesemiconductor diode laser is firstrecorded as a function of the injec-tion current. The fluorescent spec-trum of the Nd-YAG rod is then de-termined and the maon absorptionlines of the Nd-atoms are verified.Conclusively, the mean life-time ofthe 4F3/2-level of the Nd-atoms ismeasured in appoximation.

Relative fluorescent power of the Nd-YAG rod as a function of the diodetemperature (wavelength) for I = 450 mA.

Tasks:1. To determine the power output of

the semiconductor diode laser as afunction of the injection current.

2. To trace the fluorescent spectrumof the Nd-YAG rod pumped by thediode laser and to verify the mainabsorption lines of neodymium.

3. To measure the mean life-time ofthe 4F3/2-level of the Nd-atoms.

4. For further applications see ex-periment 2.6.09 “Nd-YAG laser”.


� Spontaneous emission� Induced emission� Mean lifetime of a

metastable state� Relaxation� Inversion� Diode laser

Basic set optical pumping 08590.93 1

Sensor f. measurem. of beam power 08595.00 1




Optional equipment for setup and storage:

Optical base plate in exp.case 08700.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedOptical pumping 2260800



LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 110



Nd-YAG laser 2.6.09-00

25

20

15

10

5

50 100 150

PNd-YAGmW

Pump powermW

From graphic:Threshold power = 57 mW

From graphic:Slope efficiency: 30%

Principle:The rate equation model for an opti-cally pumped four-level laser systemis determined. As lasing medium, aNd-YAG (Neodymium-Yttrium Alu-minium Garnet) rod has been select-ed which is pumped by means of asemiconductor diode laser.

The IR-power output of the Nd-YAGlaser is measured as a function of theoptical power input and the slope ef-ficiency as well as the thresholdpower are determined.

Finally, a KTP-crystal is inserted intothe laser cavity and frequency dou-bling is demonstrated. The quadraticrelationship between the power ofthe fundamental wave and the beampower for the second harmonic isthen evident.

Nd-YAG laser power output as a function of the pump power � = 808.4 nm.

Tasks:1. Set up the Nd-YAG laser and opti-

mize its power output.

2. The IR-power output of the Nd-YAG laser is to be measured as afunction of the pump power. Theslope efficiency and the thresholdpower are to be determined.

3. Verify the quadratic relationshipbetweenthe power of the funda-mental wave, with � = 1064 nm,and the beam power of the secondharmonic with � = 532 nm.

Basic set optical pumping 08590.93 1

Sensor f. measurem. of beam power 08595.00 1

Nd-YAG laser cavity mirror/holder 08591.01 1

Laser cav.mirror frequ. doubling 08591.02 1

Frequ. doubling crystal in holder 08593.00 1

Filter plate, short pass type 08594.00 1


Oscilloscope, 30 MHZ, 2 channels 11459.95 1

Screened cable, BNC, l 750 mm 07542.11 3

Optional equipment for setup and storage:

Optical base plate in exp.case 08700.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedNd-YAG laser P2260900


� Optical pumping� Spontaneous emission� Induced emission� Inversion� Relaxation� Optical resonator� Resonator modes� Polarization� Frequency doubling

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 111


Principle:The beam of a laser diode is treatedin a way that it can be coupled intoa monomode fibre. The problemsrelated to coupling the beam intothe fibre are evaluated and verified.In consequence a low frequency sig-nal is transmitted through the fibre.The numerical aperture of the fibre isrecorded. The transit time of light

through the fibre is measured andthe velocity of light within the fibreis determined. Finally the measure-ment of the relative output power ofthe diodelaser as a function of thesupply current leads to the charac-teristics of the diodelaser such as“threshold energy” and “slopeefficiency”.

Tasks:1. Couple the laser beam into the

fibre and adjust the setting-up ina way that a maximum of output

Relative output power at the fibre end versus angle readout.

power is achieved at the exit ofthe fibre.

2. Demonstrate the transmission of aLF – signal through the fibre.

3. Measure the numerical apertureof the fibre.

4. Measure the transit time of lightthrough the fibre and determinethe velocity of light within thefibre.

5. Determine the relative outputpower of the diodelaser as a func-tion of the supply current.


� Total reflection� Diode laser� Gaussian beam� Monomode and multimode

fibre� Numerical aperture� Transverse and longitudinal

modes� Transit time� Threshold energy� Slope efficiency� Velocity of light

Exp.Set Fibre Optics 08662.93 1


Oscilloscope 100MHz, 2-channel 11450.95 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFibre optics P2261000



LEP 2.1.00-01_2.6.12-00 12.10.2003 13:56 Uhr Seite 112



Fourier optics – 2f Arrangement 2.6.11-00

Principle:The electric field distribution of lightin a specific plane (object plane) isFourier transformed into the 2 f con-figuration.

Experimental set-up for the fundamental principles of Fourier optic (2f set-up). *only required for the 5 mW laser!

Tasks:Investigation of the Fourier trans-form by a convex lens for differentdiffraction objects in a 2 f set-up.

Optical base plate w. rubber ft. 08700.00 1

He/Ne Laser, 5 mW with holder* 08701.00 1

Power supply f. laser head 5 mW* 08702.93 1





Lens, mounted, f = +150 mm 08022.01 1

Lens, mounted, f = +100 mm 08021.01 1

Lensholder f. optical base plate 08723.00 2

Screen, white, 150�150 mm 09826.00 1



Qbjective 25� N.A. 0.45 62470.00 1




Pin hole 30 µm 08743.00 1

Rule, plastic, l = 200 mm 09937.01 1

*Alternative to laser 5 mW, power supply and shutter:

Laser, He-Ne 0.2/1.0 mW, 220 VAC 08180.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFourier optics– 2f Arrangement P2261100


� Fourier transform� Lenses� Fraunhofer diffraction� Index of refraction� Huygens’ principle

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:57 Uhr Seite 113


Principle:The electric field distribution of lightin a specific plane (object plane) isFourier transformed into the 4fconfiguration by 2 lenses and opti-cally filtered with appropriate dia-phragms.

Tasks:1. Optical filtration of diffraction

objects in 4f set-up.

2. Reconstruction of a filtered image.


� Fourier transform� Lenses� Fraunhofer diffraction� Index of refraction� Huygens’ principle� Debye-Sears-effect

Optical base plate with rubber feet 08700.00 1







Lens, mounted, f = +100 mm 08021.01 3

Lensholder f. optical base plate 08723.00

Screen, white, 150�150 mm 09826.00 1

Slide -Emperor Maximilian- 82140.00 1

Screen, with arrow slit 08133.01 1



Diaphragms, d = 1, 2, 3, 5 mm 09815.00 1




Achromatic objective 20� N.A. 0.45 62174.20 1


Pin hole 30 micron 08743.00 1

Ruler, plastic, 200 mm 09937.01 1


Glass cell, 150�55�100 mm 03504.00 1

Table with stem 09824.00 2

Support rod,stainl.steel, 250 mm 02031.00 1

Bosshead 02043.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedFourier optics – 4f Arrangement –Filtering and reconstruction P2261200



Principle of the set-up for coherent optical filtration.


Laser, He/Ne 0.2/1.0 mW, 220 V AC 08701.00 1

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:57 Uhr Seite 114

Handbooks Optics



Advanced Optics and Laser Physics

Laser Physics I – Experiments with coherent light 01179.02

16 described ExperimentsPlease ask for a complete equipmentlist Ref. No. 227021 Diffraction of lightLP 1.1 (12166)Diffraction of light through a slit and atan edge.LP 1.2 (12167)Diffraction through a slit andHeisenberg’s uncertainty principle.LP 1.3 (12168)Diffraction of light through a double slitor by a grid. LP 1.4 (12169)Diffraction of light through a slit andstripes, Babinet’s theorem

2 Interference of lightLP 2.1 (12170)Fresnel mirror and biprismLP 2.2 (12171)Michelson interferometerLP 2.3 (12172)Newton’s rings

3 Polarisation of lightLP 3.1 (12173)Fresnel’s law, theory of reflectionLP 3.2 (12174)Polarisation through λ/4 platesLP 3.3 (12175)Half shadow polarimeter, rotation of pola-risation through an optically active mediumLP 3.3 (12176)Kerr effectLP 3.5 (12177)Faraday effect

4 Refraction of lightLP 4.1 (12178)Index of refraction n of a flint glass prismLP 4.2 (12179)Determination of the index of refractionof air with Michelson’s interferometerLP 4.3 (12180)Determination of the index of refractionof CO2 with Michelson’s interferometer

5 Law of radiationLP 5.1 (12181)Lambert’s law of radiation

Laser Physics IIHolography 01400.02

11 described ExperimentsPlease ask for a complete equipmentlist Ref. No. 22703LH 1 (12900)Fresnel zone plate

LH 2 (12901)White light hologram

LH 3 (12902)White light hologram with expansion system

LH 4 (12903)Transmission hologram

LH 5 (12904)Transmission hologram with expansion system

LH 6 (12905)Transfer hologram from a master hologram.

LH 7 (12906)Double exposure procedure

LH 8 12907)Time-averaging procedure I (with tuning fork).

LH 9 (12908)Time-averaging procedure II (with loudspeaker).

LH 10 12909)Real time procedure I (bending of a plate).

LH 11 (12910)Real time procedure II (oscillating plate).

Laser Physics IIIInterferometry 01401.02

18 described ExperimentsPlease ask for a complete equipmentlist Ref. No. 22704LI 1 (13066)Michelson interferometerLI 2 (13067)Michelson interferometer – high resolutionLI 3 (13068)Mach - Zehnder interferometerLI 4 (13069)Sagnac interferometerLI 5 (13070)Doppler-Effect with Michelson interferom.LI 6 (13071)Magnetostriction with Michelson interferometerLI 7 (13072)Thermal expansion of solids with Michelson interferometerLI 8 (13073)Refraction index of CO2-gas withMichelson interferometerLI 9 (13074)Refraction index of air with Michelson interferometerLI 10 (13075)Refraction index of air with Mach-Zehnder interferometerLI 11 (13076)Refraction index of of CO2-gas withMach-Zehnder interferometerLI 12 (13077)Fabry - Perot interferometer – determi-nation of the wavelength of laserlightLI 13 (13078)Fabry - Perot interferometer – optical resonator modesLI 14 (22611)Fourier optics –2 f arrangementLI 15 (22612)Fourier optics – 4 f arrangement, filteringand reconstructionLI 16 (13079)Optical determination of the velocity ofultrasound in liquids – phasemodulationof laserlight by ultrasonic wavesLI 17 (13080)LDA – Laser Doppler AnemometryLI 18 (13081)Twyman-Green interferometer

Advanced Opticsand Laser Physics 00117.02

23 described ExperimentsPlease ask for a complete equipmentlist Ref. No. 22614Laser PhysicsLEP (P2260700)Helium Neon LaserLEP (P2260400)CO2-laserLEP (P2260900)Nd-YAG-laser

Advanced OpticsLP 1.3 (P1216800)Diffraction of light through a double slit or by a gridLP 1.4 (P1216900)Diffraction of light through a slit and stripes, Babinet’s theoremLP 2.2 (P1217100)Michelson interferometerLP 2.3 (P1217200)Newton’s ringsLP 2.3 (P1217400)Polarisation through �/4 platesLP 3.4 (P1217600)Kerr effectLP 3.5 (P1217700)Faraday effectLP 4.3 (P1218000)Determination of the index of refractionof CO2 with Michelson’s interferometerLH 3 (P1290200)White light hologram with expansionsystemLH 5 (P1290400)Transmission hologram with expansionsystemLH 6 (P1290500)Transfer hologram from a master hologramLH 10 (P1290900)Real time procedure I (bending of a plate)LI 3 (P1306700)Michelson interferometer – High ResolutionLI 5 (P1307000)Doppler effect with the MichelsoninterferometerLI 6 (P1307100)Magnetostriction with the MichelsoninterferometerLI 10 (P1307500)Determination of the refraction index ofair with the Mach-Zehnder interfero-meter

LI 12 (P1307700)Fabry-Perot interferometer – Determina-tion of the laser light’s wavelengthLI 13 (P1307800)Fabry-Perot interferometer – optical resonator modes

LI 15 (P2261200)Fourier optics – optical filtration – 4f ArrangementLI 17 (P1308000)LDA – Laser Doppler Anemometry

For free

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:57 Uhr Seite 115


Optics Handbooks

1 Propagation of light

OT 1.1 (11000)Rectilinear propagation of lightOT 1.2 (11001)Shadow formation by a point light sour-ceOT 1.3 (11002)Umbra and penumbra with two pointlight sourcesOT 1.4 (11003)Umbra and penumbra with an extensivelight sourceOT 1.5 (11004)Length of shadowsOT 1.6 (11005)Solar and lunar eclipses with a pointlight sourceOT 1.7 (11006)Solar and lunar eclipses with anextensive light source

2 Mirrors

OT 2.1 (11007)Reflection of lightOT 2.2 (11008)The law of reflectionOT 2.3 (11009)Formation of an image point by a planemirrorOT 2.4 (11010)Image formation by a plane mirrorOT 2.5 (11011)Applications of reflection by plane mir-rorsOT 2.6 (11012)Reflection of light by a concave mirrorOT 2.7 (11013)Properties of a concave mirrorOT 2.8 (11014)Real images with a concave mirrorOT 2.9 (11015)Law of imagery and magnification of aconcave mirrorOT 2.10 (11016)Virtual images with a concave mirrorOT 2.11 (11017)Aberrations with a concave mirrorOT 2.12 (11018)Reflection of light by a convex mirror

OT 2.13 (11019)Properties of a convex mirrorOT 2.14 (11020)Image formation by a convex mirrorOT 2.15 (11021)Law of imagery and magnification of aconvex mirrorOT 2.16 (11022)Reflection of light by a parabolic mirror

3 Refraction

OT 3.1 (11023)Refraction at the air-glass boundaryOT 3.2 (11024)Refraction at the air-water boundaryOT 3.3 (11025)The law of refractionOT 3.4 (11026)Total reflection at the glass-air boundaryOT 3.5 (11027)Total reflection at the water-airboundaryOT 3.6 (11028)Passage of light through a planoparallelglass plateOT 3.7 (11029)Refraction by a prismOT 3.8 (11030)Light path through a reversing prismOT 3.9 (11031)Light path through a deflection prismOT 3.10 (11032)Light transmission by total reflection

4 Lenses

OT 4.1 (11033)Refraction of light by a convergent lensOT 4.2 (11034)Properties of a convergent lensOT 4.3 (11035)Real images with a convergent lensOT 4.4 (11036)Law of imagery and magnification of aconvergent lensOT 4.5 (11037)Virtual images with a convergent lensOT 4.6 (11038)Refraction of light at a divergent lensOT 4.7 (11039)Properties of a divergent lens

OT 4.8 (11040)Image formation by a divergent lensOT 4.9 (11041)Law of imagery and magnification of adivergent lensOT 4.10 (11042)Lens combination consisting of two convergent lensesOT 4.11 (11043)Lens combination consisting of aconvergent and a divergent lensOT 4.12 (11044)Spherical aberrationOT 4.13 (11045)Chromatic aberration

5 Colours

OT 5.1 (11046)Colour dispersion with a prismOT 5.2 (11047)Non-dispersivity of spectral coloursOT 5.3 (11048)Reunification of spectral coloursOT 5.4 (11049)Complementary colours

OT 5.5 (11050)Additive colour mixingOT 5.6 (11051)Subtractive colour mixing

6 The human eye

OT 6.1 (11052)Structure and function of the human eyeOT 6.2 (11053)Short-sightedness and its correctionOT 6.3 (11054)Long-sightedness and its correction

7 Optical equipment

OT 7.1 (11055)The magnifying glassOT 7.1 (11056)The cameraOT 7.3 (11057)The astronomical telescopeOT 7.4 (11058)The Newtonian reflecting telescopeOT 7.5 (11059)Herschel’s reflecting telescope


Magnet Board Optics

0115

1.02

Georg Schollmeyer

Geometrical optics and theory of colours on the magnetic boardThe demonstration system presents the following advantages:

● simple handling and minimum preparation time through components with magnets

● clear length of beams through 50 W halogen lamp with magnet and large model objects

● clear and dust proof storage of all components in the device shapedwooden tray

● detailed description of experiments with figures.60 experiments covering light propagation (7), mirror (16), diffraction (10), lenses (13),colours (6), eye (3), optical instruments (5)


Physics Demonstration Experiments – Magnet Board Optics • No. 01151.02 • 60 described ExperimentsPlease ask for a complete equipment list Ref. No. 22701

Light guide

LEP 2.1.00-01_2.6.12-00 12.10.2003 13:57 Uhr Seite 116

3Thermodynamics

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:32 Uhr Seite 117


Contents

3.1 Thermal Expansion

3.1.01-00 Thermal expansion in solids and liquids

3.2 Ideal and Real Gases


3.2.02-01 Heat capacity of gases


3.2.03-00 Maxwellian velocity distribution


3.2.05-00 Adiabatic coefficient of gases – Flammersfeld oscillator

3.2.06.00 Joule-Thomson effect

3.3 Calorimetry, Friction Heat

3.3.01-01 Heat capacity of metals


3.3.02-00 Mechanical equivalent of heat

Thermodynamics

3.4 Phase Transitions


3.4.02-00 Vapour pressure of water below 100°C Molar heat of vaporization


3.4.04-00 Freezing point depression

3.5 Transport and Diffusion


3.5.02-00 Thermal and electrical conductivity of metals

3.6 Applied Thermodynamics


3.6.02-00 Heat pump

3.603-00 Heat insulation / Heat conduction

3.6.04-00 Stirling engine

3.7 Handbooks

Glas jacket system

Air Cushion Table

Demonstration Experiments Physics – Magnetic Board Heat

3LEP 3.1.01-00_3.6.04-00 12.10.2003 10:32 Uhr Seite 118


Thermal expansion in solids and liquids 3.1.01-00

Thermal Expansion Thermodynamics

Principle:The volume expansion of liquids andthe linear expansion of various ma-terials is determined as a function oftemperature.

Tasks:1. To determine the volume expan-

sion of ethyl acetate (C4H8O2),methylated spirit, olive oil, glyceroland water as a function of temper-ature, using the pycnometer.

2. To determine the linear expansionof brass, iron, copper, aluminium,

Relationship between length l and temperature �, for a) aluminium, b) brass,c) copper, d) steel, e) duran glass, f) quartz glass (lo = 600 mm)

duran glass and quartz glass as afunction of temperature using adilatometer.

3. To investigate the relationship be-tween change in length and over-all length in the case of alumini-um.


� Linear expansion� Volume expansion of liquids� Thermal capacity� Lattice potential� Equilibrium spacing� Grüneisen equation

Dilatometer with clock gauge 04233.00 1

Copper tube for 04231.01 04231.05 1

Aluminium tube for 04231.01 04231.06 1

Tube, quartz for 04231.01 04231.07 1


Cooling coil f. A100 46994.01 1



Lab thermometer, -10…+100°C 38056.00 1


Syringe 1ml, Luer, 10 pcs 02593.03 1

Cannula 0.6�60 mm, Luer, 20 pcs 02599.04 1

Measuring tube, l = 300 mm, NS19/26 03024.00 2


Flask, flat bottom, 50 ml, IGJ 19/26 35810.01 2


Ethyl acetate, 250 ml 30075.25 1

Glycerol, 250 ml 30084.25 1

Olive oil, pure, 100 ml 30177.10 1

Laboratory balance w. RS 232, 310 g 45025.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedThermal expansion in solids and liquids P2310100

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:32 Uhr Seite 119



Principle:The state of a gas is determined byits temperature, its pressure and theamount of substance. For the limit-ing case of an ideal gas these statevariables are linked by the generalequation of state, from which specialcorrelations can be derived for spe-cific changes of state.

Tasks:For a constant amount of gas (air)investigate the correlation of

1. Volume and pressure at constanttemperature (Boyle and Mariotte’slaw)

2. Volume and temperature at con-stant pressure (Gay-Lussac’s law)

3. Pressue and temperature at con-stant volume (Charles’ (Amontons’law)

Correlation between pressure p and volume V for a constant quantity of air(n = 0.9536 mmol) during an isothermic change of state (T = 298.15 K).

From the relationships obtained cal-culate the universal gas constant aswell as the coefficient of thermal ex-pansion, the coefficient of thermaltension, and the coefficient of cubiccompressibility.

Gas laws apparatus 04362.00 1




Digital barometer 03099.00 1


Mercury tray 02085.00 1


Support rod, stainl. steel, l = 1000 mm 02034.00 1



Pinchcock, width 15 mm 43631.15 1

Hose clip, d = 8-12 mm 40996.01 6


Mercury, filtered, 1000 g 31776.70 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedEquation of state of ideal gases P2320100

Thermodynamics Ideal and Real Gases


� Pressure and temperature� Volume� Coefficient of thermal

expansion� Coefficient of thermal

tension� Coefficient of cubic

compressibility� General equation of state for

ideal gases� Universal gas constant� Boyle and Mariotte’s law� Gay-Lussac’s law� Charles’ (Amontons’) law

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:32 Uhr Seite 120


Heat capacity of gases 3.2.02-01

Ideal and Real Gases Thermodynamics

Principle:Heat is added to a gas in a glass ves-sel by an electric heater which isswitched on briefly. The temperatureincrease results in a pressureincrease, which is measured with amanometer. Under isobaric condi-tions a temperature increase resultsin a volume dilatation, which can beread from a gas syringe. The molarheat capacities CV and Cp are calcu-lated from the pressure or volumechange.

Pressure change �p as a function of the heat-up time �t. U = 4.59 V, I = 0.43 A

Tasks:Determine the molar heat capacitiesof air at constant volume CV and atconstant pressure Cp.


� Equation of state for idealgases

� 1st law of thermodynamics� Universal gas constant� Degree of freedom� Mole volumes� Isobars� Isotherms� Isochors and adiabatic

changes of slate


Barometer/Manometer, hand-held 07136.00 1



Aspirator bottle, clear glas 10000 ml 02629.00 1

Gas syringe, 100 ml 02614.00 2

Stopcock, 1-way, straight, glass 36705.00 1

Stopcock, 3-way, t-sh., capil., glass 36732.00 1

Rubber stopper, d = 32/26 mm, 3 holes 39258.14 1

Rubber stopper, d = 59,5/50,5 mm, 1 hole 39268.01 1

Rubber tubing, d = 7 mm 39282.00 2

Nickel electrode, d = 3 mm, w. socket 45231.00 2

Nickel electrode 76340 mm 45218.00 1

Chrome-nickel wire, d = 0.1 mm, 100 m 06109.00 1

Scissors, straight, l = 140 mm 64625.00 1

Push-button switch 06039.00 1

Connection box 06030.23 1

PEK carbon resistor 1 W 5% 1 kOhm 39104.19 1

PEK electrol.capacitor 2 mmF/ 250 V 39105.29 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat capacity of gases P2320201

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:32 Uhr Seite 121



Principle:Heat is added to a gas in a glass ves-sel by an electric heater which isswitched on briefly. The temperatureincrease results in a pressureincrease, which is measured with amanometer. Under isobaric condi-tions a temperature increase resultsin a volume dilatation, which can beread from a gas syringe. The molarheat capacities CV and Cp are calcu-lated from the pressure or volumechange.

Volume change �V as a function of the heat-up time �t. U = 4.59 V, I = 0.43 A.

Tasks:Determine the molar heat capacitiesof air at constant volume CV and atconstant pressure Cp.


Barometer/Manometer, hand-held 07136.00 1


Cobra3 Power supply unit 12151.99 1

Cobra3 Universal writer software 14504.61 1

RS 232 data cable 14602.00 1

Aspirator bottle, clear glas 10000 ml 02629.00 1


Rubber stopper, d = 59.5/50.5 mm, 1 hole 39268.01 1

Gas syringe, 100 ml 02614.00 2



Rubber tubing, d = 7 mm 39282.00 2

Nickel electrode, d = 3 mm, w. socket 45231.00 2

Nickel electrode 76340 mm 45218.00 1

Chrome-nickel wire, d = 0.1 mm, 100 m 06109.00 1

Scissors, straight, l = 140 mm 64625.00 1

Push-button switch 06039.00 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat capacity of gases with Cobra3 P2320211



� Equation of state for idealgases

� 1st law of thermodynamics� Universal gas constant

Degree of freedom� Mole volumes� Isobars� Isotherms� Isochors and adiabatic

changes of slate

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:32 Uhr Seite 122


Maxwellian velocity distribution 3.2.03-00


Principle:By means of the model apparatus forkinetic theory of gases the motion ofgas molecules is simulated and thevelocity is determined by registrationof the throw distance of the glassballs. This velocity distribution iscompared to the theoretical MAX-WELL-BOLTZMANN equation.

Experimental and theoretical velocity distribution in the model experiment.

Tasks:1. Measure the velocity distribution

of the “model gas”.

2. Compare the result to theoreticalbehaviour as described by theMAXWELL-BOLTZMANN distribu-tion.

3. Discuss the results.


� Kinetic theory of gases� Temperature� Gas� Molecules� Model kinetic energy� Average velocity� Velocity distribution

Kinetic gas theory apparatus 09060.00 1

Receiver with recording chamber 09061.00 1







Test tube, d = 16 mm, l = 16 cm, 100 pcs 37656.10 1

Test tube rack f. 12 tubes, wood 37686.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMaxwellian velocity distribution P2320300

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:32 Uhr Seite 123



Principle:A substance which is gaseous undernormal conditions is enclosed in avariable volume and the variation ofpressure with the volume is recordedat different temperatures. The criti-cal point is determined graphicallyfrom a plot of the isotherms.

p-V-isotherms of ethane.

Tasks:1. Measure a number of p-V-iso-

therms of ethane.

2. Determine the critical point andthe critical quantities of ethane.

3. Calculate the constants of theVan der WAALS equation, theBOYLE-temperature, the radius ofthe molecules and the parametersof the interaction potential.

Critical point apparatus 04364.10 1




Jointing f. GL18, 8 mm hole, 10 pcs 41240.03 1

Vacuum pump, one stage 02750.93 1

Adapter for vacuum pump 02657.00 1

Security bottle 500 ml, 2� GL18/8 34170.88 1


Support rod, stainl.steel, l = 500 mm 02032.00 1

Thermometer, -10...+ 50 °C 38033.00 1

Glass tubes, right angle 36701.57 1




Rubber tubing, vacuum, i.d. 8 mm 39288.00 1



Hose clip, diam. 8-12 mm 40996.01 2

Hose clip f. 12-20 diameter tube 40995.00 2

Mercury tray 02085.00 1

Compressed gas, ethane, 14 g 41772.09 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedThermal equation of state and critical point P2320400



� Ideal gas� Real gas� Equation of state� Van der WAALS equation� BOYLE temperature� Critical point� Interaction potential� Molecule radius

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:32 Uhr Seite 124


Adiabatic coefficient of gases – Flammersfeld oscillator 3.2.05-00


Principle:A mass oscillates on a volume of gasin a precision glass tube. The oscilla-tion is maintained by leading escap-ing gas back into the system. Theadiabatic coefficient of various gasesis determined from the periodic timeof the oscillation.

Tasks:

Determine the adiabatic coefficient� of air nitrogen and carbon dioxide(and also of argon, if available) fromthe periodic time of the oscillation Tof the mass m on the volume V ofgas


� Equation of adiabatic changeof slate

� Polytropic equation� Rüchardt’s experiment� Thermal capacity of gases

Gas oscillator, Flammersfeld 04368.00 1

Graduated cylinder 1000 ml 36632.00 1

Aspirator bottle, clear gl. 1000 ml 34175.00 1

Air control valve 37003.00 1



Micrometer 03012.00 1

Glass tubes, right-angled, 10 36701.52 1

Hose connector, straight, PP 47515.00 1





Slinding weight balance, 101 g 44012.01 1

Aquarium pump, 220 V AC 64565.93 1

Aneroid barometer 03097.00 1







Reducing valve f. nitrogen 33483.00 1


Steel cylinder, nitrogen, 10 l, full 41763.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedAdiabatic coefficient of gases –Flammersfeld oscillator P2320500

Ten measurements, each of about n = 300 oscillations, gave for theadiabatic coefficients

Argon � = 1.62 ± 0.09

Nitrogen � = 1.39 ± 0.07

Carbon dioxide � = 1.28 ± 0.08

Air � = 1.38 ± 0.08

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:32 Uhr Seite 125


3.2.06.00 Joule-Thomson effect

Principle:A stream of gas is fed to a throttlingpoint, where the gas (CO2 or N2) un-dergoes adiabatic expansion. The dif-ferences in temperature establishedbetween the two sides of the throt-tle point are measured at variouspressures and the Joule-Thomsoncoefficients of the gases in questionare calculated.

Temperature differences measured at various ram pressures.

Tasks:1. Determination of the Joule-Thom-

son coefficient of CO2.

2. Determination of the Joule-Thom-son coefficient of N2.

Joule-Thomson apparatus 04361.00 1

Temperature meter digital, 4-2 13617.93 1

Temperature probe, immers.type 11759.01 2


Hose clip f. 12-20 diameter tube 40995.00 2


Reducing valve f. nitrogen 33483.00 1

Wrench for steel cylinders 40322.00 1

Steel cylinder rack, mobile 54042.00 1


Steel cylinder, nitrogen, 10 l, full 41763.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedJoule-Thomson effect P2320600



� Real gas� Intrinsic energy� Gay-Lussac theory� Throttling� Van der Waals equation� Van der Waals force� Inverse Joule-Thomson effect� Inversion temperature

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 126


Heat capacity of metals 3.3.01-01

Calorimetry, Friction Heat Thermodynamics

Principle:Heated specimens are placed in acalorimeter filled with water at lowtemperature. The heat capacity ofthe specimen is determined from therise in the temperature of the water.

Temperature as a function of time in the method of mixtures experiment a) steel, b) brass, c) aluminium.

Tasks:1. To determine the heat capacity of

the calorimeter by filling it withhot water and determining therise in temperature.


� Mixture temperature� Boiling point� Dulong Petit’s law� Lattice vibration� Internal energy� Debye temperature

Calorimeter, 500 ml 04401.00 1

Metal bodies, set of 3 04406.00 4

Aluminium pot, 3000 ml 05934.00 1

Butane burner, Labogaz 206 type 32178.00 1

Butane cartridge 47535.00 1

Aneroid barometer 03097.00 1


Thermometer, -10...+ 50 °C 38033.00 1


Fish line, l = 100 m 02090.00 1

Triangle w. pipeclay, l = 60 mm 33278.00 1

Tripod, ring dia. 140 mm, h = 240 mm 33302.00 1



Glass beads, d = 6 mm, 850 pcs. 36756.25 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat capacity of metals P2330101

2. To determine the specific heatcapacity of aluminium, iron andbrass.

3. To verify Dulong Petit’s law withthe results of these experiments.

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 127


Thermodynamics Calorimetry, Friction Heat


Principle:Heated specimens are placed in acalorimeter filled with water at lowtemperature. The heat capacity ofthe specimen is determined from therise in the temperature of the water.

Course of temperature in the calorimeter.For 180 g Iron (100 °C) and 200 g water (room-temperature).

Tasks:1. To determine the specific heat

capacity of aluminium, iron andbrass.

2. To verify Dulong Petit’s law withthe results of these experiments.

Cobra3-Basic Unit 12150.00 1

Power Supply, 12 V- 12151.99 1

RS232-Data Cable 14602.00 1

Software Cobra3 Temperature 14503.61 1

Measurement Module Temperature NiCr-Ni 12104.00 1

Immersion Probe NiCr-Ni 13615.03 1

H-base “Pass” 02009.55 1

Support Rod, Stainless Steel 18/8, 600 mm 02037.00 2

Bosshead 02043.00 2


Support ring, with clamp 37704.01 1

Wire gauz with ceramic 33287.01 1

Metal bodies, set of 3 04406.00 3

Calorimeter vessel, 500 ml 04401.10 1



Agitator rod 04404.10 1

Pipette, with rubber bulb 64701.00 1

Portable balance Mod. CS200 46001.93 1


Butane cartridge, C206 47535.00 1

Beads, 200 g 36937.20 1

Fish line, 100 m 02090.00 1


Paper tissues

What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat capacity of metals with Cobra3 P2330111


� Mixture temperature� Boiling point� Dulong Petit’s law� Lattice vibration� Internal energy� Debye temperature

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 128


Mechanical equivalent of heat 3.3.02-00

Calorimetry, Friction Heat Thermodynamics

�T

A1

A2

T2

28

27

26

25

24

T°C

X

XXX X

XXXX

X

120 240 360 480 600 7200

XX

X

X

X X X X X X X X XT1

ts

Principle:In this experiment, a metal test bodyis rotated and heated by the frictiondue to a tensed band of syntheticmaterial. The mechanical equivalentof heat for problem 1 is determinedfrom the defined mechanical workand from the thermal energyincrease deduced from the increaseof temperature. Assuming the equiv-alence of mechanical work and heat,the specific thermal capacity of alu-minum and brass is determined.

Temperature-time diagram for a measurement example.

Tasks:1. Determination of the mechanical

equivalent of heat.

2. Determination of the specificthermal capacity of aluminum andbrass.


� Mechanical equivalent of heat� Mechanical work� Thermal energy� Thermal capacity� First law of thermodynamics� Specific thermal capacity

Mechanical equiv. of heat app. 04440.00 1

Friction cylinder CuZn, m = 1.28 kg 04441.02 1

Friction cylinder Al, m 0.39 kg 04441.03 1

Support rod -PASS-, square, l =250 mm 02025.55 1





Thermometer -10...+30°C 05949.00 1



Commercial weight, 1000 g 44096.70 1

Commercial weight, 5000 g 44096.81 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMechanical equivalent of heat P2330200

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 129



Principle:Water is heated in a closed pressurechamber; as much water vaporises asto make the pressure in the chambercorrespond to the vapour pressure atthe temperature at any time. Theheat of vaporisation is determined atvarious temperatures from the meas-urement of vapour pressure as afunction of temperature.

Natural logarithm of vapour pressure p as a function of the reciprocal of thetemperature (1/T): Tb = boiling point at normal pressure.

Tasks:1. To measure the vapour pressure of

water as a function of tempera-ture.

2. To calculate the heat of vaporisa-tion at various temperatures fromthe values measured.

3. To determine boiling point at nor-mal pressure by extrapolation.

High pressure vapour unit 02622.10 1

Heat conductive paste, 50 g 03747.00 1

Heating apparatus 32246.93 1

Pipette, with rubber bulb, long 64821.00 1


Bosshead 02043.00 1

Support rod, stainl. steel, 250 mm 02031.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedVapour pressure of water at hightemperature P2340100

Thermodynamics Phase Transitions


� Boiling point� Heat of vaporisation� Clausius-Clapeyron equation� Van’t Hoff law� Carnot cycle

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 130


Phase Transitions Thermodynamics

Vapour pressure of water below 100°C Molar heat of vaporization 3.4.02-00

Principle:The vapour pressure of water in therange of 40°C to 85°C is investigat-ed. It is shown that the Clausius-Clapeyron equation describes the re-lation between temperature andpressure in an adequate manner. Anaverage value for the heat of vapor-ization of water is determined.

Tasks:1. About 250 ml of de-mineralized

water are allowed to boil forabout 10 minutes to eliminate alltraces of dissolved gas. The wateris then cooled down to room tem-perature.

2. The 3-neck round flask is filledabout three-quarters full with

Semilogarithmic representation of vapour pressure p as a function of 1/T.

gas-free water and heated. At 35°Cthe space above the water within theround flask is evacuated. Furtherheating causes an increase in pressure p and temperature t ofwater within the round flask. p and tare read in steps of 5 °C up to a max-imum of t = 85°C.

Manometer 0-1.6 bar 03105.00 1

Students thermometer, -10...+110°C 38005.02 2

Round flask, 100 ml, 3-n., GL25/2�GL1 35677.15 1

Stopcock, 1-way, r.-angled, glass 36705.01 1

Vacuum pump, one stage 02750.93 1

Magnetic stirrer w. heat., 230 V 35684.93 1

Magn.stirring bar 30 mm, cyl. 46299.02 2

Glass tube 200 mm ext. d = 8 mm 64807.00 1






Support rod, l = 500 mm/M10 thread 02022.05 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedVapour pressure of water below 100°C Molar heat of vaporization P2340200


� Pressure� Temperature� Volume� Vaporization� Vapour pressure� Clausius-Clapeyron equation

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 131


Principle:The boiling point of a solution isalways higher than that of the puresolvent. The dependence of the tem-perature difference (elevated boilingpoint) on the concentration of thesolute can be determined using asuitable apparatus.

Example of a measurement: boiling point increase as function of concentra-tion of table salt in an aqueous solution.

Tasks:1. Measure the increase in boiling

point of water as a function of theconcentration of table salt, ureaand hydroquinone.

2. Investigate the relationshipbetween the increase in boilingpoint and the number of particles.

3. Determine the molar mass of thesolute from the relationshipbetween the increase in boilingpoint and the concentration.


� Raoult’s law� Henry’s law� Ebullioscopic constants� Chemical potential� Gibbs-Helmholtz equation� Concentration ratio� Degree of dissociation

Appar. for elev. of boiling point 36820.00 1Heat. mantle f. round bott.fl. 250 ml 47550.93 1Clamp for heating mantle 47557.01 1Power regulator 32247.93 1Laboratory balance, data outp. 620 g 45023.93 1Weighing dishes, 85�85�7 mm, 100 45019.01 1Temperature meter, digital, 4-2 13617.93 1Temperature probe, immers.type 11759.01 1Protective sleeves f. temp. probe, 2 11762.05 1Retort stand, h = 750 mm 37694.00 1Right angle clamp 37697.00 3Universal clamp 37715.00 3Flask, round, 1-neck, 250 ml, GL25/13 35812.15 1Glass beaker, tall, 250 ml 36004.00 1Jointing f. GL25, 8 mm hole, 10 pcs 41242.03 1Silicone tubing i.d. 7 mm 39296.00 1Mortar w. pestle, 150 ml, porcelain 32604.00 3Pinchcock, width 15 mm 43631.15 1Microspoon, special steel 33393.00 1Wash bottle, plastic, 500 ml 33931.00 1Pellet press for calorimeter 04403.04 1Funnel, glass, top dia. 80 mm 34459.00 1Pasteur pipettes, 250 pcs 36590.00 1Rubber caps, 10 pcs 39275.03 1Beads, 200 g 36937.20 1Sodium chloride, 500 g 30155.50 1Urea, 250 g 30086.25 1Hydroquinone, 250 g 30089.25 1Glycerol, 250 ml 30084.25 1Water, distilled, 5 l 31246.81 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedBoiling point elevation P2340300


Thermodynamics Phase Transitions

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 132


Phase Transitions Thermodynamics

Freezing point depression 3.4.04-00

Principle:The freezing point of a solution islower than that of the pure solvent.The depression of the freezing pointcan be determined experimentallyusing a suitable apparatus (cryosco-py). If the cryoscopic constants ofthe solvent are known, the molecularmass of the dissolved substances canbe determined.

Cooling curve of water/table salt (NaCI) mixture.

Tasks:1. Determine the size of freezing

point depression after dissolving astrong electrolyte (NaCI) in water.By comparing the experimentalvalue with the theoretical onepredicted for this concentration,determine the number of ions intowhich the electrolyte dissociates.

2. Determine the apparent molarmass of a non-electrolyte (hydro-quinone) from the value of freez-ing point depression.

App. for freezing point depr. 36821.00 1


Temperature meter digital, 4-2 13617.93 1

Temperature probe, immers. type 11759.01 2

Protective sleeves f. temp.probe, 2 11762.05 1

Pellet press for calorimeter 04403.04 1

Magn. stirrer, mini, controlable 35712.93 1




Volumetric pipette, 50 ml 36581.00 1

Pipettor 36592.00 1

Retort stand, h = 1000 mm 37695.00 1


Magn.stirring bar 15 mm, cyl. 46299.01 1

Balance SBA42, 120 g/1 mg, ext. Cal. 46034.93 1


Mortar w. pestle, 70 ml, porcelain 32603.00 2

Microspoon, special steel 33393.00 1

Spoon, special steel 33398.00 1

Funnel, plastic, dia. 50 mm 36890.00 1

Weighing dishes, 85�85�7 mm, 100 45019.01 1

Pasteur pipettes, 250 pcs 36590.00 1

Rubber caps, 10 pcs 39275.03 1



Hydroquinone, 250 g 30089.25 1

Raw alcohol for burning, 1000 ml 31150.70 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFreezing point depression P2340400


� Raoult’s law� Cryoscopic constants� Chemical potential� Gibbs-Helmholtz equation� Concentration ratio� Degree of dissociation� Van’t Hoff factor� Cryoscopy

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 133


Principle:According of Stefan-Boltzmann’slaw, the energy emitted by a blackbody per unit area and unit time isproportional to the power “four” ofthe absolute temperature of thebody. Stefan-Boltzmann’s law is alsovalid for a so-called “grey” bodywhose surface shows a wavelength-independent absorption-coefficientof less than one. In the experiment,the “grey” body is represented by thefilament of an incandescent lampwhose energy emission is investigat-ed as a function of the temperature.

Thermoelectric e.m. f. of thermopile as a function of the filament’s absolutetemperature.

Tasks:1. To measure the resistance of the

filament of the incandescent lampat room temperature and to ascer-tain the filament’s resistance R0

at zero degrees centrigrade.

2. To measure the energy flux densityof the lamp at different heatingvoltages. The corresponding heat-ing currents read off for eachheating voltage and the corre-sponding filament resistance cal-culated. Anticipating a tempera-ture-dependency of the secondorder of the filament-resistance,the temperature can be calculatedfrom the measured resistances.


� Black body radiation� Thermoelectric e.m. f.� Temperature dependence of

resistances

Thermopile, molltype 08479.00 1

Shielding tube, for 08479.00 08479.01 1


Power supply var.15 VAC/12 VDC/5 A 13530.93 1


Filament lamp 6V/5A, E14 06158.00 3


Resistor in plug-in box 100 � 06057.10 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedStefan-Boltzmann’s law of radiation P2350100


Thermodynamics Transport and Diffusion

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 134


Transport and Diffusion Thermodynamics

Thermal and electrical conductivity of metals 3.5.02-00

Principle:The thermal conductivity of copperand aluminium is determined in aconstant temperature gradient fromthe calorimetrically measured heatflow.

The electrical conductivity of copperand aluminium is determined, andthe Wiedmann-Franz law is tested.

Multitap transf., 14 VAC/12 VDC, 5A 13533.93 1Digital multimeter 07134.00 2Universal measuring amplifier 13626.93 1Connecting cord, l = 500 mm, red 07361.01 4Connecting cord, l = 500 mm, blue 07361.04 4

Diagram: Heat of surroundings overtime.

Tasks:1. Determine the heat capacity of

the calorimeter in a mixtureexperiment as a preliminary test.Measure the calefaction of waterat a temperature of 0 °C in a calo-rimeter due to the action of theambient temperature as a func-tion of time.

2. To begin with, establish a constanttemperature gradient in a metalrod with the use of two heat res-ervoirs (boiling water and icewater) After removing the piecesof ice, measure the calefaction ofthe cold water as a function oftime and determine the thermalconductivity of the metal rod.

3. Determine the electrical conduc-tivity of copper and aluminium byrecording a current-voltage char-acteristic line.

4. Test of the Wiedmann-Franz law.

Calorimeter vessel, 500 ml 04401.10 1Calor. vessel w. heat conduct. conn. 04518.10 1Heat conductivity rod, Cu 04518.11 1Heat conductivity rod, Al 04518.12 1Magn. stirrer, mini, controlable 35712.93 1Heat conductive paste, 50 g 03747.00 1Gauze bag 04408.00 1Rheostat, 10 �, 5.7 A 06110.02 1Immers.heater, 300 W, 220-250 VDC/AC 05947.93 1Temperature meter digital, 4-2 13617.93 1Temperature probe, immers. type 11759.01 1Surface temperature probe PT100 11759.02 2Stopwatch, digital, 1/100 sec. 03071.01 1Tripod base -PASS- 02002.55 1Bench clamp -PASS- 02010.00 1Support rod -PASS-, square, l = 630 mm 02027.55 1Support rod -PASS-, square, l = 1000 mm 02028.55 1Universal clamp 37715.00 4Right angle clamp -PASS- 02040.55 6Supporting block 105�105�57 mm 02073.00 1Glass beaker, short, 400 ml 36014.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedThermal and electrical conductivity of metals P2350200


� Electrical conductivity� Wiedmann-Franz law� Lorenz number� Diffusion� Temperature gradient� Heat transport� Specific heat� Four-point measurement

For the electrical conductivity you need:

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 135


Principle:The solar ray collector is illuminatedwith a halogen lamp of known lightintensity. The heat energy absorbedby the collector can be calculatedfrom the volume flow and the differ-ence in the water temperatures atthe inlet and outlet of the absorber,if the inlet temperature stays almostconstant by releasing energy to areservoir. The efficiency of the col-lector is determined from this. Themeasurement is made with variouscollector arrangements and at vari-ous absorber temperatures.

Tasks:To determine the efficiency of thesolar ray collector under various ex-perimental conditions.

1. Absorption of energy from the en-vironment (20°C) without illumi-nation by sun or halogen lamp,water temperature at the absorberinlet �e ≈ 5°C.

1.1 Absorber with insulation andglass plate (complete collec-tor)

1.2 Absorber alone(energy ceiling)

Water Temperatures and Collector Efficiency under VariousExperimental Conditions, m· = 100 cm3/min, qi = 1 kW/m2, A = 0 · 12 m2.

2. Illumination with halogen lamp.Water temperature qe≈ 20°C.

2.1 Complete collector

2.2 Collector without glass plate

3. Illumination with halogen lamp.Water temperature qe ≈ 50°C.

3.1 Complete collector

3.2 Complete collector, cold jet ofair impinges

3.3 Collector without glass plate

3.4 Collector without glass plate,cold jet of air impinges.


� Absorption� Heat radiation� Greenhouse effect� Convection� Conduction of heat� Collector equations� Efficiency� Energy ceiling

Solar ray collector 06753.00 1

Lab thermometer, -10..+100°C 38056.00 2

Lab thermometer, w. stem, -10..+110°C 38060.00 1

Circulating pump w. flowmeter 06754.01 1

Power supply 0-12 VDC/6 V; 12 VAC 13505.93 1

Heat exchanger 06755.00 1

Solar coll.stand, teaching aid 06757.00 1

Immersion heater, 1000 W, 220-250 V 04020.93 1

Hot-/Cold air blower, 1000 W 47540.93 1

Halogen lamp 1000 W 08125.93 1







Safety gas tubing, DVGW, 1 m 39281.10 3





What you need:

Complete Equipment Set, Manual on CD-ROM includedSolar ray Collector P2360100

136 PHYWE Systeme GmbH & Co. KG · D-37070 Göttingen

Thermodynamics Applied Thermodynamics

No. Glass Light Cold �plate air 0C K %

1.1 +* – – ≈ 5 2.5 15

1.2 –* – – ≈ 5 5.0 29

2.1 + + – ≈ 20 11.0 64

2.2 – + – ≈ 20 12.5 73

3.1 + + – ≈ 50 8.0 47

3.2 – + + ≈ 50 8.0 47

3.3 + + – ≈ 50 6.0 35

3.4 – + + ≈ 50 3.0 17

* This series of measurements without rear insulation

�a – �e�e

Laboratory Experiments Physics

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 136


Applied Thermodynamics Thermodynamics

Heat pump 3.6.02-00

�°C

60

50

40

30

20

10

0

-10

10 20 30 tmin�Vi

�2

�V0

�c0

�1

�ci

Principle:Pressures and temperatures in thecirculation of the heat electricalcompression heat pump are mea-sured as a function of time when it isoperated as a water-water heatpump.

The energy taken up and released iscalculated from the heating andcooling of the two water baths.

When it is operated as an air-waterheat pump, the coefficient of perfor-mance at different vaporiser temper-atures is determined.

Tasks:1. Water heat pump:

To measure pressure and tempera-ture in the circuit and in the waterreservoirs on the condenser sideand the vaporiser side alternately.To calculate energy taken up andreleased, also the volume concen-tration in the circuit and the volu-metric efficiency of the compres-sor.

2. Air-water heat pump:To measure vaporiser temperatureand water bath temperature on

Temperatures at the inlet and outlet of the vaporiser �Vi (�), �Vo (�) andcondenser �Ci (�), �Co (�) as a function of the operating time; continuouscurves: temperature in water reservoirs.

the condenser side under differentoperating conditions on the va-poriser side,

2.1 with stream of cold air

2.2 with stream of hot air

2.3 without blower.

If a power meter is available, theelectric power consumed by thecompressor can be determined withit and the coefficient of performancecalculated.

Heat pump, compressor principle 04370.88 1


Lab thermometer, w. stem, -10…+110°C 38060.00 2









Option

Work and power meter 13715.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat pump P2360200


� Refrigerator� Compressor� Restrictor valve� Cycle� Vaporization� Condensation� Vapour pressure� Vaporisation enthalpy

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 137

3.6.03-00 Heat insulation / Heat conduction

Principle:A model house with replaceable sidewalls is used for determining theheat transition coefficients (k val-ues) of various walls and windowsand for establishing the heat con-ductivities of different materials. Forthis purpose the temperatures on theinside and outside of the walls aremeasured at a constant interior andouter air temperature (in the steadystate).

With a multilayer wall structure thetemperature difference over a layeris proportional to the particular ther-

mal transmission resistance. Thethermal capacity of the wall materi-al affects the wall temperatures dur-ing heating up and temporary expo-sure to solar radiation.

Heat transition resistance 1/k as a function of the wall thickness d.

Tasks:1. Measurement and interpretation

of water temperatures during theheating up and during temporaryexternal illumination of the walls.

2. Determination of the heat con-ductivities of wood and Styropor.

3. Determination of the k values ofordinary glass and insulating glasswindows and of wooden walls ofdifferent thicknesses, and of wallswith wood, Styropor or cavitylayers.


� Heat transition� Heat transfer� Heat conductivity� Thermal radiation� Hothouse effect� Thermal capacity� Temperature amplitude

attenuation

High insulation house 04507.93 1

Thermal regul. f. high insul. house 04506.93 1

Partitions, plastic foam, 5 off 44536.02 1

Lamp socket E27, mains conn. 06751.00 1

Filament lamp, 220 V/120 W, w. refl. 06759.93 1

Temp. meter 2� NiCr-Ni, hand-held 07140.00 2

Thermocouple NiCr-Ni, 500 °C max. 13615.02 4



What you need:

Complete Equipment Set, Manual on CD-ROM includedHeat insulation / Heat conduction P2360300


Thermodynamics Applied Thermodynamics

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 138


Stirling engine 3.6.04-00

Principle:The Stirling engine is submitted to aload by means of an adjustabletorque meter, or by a coupled gener-ator. Rotation frequency and tem-perature changes of the Stirlingengine are observed. Effectivemechanical energy and power, aswell as effective electrical power, areassessed as a function of rotationfrequency. The amount of energyconverted to work per cycle can be

determined with the assistance ofthe pV diagram. The efficiency of theStirling engine can be estimated.

Tasks:1. Determination of the burner’s

thermal efficiency

2. Calibration of the sensor unit

3. Calculation of the total energyproduced by the engine throughdetermination of the cycle area onthe oscilloscope screen, usingtransparent paper and coordinatepaper.

Mechanical and electric power as a function of rotation frequency.

4. Assessment of the mechanicalwork per revolution, and calcula-tion of the mechanical power out-put as a function of the rotationfrequency, with the assistance ofthe torque meter.

5. Assessment of the electric poweroutput as a function of the rota-tion frequency.

6. Efficiency assessment.


� First and second law of thermodynamics

� Reversible cycles� Isochoric and isothermal

changes� Gas jaws� Efficiency� Stirling engine� Conversion of heat� Thermal pump

Stirling engine, transparent 04372.00 1

Motor/generator unit 04372.01 1

Torque meter 04372.02 1

Chimney for stirling engine 04372.04 1

Meter f. stirling engine, pVnT 04371.97 1

Sensor unit pVn for stirl.eng. 04371.00 1

Syringe 20ml, Luer, 10 pcs 02591.03 1

Rheostat, 330 Ohm , 1.0 A 06116.02 1






Thermocouple NiCr-Ni, sheathed 13615.01 2

Graduated cylinder, 50 ml, plastic 36628.01 1

Raw alcohol for burning, 1000 ml 31150.70 1

Optional accessories for solar motor work

Accessories f. solar motor work 04372.03 1


Extension coupling, hinged 02045.00 1

Support rod, stainl. steel, l = 500 mm 02032.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedStirling engine P2360400

Applied Thermodynamics Thermodynamics

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:33 Uhr Seite 139


Thermodynamics Handbooks

GL 1 (12229)Gay-Lussac’s law

GL 2 (12230)Amonton’s law

GL 3 (12231)The Boyle-Mariotte law

GL 4 (12232)The gas laws of Boyle-Marriotte,Gay-Lussac and Amontons

GL 5 (12233)Determination of molar masses bymeans of vapour density method

GL6 (12234)The law of integral volumes

GL 7 (12235)Gay-Lussac’s law of gaseouscombustion

GL 8 (12236)Avogadro’s law

GL 9 (12237)The chemical formulafor methane, ethane and propane

GL 10 (12238)Determination of the heat offormation of water

GL 11 (12239)Determination of the heat offormation of CO2 and CO and Hess’slaw

GL 12 (12240)Determination of heating value (fuelvalue) of solid and gaseous fuels ina horizontal calorimeter

GL 13 (12241)Determination of the calorific valueof some foods

GL 14 (12242)Determination of the heating value(fuel value) of liquids in the verticalcalorimeter

GL 15 (12243)Determination of the fuel value ofheating oil and diesel fuel and thecalorific value of olive oil

GL 16 (12244)Chromatographic separation techni-ques: gas chromatography

GL 17 (12245)Distillation with steam

HANDBOOKCHEMISTRY

Glass jacket system

0119

6.12

F. Lindenblatt / W. Jung

Glass jacket equipment systemThis system consists of a glass jacket, special inserts and accessories. It was mainlydeveloped for experiments with gases and can be used at school for teaching physics,chemistry and biology.● Demonstrative and transparent● Versatile and easily assembled● Water bath for accurate measurements

Fields of application:● Working out the laws of gases● Determination of molar masses● Determination of combustion enthalpies.

Glass jacket system

Glass jacket system • No. 01196.12 • 17 described ExperimentsPlease ask for a complete equipment list Ref. No. 23701

Amonton’s law (GL 2)

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:34 Uhr Seite 140


Handbooks Thermodynamics

1 Introduction1.1Use of the air cushion table forinstructional purposes1.1.1General information on methods1.1.2Model experiments on heat theory1.1.3Model experiments on electricalconductivity1.1.4Quantitative experiments on the aircushion table1.2General instructions onexperiments1.2.1Procurement instructions1.2.2Operating instructions1.2.3Observation instructions1.2.4Supply of energy to the particles1.2.5Photographic recording of themovement processes1.2.6Preparation of cinematographcharts1.2.7Film strips for particle statistics

2 Model experiments onheat theory/gases

2.1Gases2.1.1Wall collisions2.1.2Collision processes with severalparticles2.1.3Mean velocity - mean value for allmolecules at any moment

2.1.4Mean velocity - mean value for anyone molecule over a period2.1.5Occupation of space by gases2.1.6Mixing of gases2.1.7Temperature-dependence of thediffusion rate2.1.8Compression of a gas2.1.9Expansion of a gas2.1.10Equipartition of the mean kineticenergy of gas molecules2.1.11Rise in gas temperature due toaddition of kinetic energy2.1.12Density distribution of a gas in thegravitational field2.1.13Diffusion of a gas through anopening2.1.14Brownian movement2.1.15Velocity distribution in a gasmixture2.2Solids2.2.1Production of solids2.2.2Temperature of solids2.2.3Melting of a solid2.2.4Elasticity of solids2.2.5Recrystallization2.2.6Diffusion of heat in solids. I

Air cushion tablecompact equipment for model experiments concerning the following subjects:● Thermal movement of molecules in gases● Structures of liquids and solids● Behaviour of electrons in conductors and semi-conductors● Atomic models and scattering experiments

The equipment consists of an air cushion table and adapted accessories.● Demonstrative experiments through projection with an overhead projector.● Coloured magnetic pucks float on an air cushion and repel each other.● Magnetic barriers limit the surface.● The air stream can be interrupted suddenly in order to allow the observation of an

instantaneous state of the pucks.● Lattices which can be fitted on allow to investigate the behaviour of electrons in solids.

Air Cushion Table

Air Cushion Table • No. 01182.02 • 69 described ExperimentsPlease ask for a complete equipment list Ref. No. 23702

2.2.7Diffusion of heat in solids. II2.3Liquids2.3.1Evaporation of a liquid2.3.2Temperature-dependence of thevapour pressure

3 Model experiments onelectricity

3.1The free electron3.2Electrical conductors3.2.1Electrical resistance3.2.2Thermal effect of electric current3.2.3Connection between voltage andcurrent strength3.2.4Thermal velocity of conductionelectrons3.2.5Drift velocity of conductionelectrons3.2.6Thermionic emission3.3Semiconductors3.3.1Bound electron - free electron3.3.2Number of mobile charge carriers3.3.3The electron hole3.3.4Conductivity of semiconductors3.3.5Electron holes in the electric field3.3.6Electron movement in the semi-conductor

3.4Insulators3.4.1Nonconductors3.4.2Bombardment of insulators withionizing radiation3.4.3Electrical polarization of aninsulator

4 Model experiments onnuclear physics

4.1Atom models4.1.1Thomson’s model of the atom4.1.2Rutherford’s model of the atom(planetary model)4.2Rutherford’s scattering experi-ments

5 Model experiments onsolid physics

5.1Electron exposed to a periodic potential5.1.1Electron in the field (potential) of anucleus5.1.2Electron in the field (potential) oftwo nuclei5.1.3Electron in a linear crystal5.1.4Electrons in the surface crystal(work function)5.2Vacancy in the crystal, trap,colour centres

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:34 Uhr Seite 141


Thermodynamics Handbooks

1 Thermal expansion1.1 (12913)Volume expansion of water

1.2 (12914)Preparing a thermometer scale

1.3 (12915)Linear expansion of solid bodies

1.4 (12916)Volume expansion of gases at constant pressure

1.5 (12917)Pressure elevation on heating gasesat constant volume

2 Heat transport2.1 (12918)Heat flux in liquids and gases

2.2 (12919)Heat conduction in solid bodies

2.3 (12920)Heat conduction in water

2.4 (12921)Absorption of thermal radiation

2.5 (12922)Utilisation of radiated energy with asolar collector

2.6 (12923)Utilisation of radiated energy with asolar cell

3 Refraction3.1 (12924)Gay-Lussac’s law

3.1 (12925)Charles’ law

3.3 (12926)Boyle and Mariotte’s law

3.4 (12927)Molar volume and universal gasconstant – Determination of therelative molar mass


Magnetic Board Heat

0115

4.02

Regina Butt

The demonstration board with support stand finds application in all fields of physics. Experi-mentation on the board has the following advantages in the range of thermodynamics:● Quantity of liquids and convection currents in liquids can easily be seen in glass vessels

placed in front of the single-color background● Observations are supported by use of colored marking arrows and points● Description of the experiments and explanatory sketches and tables can be made directly

on the board● Individual positioning and simple movement of the holders● Secure positioning through strong magnets

Special holders and equipment allow a secure, simple and clear method of experimentation onthe demonstration board.The distance of the experimental equipment to the board are correlative and optimised for thespecified application.

Demonstration Experiments Physics– Magnetic Board Heat

Demonstration Experiments Physics – Magnetic Board Heat • No. 01154.02 • 15 described ExperimentsPlease ask for a complete equipment list Ref. No. 23703

Volume expansion of gases at constant pressure (1.4)

Linear expansion of solid bodies (1.3)

LEP 3.1.01-00_3.6.04-00 12.10.2003 10:34 Uhr Seite 142

4Electricity

LEP 4.1.01-00_4.5.09-00 12.10.2003 16:59 Uhr Seite 143


Contents

4.1 Stationary Currents

4.1.01-00 Measurement of low resistance


4.1.03-00 Internal resistance and matching in voltage source


4.1.06-00 Current balance / Force acting on a current-carrying conductor


4.1.08-00 Peltier heat pump


4.1.11-00 Characteristic and efficiency of PEM fuel cell and PEM electrolyser


4.2 Electric Field

4.2.01-00 Electrical fields and potentials in the plate capacitor


4.2.03-00 Capacitance of metal spheres and of a spherical capacitor


4.2.05-00 Coulomb potential and Coulomb field of metal spheres


4.3 Magnetic Field

4.3.01-00 Earth’s magnetic field


4.3.03-00 Magnetic field of paired coils in Helmholtz arrangement


4.3.05-00 Magnetic field outside a straight conductor


4.3.07-11 Ferromagnetic hysteresis


Electricity

4.4 Electrodynamics

4.4.01-00 Transformer


4.4.03-01 Inductance of solenoids


4.4.04-01 Coil in the AC circuit


4.4.05-00 Capacitor in the AC circuit


4.4.06-11 RLC Circuit with Cobra3


4.4.08-00 RC Filters


4.4.10-00 RLC measuring bridge


4.4.12-11 Induction impulse

4.5 Electromagnetic Oscilations and Waves


4.5.04-00 Interference of microwaves


4.5.06-00 Diffraction and polarization of microwaves


4.5.09-00 Frustrated total reflection / Microwaves

4.6 Handbooks

Demonstration Experiments Physics – Electricity/Electronics on the Magnetic Board 1 + 2

4LEP 4.1.01-00_4.5.09-00 12.10.2003 16:59 Uhr Seite 144


Measurement of low resistance 4.1.01-00

Stationary currents Electricity

Principle:The resistances of various DC con-ductors are determined by recordingthe current/voltage characteristic.The resistivity of metal rods and thecontact resistance of connectingcords are calculated.

Tasks:1. To plot the current/voltage char-

acteristics of metal rods (copperand aluminium) and to calculatetheir resistivity.

2. To determine the resistance ofvarious connecting cords by plot-ting their current/voltage charac-teristics and calculating the con-tact resistances.

Current/voltage characteristics of a copper rod and an aluminium rod.


� Ohm’s law� Resistivity� Contact resistance� Conductivity� Four-wire method of

measurement

Heat conductivity rod, Cu 04518.11 1

Heat conductivity rod, Al 04518.12 1













What you need:

Complete Equipment Set, Manual on CD-ROM includedMeasurement of low resistance P2410100

LEP 4.1.01-00_4.5.09-00 12.10.2003 16:59 Uhr Seite 145



Principle:The Wheatstone bridge circuit isused to determine unknown resis-tances. The total resistance of resis-tors connected in parallel and inseries is measured.

Tasks:1. Determination of unknown resist-

ances.

Determination of the total resist-ance

2. of resistors in series,

Resistance of a conductor wire as a function of its radius r.

3. of resistors in parallel.

4. Determination of the resistance ofa wire as a function of its cross-section.

Resistance board, metal 06108.00 1

Slide wire meas. bridge, simple 07182.00 1


PEK carbon resistor 1 W 5% 10 � 39104.01 1





PEK carbon resistor 1 W 5% 1 k� 39104.19 1






Power supply, 5 V/1 A, +/-15 V 13502.93 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedWheatstone Bridge P2410200

Electricity Stationary currents


� Kirchhoff’s laws� Conductor� Circuit� Voltage� Resistance� Parallel connection� Series connection

LEP 4.1.01-00_4.5.09-00 12.10.2003 16:59 Uhr Seite 146


Internal resistance and matching in voltage source 4.1.03-00


Principle:Both the terminal voltage of a volt-age source and the current dependon the load, i. e. on the external re-sistance. The terminal voltage ismeasured as a function of the cur-rent and from it the internal resist-ance and no-load voltage of thevoltage source are determined andthe power graph plotted.

Tasks:1. To measure the terminal voltage

Ut of a number of voltage sourceas a function of the current, vary-ing the external resistance Re, andto calculate the no-load voltageU0 and the internal resistance Ri.

1.1 Slimline battery1.2 Power supply1.2.1 Alternating voltage out-put

Power diagram of a voltage source.

1.2.2 Direct voltage output

2. To measure directly the no-loadvoltage of the slimline battery(with no external resistance) andits internal resistance (by powermatching, Ri = Re).

3. To determine the power diagramfrom the relationship betweenterminal voltage and current, asillustrated by the slimline battery.


� Voltage source� Electromotive force (e.m.f.)� Terminal voltage� No-load operation� Short circuit� Ohm’s law� Kirchhoff’s laws� Power matching

Battery box 06030.21 1


Flat battery, 4.5 V 07496.01 1


Rheostat, 10 �, 5.7 A 06110.02 1

Rheostat, 100 �, 1.8 A 06114.02 1


Double sockets, 1 pair, red a. black 07264.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedInternal resistance and matchingin voltage source P2410300

LEP 4.1.01-00_4.5.09-00 12.10.2003 16:59 Uhr Seite 147

148 PHYWE Systeme GmbH & Co. KG · D-37070 GöttingenLaboratory Experiments, Physics


Principle:The temperature dependence of anelectrical parameter (e.g. resistance,conducting-state voltage, blockingvoltage) of different components isdetermined. To do this, the immer-sion probe set is immersed in a waterbath and the resistance is measuredat regular temperature intervals.

Diagram of resistances.

Tasks:1. Measurement of the temperature

dependence of the resistance ofdifferent electrical components.

2. Measurement of the temperaturedependence of the conductingstate voltage of semiconductingdiodes.

3. Measurement of the temperaturedependence of the voltage in theZener and the avalanche effects.

Immersion probes f. determining ct 07163.00 1











What you need:

Complete Equipment Set, Manual on CD-ROM includedTemperature dependence of differentresistors and diodes P2410400



� Carbon film resistor� Metallic film resistor� PTC� NTC� Z diode� Avalanche effect� Zener effect� Charge carrier generation� Free path� Mathie’s rule

LEP 4.1.01-00_4.5.09-00 12.10.2003 16:59 Uhr Seite 148

149PHYWE Systeme GmbH & Co. KG · D-37070 Göttingen Laboratory Experiments, Physics

Current balance / Force acting on a current-carrying conductor 4.1.06-00


Principle:The force acting on a current-carry-ing conductor loop in a uniformmagnetic field (Lorentz force) ismeasured with a balance.

Conductor loops of various sizes aresuspended in turn from the balance,and the Lorentz force is determinedas a function of the current andmagnetic induction. The uniformmagnetic field is generated by anelectromagnet. The magnetic induct-ion can be varied with the coil cur-rent.

Tasks:1. The direction of the force is to be

determined as a function of thecurrent and the direction of themagnetic field.

2. The force F is to be measured, asa function of the current IL in theconductor loop, with a constantmagnetic induction B and forconductor loops of various sizes.

Lorentz force F as a function of the current IL in the conductor loop.Parameter: lenght l Coil current IM = 870 mA.

The magnetic induction is to becalculated.

3. The force F is to be measured, asa function of the coil current IM,for a conductor loop. In the rangebeing considered, the magneticinduction B is, with sufficient ac-curay, proportional to the coil cur-rent IM.


� Uniform magnetic field� Magnetic induction (formerly

magnetic-flux densitiy)� Lorentz force� Moving charges� Current

Current balance 11081.88 1consisting ofBalance LGN 310, on rod 11081.01 1Pole pieces, rectangular, 1 pair 11081.02 1Wire loop, l = 12.5 mm, n = 1 11081.05 1Wire loop, l = 25 mm, n = 1 11081.06 1Wire loop, l = 50 mm, n = 2 11081.07 1Wire loop, l = 50 mm, n = 1 11081.08 1Iron core, U-shaped, laminated 06501.00 1Base for iron cores 06508.00 2Coil, 900 turns 06512.01 2Metal strip, with plugs 06410.00 2Distributor 06024.00 1Bridge rectifier, 30 V AC/1 A DC 06031.10 1On/off switch 06034.01 1Power supply, universal 13500.93 1Ammeter 1/5 A DC 07038.00 2Tripod base -PASS- 02002.55 2Stand tube 02060.00 1Support rod-PASS-, square, l = 1000 mm 02028.55 1Right angle clamp -PASS- 02040.55 1Connecting cord, l = 100 mm, red 07359.01 1Connecting cord, l = 250 mm, black 07360.05 2Connecting cord, l = 250 mm, blue 07360.04 2Connecting cord, l = 500 mm, red 07361.01 2Connecting cord, l = 500 mm, blue 07361.04 1Connecting cord, l = 1000 mm, red 07363.01 1Connecting cord, l = 1000 mm, blue 07363.04 1

Recommended accessories for measuring the magnetic field :Teslameter, digital 13610.93 1Hall probe, tangent., prot. cap 13610.02 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedCurrent balance / Force acting on a current-carrying conductor P2410600

LEP 4.1.01-00_4.5.09-00 12.10.2003 16:59 Uhr Seite 149



Principle:In a semi-conductor thermogenera-tor, the no-load voltage and theshort-circuit current are measured asa function of the temperature differ-ence. The internal resistance, theSeebeck coefficient and the efficien-cy are determined.

Tasks:1. To measure no-load voltage Uo

and short-circuit current Is at dif-ferent temperature differencesand to determine the Seebeck co-efficient.

2. To measure current and voltage ata constant temperature differencebut with different load resistors,

Electrical power generated as a function of the temperature difference.

and to determine the internal re-sistance Ri from the measuredvalues.

3. To determine the efficiency of en-ergy conversion, from the quantityof heat consumed and the electri-cal energy produced per unit time.

Thermogenerator 04366.00 1

Flow-through heat exchanger 04366.01 2



Rheostat, 33 �, 3.1 A 06112.02 1

Voltmeter, 0.3-300 VDC, 10-300 VAC 07035.00 1

Ammeter 1/5 A DC 07038.00 1





Lab thermometer, -10...+100°C 38056.00 1

Thermometer, -10...+ 50°C 38033.00 1

PEK wire resistor 2.7 � 39104.72 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedSemiconductor thermogenerator P2410700



� Seebeck effect (thermoelectric effect)

� Thermoelectric e.m.f.� Efficiency� Peltier coefficient� Thomson coefficient� Seebeck coefficient� Direct energy conversion� Thomson equations

LEP 4.1.01-00_4.5.09-00 12.10.2003 16:59 Uhr Seite 150


Peltier heat pump 4.1.08-00


Principle:The cooling capacity heating capac-ity and efficiency rating of a Peltierheat pump are determined under dif-ferent operating conditions.

Tasks:1. To determine the cooling capacity

Pc the pump as a function of thecurrent and to calculate the effi-ciency rating hc at maximum out-put.

2. To determine the heating capacityPw of the pump and its efficiencyrating hw at constant current andconstant temperature on the coldside.

Pump cooling capacity as a function of the operating current.

3. To determine Pw , �w and Pc , �c

from the relationship betweentemperature and time on the hotand cold sides.

4. To investigate the temperaturebehaviour when the pump is usedfor cooling, with the hot side air-cooled.


� Peltier effect� Heat pipe� Termoelectric e.m. f.� Peltier coefficient� Cooling capacity� Heating capacity� Efficiency rating� Thomson coefficient� Seebeck coefficient� Thomson equations� Heat conduction� Convection� Forced cooling� Joule effect

Thermogenerator 04366.00 1

Flow-through heat exchanger 04366.01 1

Air cooler 04366.02 1

Heating coil with sockets 04450.00 1


Rheostat, 33 �, 3.1 A 06112.02 1

Connecting plug, 2 pcs. 07278.05 1




Cold a. hot air blower, 1000 W 47540.93 1


Thermometer, -10…+ 50°C 38033.00 2




Support rod, l = 250 mm 02021.00 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedPeltier heat pump P2410800

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 151



Principle:The current-voltage characteristicsof a solar cell are measured at differ-ent light intensities, the distance be-tween the light source and the solarcell being varied.

The depencence of no-load voltageand short-circuit current on temper-ature is determined.

Tasks:1. To determine the light intensity

with the thermopile at variousdistances from the light source.

2. To measure the short-circuit cur-rent and no-load voltage at vari-ous distances from the lightsource.

3. To estimate the dependence ofno-load voltage, and short-circuitcurrent on temperature.

4. To plot the current-voltage char-acteristic at different light inten-sities.

Current-voltage characteristic at different light intensities J.

5. To plot the current-votlage char-acteristic under different operat-ing conditions: cooling the equip-ment with a blower, no cooling,shining the light through a glassplate.

6. To determine the characteristiccurve when illuminating by sun-light.

Solar battery, 4 cells, 2.5�5 cm 06752.04 1

Thermopile, molltype 08479.00 1


Rheostat, 330 �, 1.0 A 06116.02 1

Lamp socket E27, mains conn. 06751.00 1

Filament lamp, 220 V/120 W, w. refl. 06759.93 1









G-clamp 02014.00 2

Glass pane, 150�100�4 mm, 2 off 35010.10 1


Lab thermometer, -10...+100°C 38056.00 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristic curves of a solar cell P2410900



� Semiconductor� p-n junction� Energy-band diagram� Fermi characteristic energy

level� Diffusion potential� Internal resistance� Efficiency� Photo-conductive effect� Acceptors� Donors� Valence band� Conduction band

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 152


Characteristic and efficiency of PEM fuel cell and PEM electrolyser 4.1.11-00


Principle:In a PEM electrolyser, the electrolyteconsists of a proton-conductingmembrane and water (PEM = Pro-ton-Exchange-Membrane). When anelectric voltage is applied, hydrogenand oxygen are formed. The PEM fuelcell generates electrical energy fromhydrogen and oxygen.

The electrical properties of the elec-trolyser and the fuel cell are investi-gated by recording a current-voltagecharacteristic line. To determine theefficiency, the gases are stored insmall gasometers in order to be ableto measure the quantities of thegases generated or consumed.

Volume of the hydrogen generated by the PEM electrolyser as a function oftime at different current I.

Tasks:1. Recording the characteristic line

of the PEM electrolyser.

2. Recording the characteristic lineof the PEM fuel cell.

3. Determination of the efficiency ofthe PEM electrolysis unit.

4. Determination of the efficiency ofthe PEM fuel cell.


� Electrolysis� Electrode polarisation� Decomposition voltage� Galvanic elements� Faraday’s law

PEM fuel cell 06747.00 1

PEM electrolyser 06748.00 1






Short-circuit plug, black 06027.05 2

Gas bar 40466.00 1

Graduated cylinder,100 ml. plastic 36629.01 1



Pinchcock. width 10 mm 43631.10 4

Tubing adaptor, ID 3-6/7-11 mm 47517.01 2


Beaker, 250 ml, bw form, plastic 36013.01 1


Barometer/Manometer. hand-held 07136.00 1

Lab thermometer, -10...+100 °C 38056.00 1





Connecting cord. l = 750 mm, red 07362.01 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristic and efficiencyof PEM fuel cell and PEM electrolyser P2411100

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 153



Principle:The correlation between theamounts of substances transformedin the electrode reaction and the ap-plied charge (amount of electricity)is described by Faraday´s law. Fara-day´s constant, which appears as aproportionality factor, can be deter-mined experimentally from this de-pendence.

Correlations between the transferred charge and the evolved volumes of hy-drogen and oxygen in the electrolysis of diluted sulphuric acid (T = 296.05 Kand p = 100.4 kPa)

Tasks:Determine Faraday´s constant fromthe dependence of the volumes ofhydrogen and oxygen evolved on theapplied charge in the hydrolysis ofdiluted sulphuric acid.

Power supply, universal 13500.93 1Digital multimeter 07134.00 1Electrolysis apparatus, after Hofmann 44518.00 1Platinum electrode in protective sleeve, d = 8 mm 45206.00 2On/Off switch 06034.01 1Connection cable, l = 750 mm, 32 A, blue 07362.04 1Connection cable, l = 500 mm, 32 A, red 07361.01 1Connection cable, l = 250 mm, 32 A, red 07360.01 2Retort stand, h = 750 mm 37694.00 1Right angle clamp 37697.00 3Universal clamp 37715.00 2Stopwatch, digital, 1/100 s 03071.01 1Barometer / Manometer, hand-held 07136.00 1Digital thermometer 07050.00 1Beaker, 600 ml, short 36015.00 1Laboratory balance with data connection, 620 g 45023.93 1Pasteur pipettes, 2 out of 36590.00 1Rubber bulbs, 1 out of 39275.03 1Funnel, do = 80 mm 34459.00 1Wash bottle, 500 ml, plastic 33931.00 1Sulphuric acid, 95 - 98 %, 500 ml 30219.50 1Water, distilled, 5 l 31246.81 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFaraday’s law P2411200



� Electrolysis� Coulometry� Charge� Amount of substance� Faraday´s law� Faraday´s contant� Avogadro´s number� General equation of state for

ideal gases

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 154


Electrical fields and potentials in the plate capacitor 4.2.01-00

Electric field Electricity

Principle:A uniform electric field E

�is pro-

duced between the charged plates ofa plate capacitor. The strength of thefield is determined with the electricfield strength meter, as a function ofthe plate spacing d and the voltageU. The potential � within the field ismeasured with a potential measur-ing probe.

Tasks:1. The relationship between voltage

and electric field strength is inves-tigated, with constant plate spac-ing.

2. The relationship between electricfield strength and plate spacing isinvestigated, with constant volt-age.

Electric field strength as a function of the plate voltage.

3. In the plate capacitor, the poten-tial is measured with a probe, as afunction of position.


� Capacitor� Electric field� Potential� Voltage� Equipotential lines

Plate capacitor, 283�283 mm 06233.02 2

Capacitor plate w. hole d = 55 mm 11500.01 1

Spacer plates, 1 set 06228.01 1

Electric field meter 11500.10 1

Potential probe 11501.00 1

Power supply, 0...600 VDC 13672.93 1

High value resistor, 10 M� 07160.00 1

Blow lamp, butan cartridge, X2000 46930.00 1




Connecting cord, l = 100 mm, green-yell 07359.15 1







Support rod, stainl.steel, 250 mm 02031.00 1



Rule, plastic, l = 200 mm 09937.01 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedElectrical fields and potentialsin the plate capacitor P2420100

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 155



Principle:A capacitor is charged by way of aresistor. The current is measured as afunction of time and the effects ofcapacitance, resistance and the volt-age applied are determined.

Tasks:To measure the charging currentover time:

1. using different capacitance valuesC, with constant voltage U andconstant resistance R

2 using different resistance values(C and U constant)

Course of current with time at different capacitance values; voltage and resistance are constant (U = 9 V, R = 2.2 M�).

3. using different voltages (R and Cconstant).

To determine the equation repre-senting the current when a capacitoris being charged, from the valuesmeasured.


Two-way switch, single pole 06030.00 1

Capacitor, 2�32 micro-F 06219.32 1


PEK carbon resistor 1 W 5% 1 m� 39104.52 4

PEK connect.plug white 19 mm pitch 39170.00 2

PEK capacitor(case 2) 1 mmF/ 400 V 39113.01 1

PEK capacitor(case 2) 4.7 mmF/400 V 39113.03 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedCharging curve of a capacitor P2420200

Electricity Electric field


� Charging� Discharging� Time constant� Exponential function� Half life

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 156


Capacitance of metal spheres and of a spherical capacitor 4.2.03-00


Principle:Metal spheres with different radiiand a spherical capacitor arecharged by means of a variable volt-age. The induced charges are deter-mined with a measuring amplifier.The corresponding capacitances arededuced from voltage and chargevalues.

Tasks:1. Determination of the capacitance

of three metal spheres with differ-ent diameters.

2. Determination of the capacitanceof a spherical capacitor.

U1 (measured voltage) as a function of U2 (charging voltage) measured onconducting spheres with three different diameters.

3. Determination of the diameters ofeach test body and calculation oftheir capacitance values.


� Voltage� Potential� Charge� Electric field� Electrostatic induction� Electrostatic induction

constant� Capacitance� Capacitor� Dielectrics

Conductor ball, d = 20 mm 06236.00 2Conductor ball, d = 40 mm 06237.00 1Conductor ball, d = 120 mm 06238.00 1Hemispheres, Cavendish type 06273.00 1Hollow plastics ball, w. eyelet 06245.00 1Capillary tube, straight, l = 250 mm 36709.00 1Copper wire, d = 0.5 mm, l = 50 m 06106.03 1Insulating stem 06021.00 2High-value resistor, 10 M� 07160.00 1High voltage supply unit, 0-10 kV 13670.93 1PEK capacitor/ case 1/ 10 nF/ 500 V 39105.14 1Universal measuring amplifier 13626.93 1Multi-range meter A 07028.01 1Digital multimeter 07134.00 1Connecting cord, 50 KV, l = 1000 mm 07367.00 1Screened cable, BNC, l = 750 mm 07542.11 1Adapter, BNC socket - 4 mm plug 07542.20 1Connector, T type, BNC 07542.21 1Adapter, BNC-plug/socket 4 mm 07542.26 1Vernier caliper, plastic 03011.00 1Barrel base -PASS- 02006.55 2Support base -PASS- 02005.55 1Right angle clamp -PASS- 02040.55 4Support rod -PASS-, square, l = 630 mm 02027.55 1Support rod -PASS-, square, l = 400 mm 02026.55 1Universal clamp with joint 37716.00 1Croco.clip, insul., strong, 10 pcs 29426.03 1Connecting cord, l = 100 mm, green-yell 07359.15 1Connecting cord, l = 750 mm, green-yell 07362.15 2Connecting cord, l = 500 mm, blue 07361.04 2Connecting cord, l = 500 mm, red 07361.01 2

What you need:

Complete Equipment Set, Manual on CD-ROM includedCapacitance of metal spheresand of sphrerical capacitor P2420300

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 157



Principle:A small electrically charged ball ispositioned at a certain distance infront of a metal plate lying at earthpotential. The surface charge on theplate due to electrostatic inductiontogether with the charged ball formsan electric field analogous to thatwhich exists between two oppositelycharged point garges.

The electrostatic force acting on theball can be measured with a sensitivetorsion dynamometer.

Tasks:1. Establishment of the relation

between the active force and thecharge on the ball.

2. Establishment of the relationbetween force and distance, ballto metal plate.

Relationsship between electrostatic force F and the square or the charge Qfor various distances (a) between ball and plate.

3. Determination of the electric con-stant.

Plate capacitor, 283�283 mm 06233.02 1

Insulating stem 06021.00 2

Conductor ball, d = 40 mm 06237.00 2

Conductor spheres, w. suspension 02416.01 1

Torsion dynamometer, 0.01 N 02416.00 1

Weight holder f.slotted weights 02204.00 1


DC measuring amplifier 13620.93 1

Power supply, high volt., 0-25 kV 13671.93 1


Connecting cord, 50 KV, l = 1000 mm 07367.00 1






Connecting cord, l = 1000 mm, green-yellow 07363.15 2




Holder for U-magnet 06509.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedCoulomb’s law / Image charge P2420400



� Electric field� Electric field strenght� Electric flux� Electrostatic induction� Electric constant� Surface charge density� Dielectric displacement� Electrostatic potential

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 158


Coulomb potential and Coulomb field of metal spheres 4.2.05-00


Principle:Conducting spheres with differentdiameters are charged electrically.The static potentials and the accom-panying electric field intensities aredetermined by means of an electricfield meter with a potential measur-ing probe, as a function of positionand voltage.

Field strenght as a function ofvoltage.

Graphs 1-3: sphere with 2R = 12 cm;r1 = 25 cm, r2 = 50 cm, r3 = 75 cm;graph 4: sphere with 2R = 4 cm; r1 = 25 cm.

Tasks:1. For a conducting sphere of diame-

ter 2R = 12 cm, electrostatic po-tential is determined as a functionof voltage at a constant distancefrom the surface of the sphere.

2. For the conducting spheres of dia-meters 2R = 12 cm and 2R = 4 cm,electrostatic potential at constantvoltage is determined as a func-tion of the distance from the sur-face of the sphere.

3. For both conducting spheres, elec-tric field strenght is determined asa function of charging voltage atthree different distances from thesurface of the sphere.

4. For the conducting sphere of dia-meter 2R = 12 cm, electric fieldstrenght is determined as a func-tion of the distance from the sur-face of the sphere at constantcharging voltage.


� Electric field� Field intensity� Electric flow� Electric charge� Gaussian rule� Surface charge density� Induction� Induction constant� Capacitance� Gradient� Image charge� Electrostatic potential� Potential difference

Electric field meter 11500.10 1

Potential probe 11501.00 1

Capacitor plate w.hole d = 55 mm 11500.01 1

High voltage supply unit, 0-10 kV 13670.93 1




High-value resistor, 10 M� 07160.00 1

Insulating stem 06021.00 2










Connecting cord, 50 KV, l = 500 mm 07366.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedCoulomb potential and Coulomb fieldof metal spheres P2420500

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 159


XX

X

X

X

XX

XX

X

X

X

X

X

X

X

1000

800

600

400

200

0

1,0 2,0 3,0 4,0

plastic

air

Principle:The electric constant �0 is deter-mined by measuring the charge of aplate capacitor to which a voltage isapplied. The dielectric constant � isdetermined in the same way, withplastic or glass filling the spacebetween the plates.

Tasks:1. The relation between charge Q

and voltage U is to be measuredusing a plate capacitor.

2. The electric constant �0 is to bedetermined from the relationmeasured under point 1.

3. The charge of a plate capacitor isto be measured as a function ofthe inverse of the distancebetween the plates, under con-stant voltage.

Electrostatic charge Q of a plate capacitor as a function of the applied volt-age Uc, with and without dielectric (plastic) between the plates (d = 0.98 cm)

4. The relation between charge Qand voltage U is to be measuredby means of a plate capacitor,between the plates of which dif-ferent solid dielectric media areintroduced. The correspondingdielectric constants are deter-mined by comparison with meas-urements performed with airbetween the capacitor plates.

Plate capacitor, d = 260 mm 06220.00 1

Plastic plate 283�283 mm 06233.01 1

Glass plates f. current conductors 06406.00 1




PEK capacitor/case 1/0.22 mmF/160 V 39105.19 1


Connecting cord, l = 100 mm, green-yell 07359.15 1



Connecting cord, 50 KV, 500 mm 07366.00 1



Connector, T type, BNC 07542.21 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedDielectric constant of different materials P2420600



� Maxwell’s equations� Electric constant� Capacitance of a plate

capacitor� Real charges� Free charges� Dielectric displacement� Dielectric polarisation� Dielectric constant

QnAs


Uc

kV

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 160


Earth’s magnetic field 4.3.01-00

Magnetic field Electricity

Principle:A constant magnetic field, its magni-tude and direction known, is super-imposed on the unknown earth-magnetic field. The earth-magneticfield can then be calculated from themagnitude and direction of the re-sulting flux density.

Linear function to determine the horizontal component hBE of the magneticflux density of the earth-magnetic field.

Tasks:1. The magnetic flux of a pair of

Helmholtz coils is to be deter-mined and plotted graphically asa function of the coil current. TheHelmholtz system calibration fac-tor is calculated from the slope ofthe line.

2. The horizontal component of theearth-magnetic field is deter-mined through superimposition ofthe Helmholtz field.

3. The angle of inclination must bedetermined in order to calculatethe vertical component of theearth-magnetic field.


� Magnetic inclination and declination

� Isoclinic lines� Isogenic lines� Inclinometer� Magnetic flow density� Helmholtz coils

Pair of Helmholtz coils 06960.00 1


Rheostat, 100 �, 1.8 A 06114.02 1

Teslameter, digital 13610.93 1

Hall probe, axial 13610.01 1


Magnetometer 06355.00 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedEarth’s magnetic field P2430100

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 161



Principle:The magnetic field along the axis ofwire loops and coils of different di-mensions is measured with a tesla-meter (Hall probe). The relationshipbetween the maximum field strengthand the dimensions is investigatedand a comparison is made betweenthe measured and the theoretical ef-fects of position.

Curve of magnetic flux density (measured values) for coils with a constantdensity of turns n/l, coils radius R = 20 mm, lengths l1 = 53 mm, l2 = 105 mmand l3 = 160 mm.

Tasks:1. To measure the magnetic flux

density in the middle of variouswire loops with the Hall probe andto investigate its dependence onthe radius and number of turns.

2. To determine the magnetic fieldconstant �0.

3. To measure the magnetic fluxdensity along the axis of long coilsand compare it with theoreticalvalues.

Induction coil, 300 turns, d = 40 mm 11006.01 1







Conductors, circular, set 06404.00 1










G-clamp 02014.00 2

Lab jack, 200�230 mm 02074.01 1

Reducing plug 4 mm/2 mm socket, 2 11620.27 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetic field of a single coils /Biot-Savart’s law P2430200

Electricity Magnetic field


� Wire loop� Biot-Savart’s law� Hall effect� Magnetic field� Induction� Magnetic flux density

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 162


Magnetic field of paired coils in Helmholtz arrangement 4.3.03-00


Principle:The spatial distribution of the fieldstrength between a pair of coils inthe Helmholtz arrangement is mea-sured. The spacing at which a uni-form magnetic field is produced isinvestigated and the superposition ofthe two individual fields to form thecombined field of the pair of coils isdemonstrated.

Tasks:1. To measure the magnetic flux

density along the z-axis of the flatcoils when the distance betweenthem a = R (R = radius of thecoils) and when it is larger andsmaller than this.

2. To measure the spatial distributionof the magnetic flux density whenthe distance between coils a = R,using the rotational symmetry ofthe set-up:

a) measurement of the axial com-ponent Bz

B (r = 0; r is the distance perpendicular to the axis of the coils) as a functionof z (z is the distance from the center of the coils in the direction of the axisof the coils) with the parameter �.

b) measurement of radial compo-nent Br.

3. To measure the radial componentsB�r and B�r of the two individualcoils in the plane midway betweenthem and to demonstrate theoverlapping of the two fields at Br = 0.


� Maxwell’s equations� Wire loop� Flat coils� Biot-Savart’s law� Hall effect










G-clamp 02014.00 3



What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetic field of paired coilsin Helmholtz arrangement P2430300

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 163

What you need:


Principle:A conductor loop carrying a currentin a uniform magnetic field experi-ences a torque. This is determined asa function of the radius, of the num-ber of turns and the current in theconductor loop and of the strengthof the external field.

Tasks:Determination of the torque due to amagnetic moment in a uniform mag-netic field, as a function

1. of the strength of the magneticfield,

Torque due to a magnetic moment in a uniform magnetic field as a functionof the angle between the magnetic field and magnetic moment.

2. of the angle between the mag-netic field in the magnetic mo-ment,

3. of the strength of the magneticmoment.


Conductors, circular, set 06404.00 1

Torsion dynamometer, 0.01 N 02416.00 1

Coil holder for 02416.00 02416.02 1






Support rod -PASS-, square, l 630 mm 02027.55 1




Complete Equipment Set, Manual on CD-ROM includedMagnetic moment in the magnetic field P2430400


� Torque� Magnetic flux� Uniform magnetic field� Helmholtz coils



LEP 4.1.01-00_4.5.09-00 12.10.2003 17:00 Uhr Seite 164



Magnetic field outside a straight conductor 4.3.05-00

Principle:A current which flows through oneor two neighbouring straight con-ductors produces a magnetic fieldaround them. The dependences ofthese magnetic fields on the dis-tance from the conductor and on thecurrent are determined.

Tasks:Determination of the magnetic field

1. of a straight conductor as a func-tion of the current,

2. of a straight conductor as a func-tion of the distance from the con-ductor,

3. of two parallel conductors, inwhich the current is flowing inthe same direction, as a function

Magnetic field component By of two parallel conductors on the x-axis as afunction of the distance from one conductor, if the current in both conduc-tors is in the same direction.

of the distance from one conduc-tor on the line joining the twoconductors,

4. of two parallel conductors, inwhich the current is flowing inopposite directions, as a functionof the distance from one conduc-tor on the line joining the twoconductors.

� Maxwell’s equations� Magnetic flux� Induction� Superimposition of magnetic

fields

Current conductors, set of 4 06400.00 1

Coil, 6 turns 06510.00 1

Coil, 140 turns, 6 tappings 06526.01 1

Clamping device 06506.00 1

Iron core, short, laminated 06500.00 1





Current transformer 07091.00 1






G-clamp 02014.00 2

Connecting cord, l= 500 mm, yellow 07361.02 2

Complete Equipment Set, Manual on CD-ROM includedMagnetic field outside a straight conductor P2430500

What you need:


LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 165



Principle:A current which produces a magnet-ic field is passed through an electro-lyte. This magnetic field inside theconductor is determined as a func-tion of position and current.

Magnetic field inside a conductor as a function of the position x (x = heightof the probe perpendicular to the axis of the cylinder).

Tasks:Determination of the magnetic fieldinside a conductor as a function

1. of the current in the conductor,

2. of the distance from the axis ofthe conductor.

Hollow cylinder, PLEXIGLAS 11003.10 1

Search coil, straight 11004.00 1


LF amplifier, 220 V 13625.93 1




Meter scale, demo, l = 1000mm 03001.00 1









Hydrochloric acid 1.19, 1000 ml 30214.70 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetic field inside a conductor P2430600



� Maxwell’s equations� Magnetic flux� Induction� Current density� Field strength

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 166



Ferromagnetic hysteresis 4.3.07-11

Principle:A magnetic field is generated in aring-shaped iron core by a continu-ous adjustable direct current appliedto two coils. The field strength Hand the flux density B are measuredand the hysteresis recorded.

The remanence and the coercive fieldstrength of two different iron corescan be compared.

Hysteresis for a massive iron core.

Tasks:Record the hysteresis curve for amassive iron core and for a laminat-ed one.


� Induction� Magnetic flux, coil� Magnetic field strength� Magnetic field of coils� Remanence� Coercive field strength

Coil, 600 turns 06514.01 2

Iron core, U-shaped, solid 06491.00 1

Iron core, solid 06490.00 1



Commutator switch 06034.03 1

Power supply, univ., anal. disp. 13501.93 1

Rheostat, 10 �, 5.7 A 06110.02 1




Support rod, l = 150 mm 02030.15 1





Force/Tesla measuring module 12109.00 1

Cobra3 Software Force/Tesla 14515.61 1

RS 232 data cable 14602.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedFerromagnetic hysteresis P2430711

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 167


Principle:With the aid of two mirrors in aMichelson arrangement, light isbrought to interference. Due to themagnetostrictive effect, one of themirrors is shifted by variation in themagnetic field applied to a sample,and the change in the interferencepattern is observed.

Measuring results of the magnetostriction of nickel with the relative changein length �l/l plotted against applied field strength H.

Tasks:1. Construction of a Michelson inter-

ferometer using separate opticalcomponents.

2. Testing various ferromagnetic ma-terials (iron and nickel) as well asa non-ferromagnetic material(copper), with regard to theirmagnetostrictive properties.


� Interference� Wavelength� Diffraction index� Speed of light� Phase� Virtual light source� Ferromagnetic material� Weiss molecular magnetic

fields� Spin-orbit coupling

Optical base plate with rubber feet 08700.00 1







Beam splitter 1/1, non polarizing 08741.00 1

Lens, mounted, f = +20 mm 08018.01 1

Lensholder f. optical base plate 08723.00 1

Screen, white, 150�150mm 09826.00 1

Faraday modulator f. opt. base plt. 08733.00 1

Rods for magnetostriction,set 08733.01 1






Laser,He-Ne 0.2/1.0 mW, 220 V AC 08180.93 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetostriction with the Michelson interferometer P2430800



LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 168


Electrodynamics Electricity

Transformer 4.4.01-00

Principle:An alternating voltage is applied toone of two coils (primary coil) whichare located on a common iron core.The voltage induced in the secondcoil (secondary coil) and the currentflowing in it are investigated asfunctions of the number of turns inthe coils and of the current flowingin the primary coil.

Tasks:The secondary voltage on the opencircuited transformer is determinedas a function1. of the number of turns in the

primary coil,2. of the number of turns in the

secondary coil,3. of the primary voltage.

The short-circuit current on the sec-ondary side is determined as a func-tion4. of the number of turns in the pri-

mary coil,

Secondary short-circuit current of the transformer as a function1. of the number of turns in the secondary coil,2. of the number of turns in the primary coil.

5. of the number of turns in thesecondary coil,

6. of the primary current.

With the transformer loaded, theprimary current is determined as afunction7. of the secondary current,8. of the number of turns in the

secondary coil,9. of the number of turns in the

primary coil.

Coil, 140 turns, 6 tappings 06526.01 2




Multitap transf., 14 VAC/12 VDC, 5 A 13533.93 1

Two-way switch, double pole 06032.00 1

Rheostat, 10 �, 5.7 A 06110.02 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedTransformer P2440100


� Induction� Magnetic flux� Loaded transformer� Unloaded transformer� Coil

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 169


Principle:A magnetic field of variable frequen-cy and varying strength is producedin a long coil. The voltages inducedacross thin coils which are pushedinto the long coil are determined asa function of frequency, number ofturns, diameter and field strength.

Induced voltage as a function of the frequency in the primary coil with a pri-mary current of 30 mA and an induction coil diameter of 41 mm.

Tasks:Determination of the induction volt-age as a function

1. of the strength of the magneticfield,

2. of the frequency of the magneticfield,

3. of the number of turns of the in-duction coil,

4. of the cross-section of the induc-tion coil.


� Maxwell’s equations� Electrical eddy field� Magnetic field of coils� Coil� Magnetic flux� Induced voltage

Field coil, 750 mm, 485 turns/m 11001.00 1














What you need:

Complete Equipment Set, Manual on CD-ROM includedMagnetic induction P2440200


Electricity Electrodynamics

f

kHz

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 170



Inductance of solenoids 4.4.03-01

Principle:A square wave voltage of low fre-quency is applied to oscillatory cir-cuits comprising coils and capacitorsto produce free, damped oscillations.The values of inductance are calcu-lated from the natural frequenciesmeasured, the capacitance beingknown.

Tasks:To connect coils of different dimen-sions (length, radius, number ofturns) with a known capacitance Cto form an oscillatory circuit. Fromthe measurements of the natural fre-quencies, to calculate the induc-tances of the coils and determine therelationships between:

Inductance per turn as a function of the length of coil, at constant radius.

1. inductance and number of turns

2. inductance and length

3. inductance and radius.








Coil, 1200 turns 06515.01 1



PEK capacitor /case 1/ 1nF/ 500 V 39105.10 1

PEK capacitor /case 1/ 470 pF/500 V 39105.07 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedInductance of solenoids P2440301


� Law of inductance� Lenz’s law� Self-inductance� Solenoids� Transformer� Oscillatory circuit� Resonance� Damped oscillation� Logarithmic decrement� Q factor

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 171


Principle:A square wave voltage of low fre-quency is applied to oscillatory cir-cuits comprising coils and capacitorsto produce free, damped oscillations.The values of inductance are calcu-lated from the natural frequenciesmeasured, the capacitance beingknown.

Tasks:To connect coils of different dimen-sions (length, radius, number ofturns) with a known capacitance Cto form an oscillatory circuit. Fromthe measurements of the natural fre-quencies, to calculate the induc-tances of the coils and determine therelationships between:

Inductance per turn as a function of the length of coil, at constant radius.

1. inductance and number of turns

2. inductance and length

3. inductance and radius.


� Lenz’s law� Self-inductance� Solenoids� Transformer� Oscillatory circuit� Resonance� Damped oscillation� Logarithmic decrement� Q factor



RS 232 data cable 14602.00 1


Cobra3 Function generator module 12111.00 1

Induction coil, 300 turns, dia. 40 mm 11006.01 1







Coil, 1200 turns 06515.01 1


PEK capacitor /case 1/ 1nF/ 500 V 39105.10 1











What you need:

Complete Equipment Set, Manual on CD-ROM includedInductance of solenoids with Cobra3 P2440311



LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 172



Coil in the AC circuit 4.4.04-01

Principle:The coil is connected in a circuit witha voltage source of variable frequen-cy. The impedance and phase dis-placements are determined as func-tions of frequency. Parallel and seriesimpedances are measured.

Phase displacement (�) between total current and total voltage as a functionof frequency.

Tasks:1. Determination of the impedance

of a coil as a function of frequen-cy.

2. Determination of the inductanceof the coil.

3. Determination of the phase dis-placement between the terminalvoltage and total current as afunction of the frequency in thecircuit.

4. Determination of the total impe-dance of coils connected in par-allel and in series.

Coil, 300 turns 06513.01 1

Coil, 600 turns 06514.01 1





Difference amplifier 11444.93 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedCoil in the AC circuit P2440401


� Inductance� Kirchhoff’s laws� Maxwell’s equations� AC impedance� Phase displacement

f

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 173


Principle:The coil is connected in a circuit witha voltage source of variable frequen-cy. The impedance and phase dis-placements are determined as func-tions of frequency. Parallel and seriesimpedances are measured.



of a coil as a function of frequen-cy.

2. Determination of the inductanceof the coil.

3. Determination of the phase dis-placement between the terminalvoltage and total current as afunction of the frequency in thecircuit.

4. Determination of the totalimpedance of coils connected inparallel and in series.


� Inductance � Kirchhoff’s laws � Maxwell’s equations � AC impedance� Phase displacement



RS 232 data cable 14602.00 1



Coil, 300 turns 06513.01 1

Coil, 600 turns 06514.01 1








T type connector, two BNC-sockets/plug 07542.21 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedCoil in the AC circuit with Cobra3 P2440411


Electricity Electrodynamicss

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 174



Capacitor in the AC circuit 4.4.05-00

Principle:A capacitor is connected in a circuitwith a variable-frequency voltagesource. The impedance and phasedisplacement are determined as afunction of frequency and ofcapacitance. Parallel and seriesimpedances are measured.



of a capacitor as a function of ca-pacitance and frequency;

2. Determination of the phase dis-placement between terminal volt-age and total current as a functionof the capacitance and the fre-quency in the circuit;

3. Determination of the totalimpedance of capacitors connect-ed in parallel and in series.









PEK capacitor (case 2) 1 mF/400 V 39113.01 1

PEK capacitor(case 2) 2.2 mF/400 V 39113.02 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedCapacitor in the AC circuit P2440500


� Capacitance� Kirchhoff’s laws� Maxwell’s equations� Parallel connection� Series connection� a.c. impedance� Phase displacement

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 175


Principle:The current and voltage of paralleland series-tuned circuits are investi-gated as a function of frequency. Q-factor and band-width are deter-mined.

Tasks:Determination of the frequency per-formance of a

1. Series-tuned circuit fora) voltage resonance without

damping resistor,b) current resonance without

damping resistor,c) current resonance with damp-

ing resistor.

Terminal voltage as a function of frequency in the series-tuned circuit.

2. parallel-tuned circuit fora) current resonance without par-

allel resistor,b) voltage resonance without par-

allel resistorc) voltage resonance with parallel

resistor.


� Tuned circuit� Series-tuned circuit� Parallel-tuned circuit� Resistance� Capacitance� Inductance� Capacitor� Coil� Phase displacement� Q factor� Band-width� Loss resistance� Damping



Coil, 300 turns 06513.01 1






PEK capacitor/case 2/1 mF/ 400 V 39113.01 1

PEK capacitor/case 1/0.1 mF/ 500 V 39105.18 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedRLC Circuit P2440601



LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 176



RLC Circuit with Cobra3 4.4.06-11

Principle:The current and voltage of paralleland series-tuned circuits are inves-tigated as a function of frequency.Q-factor and band-width are deter-mined.

Tasks:Determination of the frequency per-formance of a

1. Series-tuned circuit for

a) voltage resonance withoutdamping resistor,

b) current resonance withoutdamping resistor,

c) current resonance with damp-ing resistor.

Terminal voltage as a function of frequency in the series-tuned circuit.

2. parallel-tuned circuit for

a) current resonance without par-allel resistor,

b) voltage resonance without par-allel resistor

c) voltage resonance with parallelresistor.


� Tuned circuit � Series-tuned circuit� Parallel-tuned circuit� Resistance� Capacitance� Inductance� Capacitor� Coil� Phase displacement� Q factor � Band-width� Loss resistance � Damping



RS 232 data cable 14602.00 1



Coil, 300 turns 06513.01 1






PEK capacitor/case 2/1 mmF/ 400 V 39113.01 1

PEK capacitor/case 1/0.1 mmF/ 500 V 39105.18 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedRLC Circuit with Cobra3 P2440611

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 177


Principle:The ripple of the output voltage ofvarious rectifier circuits is measuredas a function of the load currentstrength and the charging capaci-tance. The characteristics of a volt-age stabilizer and of a multiplier areinvestigated.

Tasks:1. Using the half-wave rectifier:a) to display the output voltage

(without charging capacitor) onthe oscilloscope

b) to measure the diode current ID asa function of the output currentstrength Io (with the charging capacitor)

c) to measure the ripple componentUACpp of the output voltage as afunction of the output current (C = constant)

d) to measure the ripple as a functionof the capacitance (Io = constant)

e) to measure the output voltage Uoas a function of the input voltageUi (Io = 0).

2. Using the bridge rectifier:a) to display the output voltage

(without charging capacitor) onthe oscilloscope

Ripple of the output voltage as a function of the charging current:a) half-wave rectifier, b) bridge rectifier.

b) to measure the current throughone diode, ID, as a function of theoutput current Io (with the charg-ing capacitor)

c) to measure the ripple of the out-put voltage as a function of theoutput current (C = constant)

d) to measure the ripple as a functionof the capacitance (Io = constant)

e) to measure the output voltage asa function of the input voltage.

3. To measure the voltage at thecharging capacitor, Uc, and theoutput voltage of a stabilizedvoltage source as a function ofthe input voltage Ui.

4. To measure the output voltage ofa voltage multiplier circuit as afunction of the input voltage.


� Half-wave rectifier� Full-wave rectifier� Graetz rectifier� Diode and Zener diode� Avalanche effect� Charging capacitor� Ripple� r.m.s. value� Internal resistance� Smoothing factor� Ripple voltage� Voltage stabilisation� Voltage doubling

Plug-in board, 4 mm plugs 06033.00 1

PEK semiconductor diode/si/IN4148 39106.02 4

PEK electrol.capacitor 500 mm F/35 V 39105.26 1

PEK electrol. capacitor 10 mF/ 70 V 39105.28 4

PEK electro. capacitor 2000 mF/25 V 39113.08 1

Capacitor, electrolytic, 1000 mF 06049.09 1



PEK low power zener diode ZF 4.7 39132.01 1

Multitap transf., 14 VAC/12 VDC, 5 A 13533.93 1



Rheostat, 330 �, 1.0 A 06116.02 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedRectifier circuits P2440700



LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 178



RC Filters 4.4.08-00

Principle:The frequency response of simple RCfilters is recorded by point-by-pointmeasurements and the sweep dis-played on the oscilloscope.

Tasks:To record the frequency response ofthe output voltage of

1. a high-pass filter

2. a low-pass filter

3. a band-pass filter

4. a Wien-Robinson bridge

5. a parallel-T filter,

point by point and to display thesweep on the oscilloscope.

Frequency response of high-pass and low pass filter.

To investigate the step response of

6. a differentiating network

7. an integrating network

Plug-in board, 4 mm plugs 06033.00 1


PEK capacitor/case 1/10 nF/ 500 V 39105.14 4




Wobble-functiongenerator 2 Hz-6 MHz 11765.93 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedRC Filters P2440800


� High-pass� Low-pass� Wien-Robinson bridge� Parallel-T filters� Differentiating network� Integrating network� Step response� Square wave� Transfer function

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:01 Uhr Seite 179


Principle:A coil, a capacitor, an ohmic resis-tance and combinations of thesecomponents are investigated fortheir filter characteristics as a func-tion of frequency. The phase dis-placement of the filters is deter-mined also as a function of frequen-cy.

Tasks:Determination of the ratio of outputvoltage to input voltage with the

1. RC/CR network,

2. RL/LR network,

3. CL/LC network,

4. 2 CR networks connected in series.

U/U1 (U1 = supply voltage) as a function of the frequency with the LR andRL network.

5. Determination of the phase dis-placement with the RC/CR net-work.

6. Determination of the phase dis-placement with 2 CR networksconnected in series.


� Circuit� Resistance� Capacitance� Inductance� Capacitor� Coil� Phase displacement� Filter� Kirchhoff’s laws� Bode diagram

Coil, 300 turns 06513.01 1


PEK capacitor(case 2) 1 mF/ 400 V 39113.01 1












What you need:

Complete Equipment Set, Manual on CD-ROM includedHigh-pass and low-pass filters P2440900



LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 180



RLC measuring bridge 4.4.10-00

Principle:Ohmic resistances, inductances andcapacitances are determined in aWheatstone bridge circuit operatedon AC. Balancing is done aurallythrough headphones, using the highsensitivity of the human ear.

Wheatstone bridge.

Tasks:To determine

1. ohmic resistances

2. inductances

3. capacitances

with the Wheatstone bridge, usingbridge balancing.

Slide wire meas. bridge, simple 07182.00 1

Headphone, stereo 65974.00 1


Coil, 6 turns 06510.00 1

Coil, 300 turns 06513.01 1

Coil, 600 turns 06514.01 1

Coil, 1200 turns 06515.01 1

Coil, 600 turns, short 06522.01 1

Induction coil, 300 turns, dia.40 mm 11006.01 1








PEK potentiometer 100 � lin 0.4 W 39103.01 1




PEK capacitor /case 1/ 1 nF/ 500 V 39105.10 1

PEK capacitor/ case 1/ 2.2 nF/500 V 39105.11 1

PEK capacitor/ case 1/ 4.7 nF/500 V 39105.13 1

PEK capacitor/ case 1/ 10 nF/ 500 V 39105.14 1





What you need:


� Wheatstone bridge� Inductive and capacitive

reactance� Ohmic resistance� Impedance� Kirchhoff’s laws

Complete Equipment Set, Manual on CD-ROM includedRLC measuring bridge P2441000

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 181


X

10 20 30 40 50 60 70 80 90 100

1100

1000

900

800

700

600

500

400

300

200

100

XX

X

X

X

X

X

X

X

1/f2

10-6 Hz2

Z2

�2

Principle:Series circuits containing self-induc-tances or capacitances and ohmicresistances are investigated as afunction of frequency. Measuring theelectrical magnitudes with a work orpower measurement instrument, realpower or apparent power can be dis-played directly.

Tasks:1. Series circuit of self-inductanceand resistor (real coil)

– Investigation of impedance andphase shift as a function of fre-quency

– Investigation of the relation be-tween real power and current in-tensity

Capacitor and resistor in series, Z2 as a function of 1/f2.

– Determination of self-inductanceand ohmic resistance

2. Series circuit of capacitor and re-sistor

– Investigation of impedance and

phase shift as a function of fre-quency


� Impedance� Phase shift� Phasor diagram� Capacitance� Self-inductance

Work and power meter 13715.93 1


Coil, 300 turns 06513.01 1


Electr.capaci. 47 mF/63 V bip 39105.45 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedResistance, phase shift and powerin AC circuits P2441100



– Investigation of the relation be-tween real power and current in-tensity

– Determination of capacitance andohmic resistance

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 182



Induction impulse with Cobra3 4.4.12-11

Principle:A permanent magnet falls with dif-ferent velocities through a coil. Thechange in the magnetic flux � gen-erates an induced voltage impulse.The induced voltage impulse USS isrecorded with a computer interfacesystem. Depending on the polarity ofthe permanent magnet the inducedvoltage impulse is negative or posi-tive.

Measured induction voltage USS versus time. Additionally the evaluation ofthe peak-to-peak voltage USS = 2.766 V is shown.

Tasks:1. Measurement of the induced volt-

age impulse USS and the fallingmagnet’s velocity.

2. Evaluation of the induced voltageimpulse USS as a function of themagnet’s velocity.

3. Calculation of the magnetic fluxinduced by the falling magnet as afunction of the magnet’s velocity.



RS232 data cable, 9 poles 14602.00 1

Cobra3 Universal Plotter Software 14504.61 1

Forked light barrier, compact 11207.20 1

Support rod, round, l = 600 mm 02037.00 1


Tripod, -PASS- 02002.55 1


Glass tube, l = 300 mm 45126.01 1

Coil holder 06528.00 1


Magnet, d = 8 mm, l = 60 mm 06317.00 1

Connecting cord, 32 A, l = 50 cm, red 07361.01 2

Connecting cord, 32 A, l = 50 cm, blue 07361.04 2

Connecting cord, 32 A, l = 50 cm, yellow 07361.02 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedInduction impulse with Cobra3 P2441211


� Law of induction� Magnetic flux� Maxwell’s equations

LEP 4.1.01-00_4.5.09-00 12.10.2003 22:38 Uhr Seite 183


Principle:The Q factor of oscillating circuits isdetermined from the bandwidth andby the Pauli method. In inductivelycoupled circuits (band-pass filters)the coupling factor is determined asa function of the coil spacing.

Tasks:1. To determine the dissipation fac-

tor tan k and the quality factorQ from the bandwidth of oscillat-ing circuits.

2. To determine the dissipation fac-tor and Q factor of oscillating cir-cuits from the resonant frequency

Coupling constant k as a function of the distance s between the coils whenthe coupling is supercritical.

(0), the capacitance Ctot. and theparallel conductance Gp determinedby the Pauli method.

3. To determine the coupling factork and the bandwidth �f of aband-pass filter as a function ofthe coil spacing s.


� Resonance� Q factor� Dissipation factor� Bandwidth� Critical or optimum coupling� Characteristic impedance� Pauli method� Parallel conductance� Band-pass filter� Sweep

Wobble-functiongenerator 2 Hz-6 MHz 11765.93 1


HF-coil, 35 turns, 75 micro-H 06915.00 2




Variable capacitor, 500 pF 06049.10 2




PEK carbon resistor 1 W 5% 1 m� 39104.52 2





G-clamp 02014.00 2






What you need:

Complete Equipment Set, Manual on CD-ROM includedCoupled oscillating circuits P2450200


Electricity Electromagnetic Oscillations and Waves

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 184


Electromagnetic Oscillations and Waves Electricity

Interference of microwaves 4.5.04-00

Principle:A microwave beam, after reflectionfrom a metal screen or glass plate,interferes with the primary waves.The wavelength is determined fromthe resultant standing waves.

Intensity distribution during interference of microwaves in the Michelsonarrangement, as a function of the position of the reflection screens.

Tasks:Measurement of the wavelength ofmicrowaves through the productionof standing waves with

1. reflection at the metal screen,

2. plane-parallel plate,

3. the Michelson interferometer.

Microwave transmitter w. klystron 11740.01 1

Microwave receiver 11740.02 1

Microwave receiving dipole 11740.03 1

Microwave power supply, 220 VAC 11740.93 1


Glass plate, 200�300�4 mm 08204.00 2

Screen, metal, 300�300 mm 08062.00 2


G-clamp 02014.00 2










What you need:

Complete Equipment Set, Manual on CD-ROM includedInterference of microwaves 2450400


� Wavelength� Standing wave� Reflection� Transmission� Michelson interferometer

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 185


Principle:Microwaves impinge on a slit andthe edge of a screen. The diffractionpattern is determined on the basis ofdiffraction at these obstacles.

Intensity distribution in the diffraction of the microwaves at the edge of ascreen, parallel to the plane of the screen.

Tasks:Determination of the diffraction pat-tern of the microwave intensity

1. behind the edge of a screen,

2. after passing through a slit,

3. behind a slit of variable width,with a fixed receiving point.


� Fresnel zones� Huygens’ principle� Fraunhofer diffraction� Diffraction at the slit




Screen, metal, 300�300 mm 08062.00 2








G-clamp 02014.00 2




What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction of microwaves P2450500



LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 186



Diffraction and polarization of microwaves 4.5.06-00

XX

X

X

XXX

X X

XX

X

X

X

X

XX

X

X

XX

XX

X

X

XX

X

-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

150

100

50

l = 20 cm

l = 40 cm

l = 30 cm

U in mV

l = W-Soin cm

with lens

without lens

Principle:The equivalence between visible lightand microwaves as special cases ofthe total spectrum of electromag-netic waves can be demonstratedusing diffraction and polarization ofmicrowaves as an example. Thefocusing of microwaves through aplane convex convergent lens isobserved and the focal distance ofthe lens is determined. After that,polarizability of microwaves is dem-onstrated by means of a metallicgrating.

Tasks:1. Measuring the irradiance of the

microwave field behind a conver-ging lens

– along the optical axis

– transversally to the optical axis.

Determination of the focal length ofa synthetic resin converging lens andcomparison of the results with the

Profile of the intensity of radiation.

distribution of irradiance when nolens is used.

2. Measurement of the irradiancetransmitted through a metal grat-ing as a function of the anglebetween the direction of polariza-tion and the grating bars.





Polarisation grid 06866.00 1

Convergent lens, synthetic resin 06872.00 1











H-base -PASS- 02009.55 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedDiffraction and polarization of microwaves P2450600


� Diffraction� Focal point� Linearity� Circularly and elliptically

polarized waves� Transverse waves� Polarizer and Analyzer� Constructive and destructive

interference

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 187


x

xx

xx

x

x

x

xx x xxx

x

x x xx

xx

x

x

x

x

r = 60 cm

0,5

�� = 45°1--4

0 30 60– 60 – 30 �� = 00in

U–Umax

r = 20 cm

1

Principle:The directional characteristic of ahorn antenna is received in two per-pendicular planes by means of areceiving dipole. The law of distancefor the antenna is verified.

Directional characteristic Cu(�, � = 0) of the horn antenna in the polariza-tion plane for different distances.

Tasks:1. Measurement of the directional

characteristic of the horn antennain two perpendicular planes andevaluation of the correspondingdirectivity from the directionalcharacteristic.

2. Determination of the microwaveirradiance I as a function of thedistance r between the receivingdipole and the horn antenna,which verifies the validity of thelaw.


� Horn antenna� Directional characteristic

pattern� Directivity� Law of distance� Phase center






Support rod -PASS-, square, l= 250 mm 02025.55 3





Graduated disk, f. demonstration 02053.02 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedRadiation field of a horn antenna /Microwaves P2450800



LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 188



Frustrated total reflection / Microwaves 4.5.09-00

k1

k2

n1

n2

n1

k1

x

y

kr

�

�

�

�

Principle:In the first part, the transmission andreflection characteristics of glass,acrylic glass and metal are studiedwith a microwave transmitter-receiver pair and are compared toeach other.

In the second part, total reflection ofmicrowaves on a prismatic surface issuppressed by bringing a secondprism with the same refractive indexclose to the first one.

Frustrated total internal reflection.

Tasks:1. Determination of the reflecting

and transmitting characteristics ofglass, acrylic glass and metal.

2. Observation of the effect of frus-trated total reflection and deter-mination of the transmitted irra-diance as a function of distance dto the prismatic surface. Therefractive index of the prismmaterial can be calculated bydetermining the attenuation coef-ficient .




Screen, metal, 300�300 mm 08062.00 2

Glass plate, 200�300�4 mm 08204.00 1

Plexiglas plate, 200�200�4 mm 11613.00 1



Supporting block 105�105�57 mm 02073.00 2

Prism, synthetic resin 06873.00 2


Screened cable, BNC, l =750 mm 07542.11 1


Vernier caliper, plastic 03011.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedFrustrated total reflection / Microwaves P2450900


� Transmission� Reflection� Absorption� Refraction� Phase velocity� Total reflection� Surface waves� Frustrated total reflection� Tunnel effect

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 189


Electricity Handbooks

36 described Experiments

Please ask for a complete equipmentlist Ref. No. 24510

1 Electric Circuits1.1 (13801)The simple circuit

1.2 (13802)Measurement of voltage

1.3 (13803)Measurement of current

1.4 (13804)Conductors and non-conductors

1.5 (13805)Changeover switches and alternateswitches

1.6 (13806)Parallel and series connection of voltagesources

1.7 (13807)The safety fuse

1.8 (13808)The bimetallic switch

1.9 (13809)AND and OR Circuits

2 Electrical Resistance2.1 (13810)Ohm’s Law

2.2 (13811)The resistance of wires – dependence onlength and cross-section

2.3 (13812)The resistance of wires – dependence onmaterial and temperature

2.4 (13813)The resistivity of wires

2.5 (13814)Current strength and resistance with resist. connec. in parallel

2.6 (13815)Current strength and resistance with resist. connec. in series

2.7 (13816)Voltage in a series connection

2.8 (13817)The potentiometer

2.9 (13818)The internal resistance of a voltagesource

3 Electric Power and Work3.1 (13819)The Power and work of electric current

4 Capacitors4.1 (13820)Capacitors in direct current circuits

4.2 (13821)The charging and discharging of a capacitor

4.3 (13822)Capacitors in alternating current circuits

5 Diodes, Part 15.1 (13823)The diode as electrical valve

5.2 (13824)The diode as rectifier

5.3 (13825)The characteristic curve of a silicondiode

5.4 (13826)Properties of solar cells – the depen-dence on the illuminating intensity

5.5 (13827)The characteristic current-voltage curvesof a solar cell

5.6 (13828)Solar cells connected in series and inparallel – characteristic current-voltagecurves and performance

5.7 (13829)Series and parallel connections of solarcells – characteristic current-voltagecurves and power

5.8 (13830)The characteristic curve of a germaniumdiode

6 Transistors, Part 16.1 (13831)The npn transistor

6.2 (13832)The transistor as direct current amplifier

6.3 (13833)The characteristic current-voltage curvesof a transistor

6.4 (13834)The transistor as a switch

6.5 (13835)The transistor as a time-delay switch

6.6 (13836)The p-n-p transistor



7 Transformation of energy7.1 (13967)The transformation of electrical energyinto heat energy7.2 (13968)The transform. of electrical energy intomechanical energy

8 Electrochemistry8.1 (13969)The conductivity of electrolytes8.2 (13970)Voltage and current strength in conductive processes in liquids8.3 (13971)Electrolysis8.4 (13972)Galvanization8.5 (13973)Galvanic cells8.6 (13974)The lead accumulator8.7 (13975)The PEM Electrolyser and PEM Fuel cell8.8 (13976)The PEM Solar-hydrogen model

9 Electromagnetism9.1 (13977)The magnetic effect of a current-carrying conductor9.2 (13978)Lorentz force: A current-carryingconductor in a mag. field9.3 (13979)The electric bell9.4 (13980)A model of an electromagnetic relay9.5 (13981)Controlling with a relay9.6 (13982)The twilight switch9.7 (13983)The galvanometer9.8 (13984)The reed switch

10 Electric motors10.1 (13985)The permanent magnet motor10.2 (13986)The main circuit motor10.3 (13987)The shunt motor10.4 (13988)The synchronous motor

11 Induction11.1 (13989)Induction voltage with a permanentmagnet11.2 (13990)Induction voltage with an electromagnet11.3 (13991)The alternating current generator11.4 (13992)The direct current generator11.5 (13993)Lenzsche’s rule11.6 (13994)The behaviour of a direct current generator under load

12 Transformers12.1 (13995)Voltage transformation

12.2 (13996)Current transformation12.3 (13997)Forces between primary and secondarycoils12.4 (13998)The heavy current transformer

13 Self-induction13.1 (13999)Self-induction on switching on13.2 (14000)Self-induction on switching off13.3 (14001)Coils in alternating current circuits13.4 (14002)Current strength on switching coils onand off

14 Safe working with electrical energy14.1 (14003)Earthing of the power supply line14.2 (14004)The protective conductor system14.3 (14005)The protective break transformer

15 Sensors15.1 (14006)The NTC resistor15.2. (14007)The PTC resistor15.3 (14008)The light dependent resistor (LDR)

16 Diodes, Part 216.1 (14009)The characteristic curve of a Z-diode16.2 (14010)The Z-diode as voltage stabilizer16.3 (14011)The light emitting diode16.4 (14012)The photo diode16.5 (14013)The bridge rectifier16.6 (14014)The filter network

17 Transistors, Part 217.1 (14015)Voltage amplification of a transistor17.2 (14016)Stabilization of the operating point17.3 (14017)Transistor control with light17.4 (14018)Temperature control of a transistor17.5 (14019)Undamped electromagnetic oscillations17.6 (14020)Transistors in a digital circuit 17.7 (14021)The Darlington circuit17.8 (14022)How phototransistors function17.9 (14023)Information transfer through a photoconductor

18 The operational amplifier and applications

18.1 (14024)The differential amplifier18.2 (14025)The digital circuit18.3 (14026)The generation of oscillations

Demonstration Experiments Physics – Electricity /Electronics on the Magnetic Board 1+ 2

Electricity/Electronics on the Magnetic Board 1 • No. 01001.02

Electricity/Electronics on the Magnetic Board 2 • No. 01003.02

LEP 4.1.01-00_4.5.09-00 12.10.2003 17:02 Uhr Seite 190

5Physical Structureof Matter

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 191


Contents

5.1 Physics of the Electron

5.1.01-00 Elementary charge and Millikan experiment


5.1.03-11 Franck-Hertz experiment with Hg-tube


5.1.04-00 Planck’s “quantum of action” from photoelectric effect (line separation by interference filters)


5.1.06-00 Fine structure, one-electron and two-electron spectra


5.1.08-00 Atomic spectra of two-electron systems: He, Hg


5.1.11-00 Stern-Gerlach experiment


5.1.13-00 Electron diffraction

5.2 Radioactivity


5.2.01-11 Half-life and radioactive equilibrium with Cobra3


5.2.03-11 Poisson’s distribution and Gaussian distribution of radioactive decaywith Cobra3 – Influence of the dead time of the counter tube


5.2.21-00 Rutherford experiment


5.2.22-11 Fine structure of the �-spectrum of 241Am with Cobra3


5.2.23-11 Study of the �-energies of 226Ra with Cobra3


5.2.24.11 Energy loss of �-particles in gases with Cobra3


5.2.32-00 �-spectroscopy


5.2.41-11 Law of distance and absorption of gamma or beta rays with Cobra3

5.2.42-01 Energy dependence of the �-absorption coefficient

5.2.42-11 Energy dependence of the �-absorption coefficient with Cobra3


5.2.44-11 Compton effect with Cobra3


5.2.45-11 Internal conversion in 137mBa with Cobra3


Physical Structure of Matter

5.2.46-11 Photonuclear cross-section / Compton scattering cross-section with Cobra3

5.2.47-01 X-ray fluorescence and Moseley’s law5.2.47-11 X-ray fluorescence and Moseley’s law with Cobra3

5.3 Solid-state physics

5.3.01-01 Hall effect in p-germanium5.3.01-11 Hall effect in p-germanium with Cobra35.3.02-01 Hall effect in n-germanium5.3.02-11 Hall effect in n-germanium with Cobra35.3.03-00 Hall effect in metals5.3.04-01 Band gap of germanium5.3.04-11 Band gap of germanium with Cobra3

5.4 X-ray Physics

5.4.01-00 Characteristic X-rays of copper5.4.02-00 Characteristic X-rays of molybdenum5.4.03-00 Characteristic X-rays of iron5.4.04-00 The intensity of characteristic X-rays as a function of anode current

and anode voltage5.4.05-00 Monochromatization of molybdenum X-rays5.4.06-00 Monochromatization of copper X-rays5.4.07-00 K� doublet splitting of molybdenum X-rays / fine structure5.4.08-00 K� doublet splitting of iron X-rays / fine structure5.4.09-00 Duane-Hunt displacement law and Planck's “quantum of action”5.4.10-00 Characteristic X-ray lines of different anode materials /

Moseley's Law; Rydberg frequency and screening constant5.4.11-00 Absorption of X-rays5.4.12-00 K- and L-absorption edges of X-rays /

Moseley's Law and the Rydberg constant5.4.13-00 Examination of the structure of NaCl monocrystals with different

orientations5.4.14-00 X-ray investigation of cubic crystal structures /

Debye-Scherrer powder method5.4.15-00 X-ray investigation of hexagonal crystal structures /

Debye-Scherrer powder method5.4.16-00 X-ray investigation of crystal structures / Laue method5.4.17-00 Compton scattering of X-rays5.4.18-00 X-ray dosimetry5.4.19-00 Contrast medium experiment with a blood vessel model5.4.20-00 Determination of the length and position of an object which cannot

be seen

6.4 Handbooks

X-Ray Experiments

Cobra3 Physics, Chemistry/Biology

5LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 192


Elementary charge and Millikan experiment 5.1.01-00

Physics of the Electron Physical Structure of Matter

1,20E-18

1,00E-18

8,00E-19

6,00E-19

4,00E-19

2,00E-19

0,00E+000,00E+00

2,00E-07 4,00E-07 6,00E-07 8,00E-07 1,00E-07 1,20E-07

r/m

Q/A

s

Principle:Charged oil droplets subjected to anelectric field and to gravity betweenthe plates of a capacitor are acceler-ated by application of a voltage. Theelementary charge is determinedfrom the velocities in the direction ofgravity and in the opposite direction.

Tasks:1. Measurement of the rise and fall

times of oil droplets with variouscharges at different voltages.

2. Determination of the radii and thecharge of the droplets.

Measurements on various droplets for determining the elementary charge bythe Millikan method.


� Electric field� Viscosity� Stokes’ law� Droplet method� Electron charge

Millikan apparatus 09070.00 1

Multi-range meter w. overl. prot. 07021.01 1

Power supply, 0…600 VDC 13672.93 1

Stage micrometer, 1 mm - 100 div. 62046.00 1


Cover glasses 18�18 mm, 50 pcs. 64685.00 1

Commutator switch 06034.03 1







Optional accessories:

Radioactive source, Am-241, 74 kBq 09047.51 1


FlexCam Scientific Pro II 88030.93 1

TV set

What you need:

Complete Equipment Set, Manual on CD-ROM includedElementary charge and Millikan experiment P2510100

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 193



Principle:Electrons are accelerated in anelectric field and enter a magneticfield at right angles to the directionof motion. The specific charge of theelectron is determined from theaccelerating voltage, the magneticfield strength and the radius of theelectron orbit.

Tasks:Determination of the specific chargeof the electron (e/m0) from the pathof an electron beam in crossedelectric and magnetic fields of vari-able strength.

Narrow beam tube 06959.00 1


Power supply, 0...600 VDC 13672.93 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedSpecific charge of the electron – e/m P2510200

Physical Structure of Matter Physics of the Electron


� Cathode rays� Lorentz force� Electron in crossed fields� Electron mass� Electron charge

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 194


Franck-Hertz experiment with Hg-tube 5.1.03-11


Principle:Electrons are accelerated in a tubefilled with mercury vapour.

The excitation energy of mercury isdetermined from the distance be-tween the equidistant minima of theelectron current in a variable oppos-ing electric field.

Example of a Franck-Hertz curve for Hg-gas recorded with T = 180°C.

Tasks:1. To record the counter current

strength Is in a Franck-Hertz tubeas a function of the anode voltageUa.

2. To determine the excitation ener-gy Ea from the positions of thecurrent strength minima or maxi-ma by difference formation.


� Energy quantum� Electron collision� Excitation energy

Franck-Hertz operating unit 09105.99 1

Franck-Hertz Hg-tube on plate 09105.10 1

Franck-Hertz oven 09105.93 1

NiCr-Ni thermocouple 13615.01 1

5-pin connecting cable, for Hg-tube 09105.30 1

Shielded BNC-cable, l = 75 cm 07542.11 1

RS 232 data cable 14602.00 1

Franck-Hertz software 14522.61 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedFranck-Hertz experiment with Hg-tube P2510311

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 195



Principle:Electrons are accelerated in a tubefilled with neon vapour.

The excitation energy of neon is de-termined from the distance betweenthe equidistant minima of the elec-tron current in a variable opposingelectric field.

Example of a Franck-Hertz curve for Ne-gas.

Tasks:1. To record the counter current

strength Is in a Franck-Hertz tubeas a function of the anode voltageUa.

2. To determine the excitation ener-gy Ea from the positions of thecurrent strength minima or maxi-ma by difference formation.

Franck-Hertz operating unit 09105.99 1

Franck-Hertz neon tube with housing 09105.40 1

5-pin connecting cable, for Ne tube 09105.50 1

Shielded BNC-cable, l = 75 cm 07542.11 1

RS 232 data cable 14602.00 1

Franck-Hertz software 14522.61 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedFranck-Hertz experiment with Ne-tube 2510315



� Energy quantum� Quantum leap� Electron collision� Excitation energy

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 196


Planck’s “quantum of action” from photoelectric effect (line separation by interference filters) 5.1.04-00


Principle:A photo-cell is illuminated with lightof different wavelengths. Planck’squantum of action, or Planck’s con-stant (h), is determined from thephotoelectric voltages measured.

Voltage of the photo-cell as a function of the frequency of the irradiatedlight.

Tasks:To determine Planck’s quantum ofaction from the photoelectric volt-ages measured at different wave-lengths.


� External photoelectric effect� Work function� Absorption� Photon energy� Anode� Cathode

Photocell, for h-det., w. housing 06778.00 1



Experiment lamp 6 11615.05 1



Mounting plate R, 32 cm�21 cm 13002.00 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedPlanck’s “quantum of action” from photoelectriceffect (line separation by interference filters) P2510400

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 197



Principle:A photocell is illuminated withmonochromatic light of differentwavelengths. Planck’s quantum ofaction, or Planck’s constant h, isdetermined from the photoelectricvoltages measured.

Voltage of the photo-cell as a function of the frequency of the irradiatedlight.

Photocell, for h-det., w. housing 06778.00 1




Diaphragm holder, attachable 11604.09 2

Slit, adjustable 08049.00 1


Lens, mounted, f = +100 mm 08021.01 1

Mercury high pressure lamp 80 W 08147.00 1









Base f.opt.profile-bench, adjust. 08284.00 3

Turning knuckle f. opt. prof.-bench 08285.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedPlanck’s “quantum of action” from the photoelectriceffect (line separation by defraction grating) P2510500



� External photoelectric effect� Work function� Adsorption� Photon energy

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 198


Fine structure, one-electron and two-electron spectra 5.1.06-00


Principle:The well-known spectral lines of Heare used for calibrating the diffrac-tion spectrometer. The wave-lengthsof the spectral lines of Na, Hg, Cdand Zn are determined using thespectrometer.

Spectrum of sodium.

Tasks:1. Calibration of the spectrometer

using the He spectrum, and thedetermination of the constant ofthe grating;

2. Determination of the spectrum ofNa;

3. Determination of the fine struc-ture splitting.

4. Determination of the most intensespectral lines of Hg, Cd and Zn.


� Diffraction spectrometer� Spin� Angular momentum� Spin-orbital angular

momentum interaction� Multiplicity� Energy level� Excitation energy� Selection rules� Doublets� Parahelium� Orthohelium� Exchange energy� Angular momentum� Singlet and triplet series� Selection rules� Forbidden transition

Spectrometer/goniom. w. vernier 35635.02 1


Spectral lamp He, pico 9 base 08120.03 1

Spectral lamp Na, pico 9 base 08120.07 1


Spectral lamp Cd, pico 9 base 08120.01 1

Spectral lamp Zn, pico 9 base 08120.11 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedFine structure, one-electron and two-electron spectra P2510600

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 199




Brackett-Series

Paschen-Series

Balmer-Series

Lyman-Series

ener

gy le

vel

ioni

zatio

n en

ergy

13.

6 eV

eV

0

–0.9

–1.5

–3.4

–13.6 n = 1

n = 2

n = 3

n = 4

n = �

H�

H�

H�

H�

H�

Principle:The spectral lines of hydrogen andmercury are examined by means of adiffraction grating. The known spec-tral lines of Hg are used to determinethe grating constant. The wavelengths of the visible lines of theBalmer series of H are measured.

Energy level diagram of the H atom.

Tasks:1. Determination of the diffraction

grating constant by means of theHg spectrum.

2. Determination of the visible linesof the Balmer series in the H spec-trum, of Rydberg’s constant and ofthe energy levels.

Spectrum tube, hydrogen 06665.00 1

Spectrum tube, mercury 06664.00 1

Holders for spectral tubes, 1 pair 06674.00 1

Cover tube for spectral tubes 06675.00 1

Connecting cord, 50 KV, 1000 mm 07367.00 2













What you need:

Complete Equipment Set, Manual on CD-ROM includedBalmer series / Determination of Rydberg’s constant P2510700


� Diffraction image of adiffraction grating

� Visible spectral range� Single electron atom� Atomic model according

to Bohr� Lyman-, Paschen-, Brackett-

and Pfund-Series� Energy level� Planck’s constant� Binding energy

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 200


Atomic spectra of two-electron systems: He, Hg 5.1.08-00


Principle:The spectral lines of He and Hg areexamined by means of a diffractiongrating. The wavelengths of the linesare determined from the geometricalarrangement and the diffractiongrating constants.

Measured spectral lines of He/Hg and the corresponding energy-level transi-tions.

Tasks:1. Determination of the wavelengths

of the most intense spectral linesof He.

2. Determination of the wavelengthsof the most intense spectral linesof Hg.


� Parahelium� Orthohelium� Exchange energy� Spin� Angular momentum� Spinorbit interaction� Singlet and triplet series� Multiplicity� Rydberg series� Selection rules� Forbidden transition� Metastable state� Energy level� Excitation energy

Spectrum tube, mercury 06664.00 1

Spectrum tube, helium 06668.00 1

Holders for spectral tubes, 1 pair 06674.00 1

Cover tube for spectral tubes 06675.00 1

Connecting cord, 50 kV, 1000 mm 07367.00 2













What you need:

Complete Equipment Set, Manual on CD-ROM includedAtomic spectra of two-electron systems: He, Hg P2510800

Colour �/nm Transition

red 665 ± 2 3 1D R 2 1P

yellow-orange 586 ± 2 3 3D R 2 3P

green 501 ± 2 3 1D R 2 1P

blue-green 490 ± 2 4 1D R 2 1P

blue 470 ± 3 4 3S R 2 3P

violet 445 ± 1 4 3D R 2 3P

Colour �/nm Transition

yellow 581 ± 1 { 6 1D1 R 6 1P16 3D1 R 6 1P1

green 550 ± 1 7 3S1 R 6 3P1

green 494 ± 2 8 1S1 R 6 1P1

blue 437 ± 2 7 1S R 6 1P1

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 201




Principle:The “Zeeman effect” is the splittingup of the spectral lines of atomswithin a magnetic field. The simplestis the splitting up of one spectral lineinto three components called the“normal Zeeman effect”. The normalZeeman effect is studied using acadmium spectral lamp as a speci-men. The cadmium lamp is submittedto different magnetic flux densitiesand the splitting up of the red cad-mium line (643.8 nm) is investigatedusing a Fabry-Perot interferometer.The evaluation of the results leads toa fairly precise value for Bohr’smagneton.

Tasks:1. Using the Fabry-Perot interferom-

eter and a selfmade telescope thesplitting up of the central line intotwo �-lines is measured in wavenumbers as a function of themagnetic flux density.

Screenshot of software used to measure the diameters of the interferencerings as captured by the CCD-Camera.

2. From the results of point 1. a valuefor Bohr’s magneton is evaluated.

3. The light emitted within the direc-tion of the magnetic field is qual-itatively investigated.

Fabry-Perot interferometer 09050.02 1Cadmium lamp for Zeeman Effect 09050.01 1Electromagnet w/o pole shoes 06480.01 1Pole pieces, drilled, conical 06480.03 1Rotating table for heavy loads 02077.00 1Power supply for spectral lamps 13662.97 1Variable transformer, 25 V AC/20 V DC, 12 A 13531.93 1Capacitor, electrolytic, 22000 µF 06211.00 1Digital multimeter 07134.00 1Optical profile-bench, l = 1000 mm 08282.00 1Base for opt.profile-bench, adjust. 08284.00 2Slide mount for optical profile-bench, h = 30mm 08286.01 5Slide mount for optical profile-bench, h = 80mm* 08286.02 2Lens holder 08012.00 4Lens, mounted, f = +50 mm 08020.01 2Lens, mounted, f = +300 mm 08023.01 1Iris diaphragm 08045.00 1Polarising filter, on stem 08610.00 1Polarization specimen, mica 08664.00 1Connecting cord, l = 25 cm, 32 A, red 07360.01 1Connecting cord, l = 25 cm, 32A , blue 07360.04 1Connecting cord, l = 50 cm, 32 A, red 07361.01 1Connecting cord, l = 50 cm, 32 A, blue 07361.04 1Connecting cord, l = 75 cm, 32 A, red 07362.01 1Connecting cord, l = 100 cm, 32 A, red 07363.01 1Connecting cord, l = 100 cm, 32 A, blue 07363.04 1CCD-Camera for PC incl. measurement software* 88037.00 1

PC with USB interface, Windows 98SE/Windows Me/Windows 2000/Windows XP

*Alternative to CCD-Camera incl. measurement software, two slide mounts,h = 80 mm for the classical version of the Zeeman Effect:Slide mount for opt.profile-bench 08286.00 1Sliding device, horizontal 08713.00 1

What you need:


� Bohr’s atomic model� Quantisation of energy levels� Electron spin� Bohr’s magneton� Interference of

electromagnetic waves� Fabry-Perot interferometer

Swinging arm 08256.00 1Plate holder with tension spring 08288.00 1Screen, with aperture and scale 08340.00 1Slide mount for opt.profile-bench, h = 80 mm 08286.02 1

Complete Equipment Set, Manual on CD-ROM includedZeeman effect with CCD-Camera incl. measurement software P2511005

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 202


Stern-Gerlach experiment 5.1.11-00


Principle:A beam of potassium atoms generat-ed in a hot furnace travels along aspecific path in a magnetic two-wirefield. Because of the magnetic mo-ment of the potassium atoms, thenonhomogeneity of the field appliesa force at right angles to the direc-tion of their motion. The potassiumatoms are thereby deflected fromtheir path.

By measuring the density of thebeam of particles in a plane of de-tection lying behind the magnetic

field, it is possible to draw conclu-sions as to the magnitude and direc-tion of the magnetic moment of thepotassium atoms.

Tasks:1. Recording the distribution of the

particle beam density in the de-tection plane in the absence of theeffective magnetic field.

2. Fitting a curve consisting of astraight line, a parabola, and an-other straight line, to the experi-

Ionization current as a function of position (u) of detector with large excita-tion currents in the magnetic analyser.

mentally determined special distri-bution of the particle beam density.

3. Determining the dependence ofthe particle beam density in thedetection plane with different val-ues of the non-homogeneity ofthe effective magnetic field.

4. Investigating the positions of themaxima of the particle beam den-sity as a function of the non-ho-mogeneity of the magnetic field.


� Magnetic moment� Bohr magneton� Directional quantization� g-factor� Electron spin� Atomic beam� Maxwellian velocity

distribution� Two-wire field

Stern-Gerlach apparatus 09054.88 1High-vacuum pump assembly 09059.93 1Vacuum pump, two-stage 02751.93 1Matching transformer 09054.04 1Electromagnet w/o pole shoes 06480.01 1Pole piece, plane 06480.02 2Rheostat, 10 �, 5.7 A 06110.02 2Commutator switch 06034.03 1Voltmeter, 0.3-300 VDC, 10-300 VAC 07035.00 2Ammeter, 1 mA - 3 A DC/AC 07036.00 2Meter, 10/30 mV, 200 deg.C 07019.00 1Moving coil instrument 11100.00 1Range multiplier, vacuum 11112.93 1Cristallizing dish, boro 3.3, 2300 ml 46246.00 1DC measuring amplifier 13620.93 1Power supply, universal 13500.93 1Rubber tubing, vacuum, i.d.6 mm 39286.00 1Potassium ampoules, set of 6 09054.05 1Isopropyl alcohol, 1000 ml 30092.70 1Connecting cord, l = 100 mm, red 07359.01 1Connecting cord, l = 250 mm, yellow 07360.02 4Connecting cord, l = 250 mm, blue 07360.04 1Connecting cord, l = 250 mm, red 07360.01 1Connecting cord, l = 500 mm, red 07361.01 2Connecting cord, l = 500 mm, blue 07361.04 2Connecting cord, l = 500 mm, yellow 07361.02 2Connecting cord, l = 750 mm, red 07362.01 1Connecting cord, l = 750 mm, blue 07362.04 1Connecting cord, l = 750 mm, yellow 07362.02 2Connecting cord, l = 1000 mm, yellow 07363.02 1Connecting cord, l = 2000 mm, yellow 07365.02 2Steel cylinder, nitrogen, 10 l, full 41763.00 1Reducing valve f. nitrogen 33483.00 1Steel cylinder rack, mobile 54042.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedStern-Gerlach experiment P2511100

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 203



Principle:The g-factor of a DPPH (Diphenyl-pikrylhydrazyl) and the half-width ofthe absorption line are determined,using the ESR apparatus.

Electron spin resonance (ESR), model experiment.

Tasks:With ESR on a DPPH specimen deter-mination of

1. the g-factor of the free electron,and

2. the half-width of the absorptionline.

ESR resonator with field coils 09050.00 1

ESR power supply 09050.93 1









Options:



What you need:

Complete Equipment Set, Manual on CD-ROM includedElectron spin resonance P2511200



� Zeeman effect� Energy quantum� Quantum number� Resonance� g-factor� Landé factor

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:31 Uhr Seite 204


Electron diffraction 5.1.13-00


Principle:Fast electrons are diffracted from apolycrystalline layer of graphite: in-terference rings appear on a fluores-cent screen. The interplanar spacingin graphite is determined from thediameter of the rings and the accel-erating voltage.

Tasks:1. To measure the diameter of the

two smallest diffraction rings atdifferent anode voltages.

2. To calculate the wavelength of theelectrons from the anode voltages.

3. To determine the interplanar spac-ing of graphite from the relation-ship between the radius of thediffraction rings and the wave-length.


� Bragg reflection� Debye-Scherrer method� Lattice planes� Graphite structure� Material waves� De Broglie equation

Electron diffr. tube a. mounting 06721.00 1



Connecting cord, 50 kV, 500 mm 07366.00 1

Power supply, 0...600 VDC 13672.93 1








What you need:

Complete Equipment Set, Manual on CD-ROM includedElectron diffraction P2511300

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 205



Principle:The half-life of a Ba-137 m daughtersubstance eluted (washed) out of aCa-137 isotope generator is meas-ured directly and is also determinedfrom the increase in activity afterelution.

Tasks:1. To record the counting rate as a

function of the counter tube volt-age (counter tube characteristic)when the isotope generator activ-ity is constant (radioactive equi-librium).

Logarithmic plot of the counting rate of the eluted daughter substance as afunction of time.

2. To measure the activity of the iso-tope generator as a function oftime immediately after elution.

3. To measure the activity of a fresh-ly eluted solution of Ba-137 m asa function of time.

Isotope generator Cs-137, 400 kBq 09047.60 1

Pulse rate meter 13622.93 1


Counter tube, type A, BNC 09025.11 1


Aluminium, sheet, 1�20�200mm, 5 pcs 31074.00 1






Test tube, 160�16 mm, 100 pcs 37656.10 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedHalf-line and radioactive equilibrium P2520101

Physical Structure of Matter Radioactivity


� Parent substance� Daughter substance� Rate of decay� Disintegration or decay

constant� Counting rate� Half life� Disintegration product

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 206


Half-life and radioactive equilibrium with Cobra3 5.2.01-11

Radioactivity Physical Structure of Matter

Principle:The half-life of a Ba-137 m daughtersubstance eluted (washed) out of aCa-137 isotope generator is meas-ured directly and is also determinedfrom the increase in activity afterelution.

Logarithmic plot of the counting rate of Ba-137m’s decay; counting rate as afunction of time, with the regression line.

Tasks:1. To record the counting rate as a

function of the counter tube volt-age (counter tube characteristic)when the isotope generator activ-ity is constant (radioactive equi-librium).

2. To measure the activity of the iso-tope generator as a function oftime immediately after elution.

3. To measure the activity of a fresh-ly eluted solution of Ba-137 m asa function of time.







Cobra3 Radioactivity Software 14506.61 1

Counter tube module 12106.00 1

Unit-construction plate for radioactivity 09200.00 1

Counter tube holder, magnet held 09201.00 1

Plate holder, magnet held 09203.00 1

Source holder, magnet held 09202.00 1

Counter tube, type A 09025.11 1


Test tube, d = 12mm, l = 100mm, 1 piece of 36307.10 (1)

Rubber stopper 14.4/20 without hole 39253.00 1

Isotope generator Cs-137/Ba, 400 kBq 09047.60 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedHalf-life and radioactive equilibriumwith Cobra3 P2520111

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 207



Principle:The particle current (quantum cur-rent) given off by the radioactive ra-diator decreases in the course oftime. The radioactive substance de-cays according to a certain law (lawof deterioration).

If the radioactive substance consistsof only one radiating component inparticular, then the quantity of itsmaterial decreases exponentiallywith time.

Increase in the counting rate due to phase separation in the sample vial.







Counter tube holder, magnet held 09201.00 1

Plate holder, magnet held 09203.00 1



Isotope generator U-238, Pa-234, 45 kBq 09048.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedLaw of radioactive decay with Cobra3 P2520211





LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 208


Poisson’s distribution and Gaussian distribution of radioactive decay with Cobra3 5.2.03-11– Influence of the dead time of the counter tube


Principle:1) The aim of this experiment is toshow that the number of pulsescounted during identical time inter-vals by a counter tube which bears afixed distance to a long-lived radia-tion emitter correspond to a Pois-son’s distribution. A special charac-teristic of the Poisson’s distributioncan be observed in the case of asmall number of counts n <20: Thedistribution is unsymmetrical, i. e.the maximum can be found among

smaller numbers of pulses than themean value. In order to show thisunsymmetry the experiment is car-ried out with a short counting periodand a sufficiently large gap betweenthe emitter and the counter tube sothat the average number of pulsescounted becomes sufficiently small.

2) Not only the Poisson’s distribution,but also the Guassian distributionwhich is always symmetrical is verysuitable to approximate the pulsedistribution measured by means of along-lived radiation emitter and a

Pulse rate distribution for high pulse rate (248 pulses/s) with an adaptedGaussian curve (left window) and a Poisson’s curve (right window).

counter tube arranged with a con-stant gap between each other. Apremise for this is a sufficiently highnumber of pulses and a large sam-pling size.

The purpose of the following experi-ment is to confirm these facts and toshow that the statistical pulse distri-bution can even be be approximatedby a Guassian distribution, when(due to the dead time of the countertube) counting errors occur leadingto a distribution which deviates fromthe Poisson’s distribution.


� Poisson’s distribution� Gaussian distribution� Standard deviation� Expected value of pulse rate� Different symmetries of

distributions� Dead time� Recovering time and

resolution time of a countertube





Cobra3 Radioactivity software 14506.61 1




Counter holder, magnet held 09201.00 1


Plate holder on fixing magnet 09203.00 1

Americium-241 source, 370 kBq 09090.11 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedPoisson’s distribution and Gaussian distribution of radioactive decay with Cobra3 – Influence of the dead time of the counter tube P2520311

3) If the dead time of the countertube is no longer small with regardto the average time interval betweenthe counter tube pulses, the fluctua-tion of the pulses is smaller than inthe case of a Poisson’s distribution.In order to demonstrate these factsthe limiting value of the mean value(expected value) is compared to thelimiting value of the variance bymeans of a sufficiently large sam-pling size.

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 209



Principle:Radioactivity is a subject in our soci-ety which has been playing animportant role throughout politics,economy and media for many yearsnow. The fact that this radiation can-not be seen or felt by the humanbeing and that the effects of thisradiation are still not fully exploredyet, causes emotions like no otherscientific subject before.

The high-performance diffusioncloud chamber serves for making the

tracks of cosmic and terrestrial radi-ation visible so that a wide range ofnatural radiation types can be iden-tified. Furthermore, the diffusioncloud chamber offers the opportu-nity to carry out physical experi-ments with the aid of artificial radi-ation sources.

Experimental set-up: deflection of �-particles.

Tasks:1. Determination of the amount of

background radiation

2. Visualisation of �, �, �-particlesand mesons

3. Visualisation of the Thorium(Radon) decay

4. Deflection of �--particles in amagnetic field

Diffusion cloud chamber PJ45, 230 V 09046.93 1

Isopropyl alcohol, 1000 ml 30092.70 2

Thorium-source 09043.41 1

Radioactive source, Sr-90, 74 kBq 09047.53 1

Support base “PASS” 02005.55 1


Support rod, stainl. steel., l = 250 mm 02031.00 1

Right angle clamp “PASS” 02040.55 1


Holder for dynamometer 03068.04 1

Scale for demonstration board 02153.00 1

Accessory set for beta deflection 09043.52 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedVisualisation of radioactive particles /Diffusion cloud chamber P2520400



� �, �, �-particles� � deflection� Ionising particles� Mesons� Cosmic radiation� Radioactive decay� Decay series� Particle velocity� Lorentz force

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 210


Rutherford experiment 5.2.21-00


Principle:The relationship between the angleof scattering and the rate of scatter-ing of �-particles by gold foil isexamined with a semiconductordetector. This detector has a detec-tion probability of 1 for �-particlesand virtually no zero effect, so thatthe number of pulses agrees exactlywith the number of �-particles strik-ing the detector.

In order to obtain maximum possiblecounting rates, a measurementgeometry is used which dates back

to Chadwick. It is also possible in thiscase to shift the foil and source in anaxial direction (thus deviating fromChadwick’s original apparatus), sothat the angle of scattering can bevaried over a wide range.

In addition to the annular diaphragmwith gold foil, a second diaphragmwith aluminium foil is provided inorder to study the influence of thescattering material on the scatteringrate.

Counting rate for gold as a function of .1(r2)2sin4(

2)

Tasks:1. The particle rates are measured at

different angles of scatteringbetween about 20 ° and 90 °. Themeasurements are compared withthe particle rates calculated bymeans of the Rutherford theoryfor the measurement geometryused.

2. The particle rates are measured inthe case of scattering by alumin-ium and gold with identical anglesof scattering in each case. Theratio of the two particle rates iscompared with the particle ratecalculated from Rutherford’s scat-tering equation.


� Scattering� Angle of scattering� Impact parameter� Central force� Coulomb field� Coulomb forces� Rutherford atomic model� Identity of atomic number

and charge on the nucleus

Annular diaphragm w. gold foil 09103.02 1

Annular diaphragm w. alumin. foil 09103.03 1

U-magnet, large 06320.00 1

Container f. nuclear phys. expts. 09103.00 1


Alpha detector 09100.00 1

Pre-amplifier f. alpha detector 09100.10 1

Impulse height analyser 13725.93 1

Geiger-Müller-Counter 13606.99 1


Hand held mano-/ barometer 07136.00 1

Pressure sensor 1 07136.01 1

Diaphragm pump, two-stage 08163.93 1


Hose connector 47518.03 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedRutherford experiment P2522100

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 211



Principle:The �-spectrum of an open 241Am-emitter is measured with a semi-conductor �-detector, maximum usebeing made in this case of the reso-lution capacity of the pulse heightanalyzer. Use is made for this pur-pose of the “Zoom” function, whichis an additional amplification stagehaving in the effect that only thatproportion of the pulses exceedingthe threshold voltage of 5 V under-goes further processing. The pulsepeaks above this threshold areamplified 5 times and restricted to amaximum of 10 V.

Measured �-spectrum of 241Am.

Tasks:1. The spectrum of an open 241Am-

emitter is recorded with the xyt-recorder at the maximum resolu-tion capacity of the measurementlayout, using automatic windowmovement. The energy of the twopeaks preceding the principal peakis calculated. The principal peak,corresponding to a particle energyof 5.486 MeV, is used for calibra-tion purposes.

2. The resolution capacity of themeasurement layout is measuredfrom the half-life width of theprincipal peak.

Americium-241 source, 3.7 kBq 09090.03 1





xyt recorder 11416.97 1









Cable connector BNC, 50 � 07542.09 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedFine structure of the �-spectrum of 241Am P2522201



� Energy level diagram (decay diagram)

� Transition probability� Excited nuclear states� �-emission� Connection between the fine

structure of the �-spectrumand the accompanying �-spectrum

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 212


Fine structure of the �-spectrum of 241Am with Cobra3 5.2.22-11


Principle:The �-spectrum of an open 241Am-emitter is measured with a semi-conductor �-detector, maximum usebeing made in this case of the reso-lution capacity of the pulse heightanalyzer. Use is made for this pur-pose of the “Zoom” function, whichis an additional amplification stagehaving in the effect that only thatproportion of the pulses exceedingthe threshold voltage of 5 V under-goes further processing. The pulsepeaks above this threshold areamplified 5 times and restricted to amaximum of 10 V.

Tasks:1. The spectrum of an open 241Am-

emitter is recorded with the xyt-recorder at the maximum resolu-tion capacity of the measurementlayout, using automatic windowmovement. The energy of the twopeaks preceding the principal peakis calculated. The principal peak,corresponding to a particle energyof 5.486 MeV, is used for calibra-tion purposes.

Measured Alpha-spectrum of Am-241.

2. The resolution capacity of themeasurement layout is measuredfrom the half-life width of theprincipal peak.


� Energy level diagram (decaydiagram)

� Transition probability� Excited nuclear states� �-emission� Connection between the fine

structure of the �-spectrumand the accompanying �-spectrum









Oscilloscope, 30 MHz, 2channels 11459.95 1













What you need:

Complete Equipment Set, Manual on CD-ROM includedFine structure of the �-spectrum of 241Amwith Cobra3 P22522211

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 213



Principle:An �-spectrometer, consisting of asilicon surface barrier layer detector,a preamplifier, a pulse height analyz-er and a recording device for regis-tration of the spectra is calibrated bymeans of an open �-emitter ofknown �-energy (241Am).

The energy spectrum of a radiumsource which is in equilibrium withits decay products, is recorded and

evaluated. The �-energies found inthis way are allocated to the corre-sponding nuclides of the radiumdecay series.

Tasks:1. The �-spectrum of the 226Ra is

recorded, the settings of the pulseanalyzer (amplification) andrecorder (x and y input sensitivity)being selected so as to make bestpossible use of the recordingwidth.

2. The calibration spectrum of theopen 241Am-emitter is recorded atthe same settings.

246Ra pulse height spectrum including the 241Am calibration line.

3. The �-energies corresponding tothe individual peaks of the �-spectrum of the radium are calcu-lated and, on the assumption of aconstant energy loss in the sourcecovering, the �-active nuclides ofthe radium decay series corre-sponding to the individual peaksare determined on the basis of thevalues in the literature.


Source Ra-226, 3.7 kBq 09042.03 1

















What you need:

Complete Equipment Set, Manual on CD-ROM includedStudy of the �-energies of 226Ra P2522301



� Decay series� Radioactive equilibrium� Isotopic properties� Decay energy� Particle energy� Potential well model of the

atomic nucleus� Tunnel effect� Geiger-Nuttal law� Semiconductor� Barrier layer

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 214


Study of the �-energies of 226Ra with Cobra3 5.2.23-11


Principle:An �-spectrometer, consisting of asilicon surface barrier layer detector,a preamplifier, a pulse height analyz-er and a recording device for regis-tration of the spectra is calibrated bymeans of an open �-emitter ofknown �-energy (241Am).

The energy spectrum of a radiumsource which is in equilibrium withits decay products, is recorded and

evaluated. The �-energies found inthis way are allocated to the corre-sponding nuclides of the radiumdecay series.

Tasks:1. The �-spectrum of the 226Ra is

recorded, the settings of the pulseanalyzer (amplification) andrecorder (x and y input sensitivity)being selected so as to make bestpossible use of the recordingwidth.

2. The calibration spectrum of theopen 241Am-emitter is recorded atthe same settings.

226Ra pulse rate dependence of pulse height.

3. The �-energies corresponding tothe individual peaks of the �-spectrum of the radium are calcu-lated and, on the assumption of aconstant energy loss in the sourcecovering, the �-active nuclides ofthe radium decay series corre-sponding to the individual peaksare determined on the basis of thevalues in the literature.


� Decay series� Radioactive equilibrium� Isotopic properties� Decay energy� Particle energy� Potential well model of the

atomic nucleus� Tunnel effect� Geiger-Nuttal law� Semiconductor� Barrier layer


Source Ra-226, 3.7 kBq 09042.03 1





















What you need:

Complete Equipment Set, Manual on CD-ROM includedStudy of the �-energies of 226Ra with Cobra3 P2522311

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 215



Principle:A study is made of the connectionbetween the energy E of �-particlesand the path x travelled by them inair at standard pressure. The meas-urements recorded enable the diffe-rencial energy loss dE/dx to be cal-culated as a function of x. Toimprove the measurement accuracyand to exclude the influence of dif-ferent measurement geometries, themeasurements are carried out in avessel with a fixed distance sbetween the source and the detector,the pressure p being varied insteadof the intervening distance. The pathx, at which the same energy losswould occur under standard pressure(1013 hPa)*, is calculated from theformula:

x = s · .

In the final stage, the influence ofthe type of gas (He, N2, CO2) on theenergy loss of �-particles is calculat-ed using the same measuring layout.

P1013 hPa

Tasks:1. The spectrum of a covered 241Am

source is measured at a fixed dis-tance s as a function of the pres-sure p. The distance s is selectedin such a way as to correspond tothe maximum range at the highestpressure measurable with themanometer used. The energy cor-responding to the central points ofthe individual spectra are deter-mined (after calibration of themeasurement layout with an open241Am-emitter, see 3.) and plottedas a function of the distance xconverted to a 1013 hPa basis.Using this function, the differen-tial energy loss (–dE/dx) is thencalculated as a function of x andagain plotted on the graph.

2. The spectrum of the source usedin 1. is measured initially underthe same geometric conditionsunder vacuum and subsequentlywith the vessel filled with helium,nitrogen or carbon dioxide, ineach case under identical pres-sures. The different energy lossvalues are compared with theelectron concentration in the par-ticluar gas.

3. The mean energy with which the�-particles leave the coveredamericium source is determinedby calibration against the openamericium emitter (E = 5.485MeV). (This value is required forthe evaluation in 1.)















Compressded gas, helium, 12 l 41772.03 1

Compressed gas, nitrogen, 12 l 41772.04 1

Compressed gas, CO2, 12 l 41772.06 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedEnergy loss of �-particles in gases P2522401



� Range� Range dispersion� Mean free path length� Mean ionization energy of

gas atoms� Mean energy loss of

�-particles per collision� Differencial energy loss� Bethe formula� Electron concentration in

gases

* 1 hPa � 1 mbar

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 216


Energy loss of �-particles in gases with Cobra3 5.2.24-11


Principle:A study is made of the connectionbetween the energy E of �-particlesand the path x travelled by them inair at standard pressure. The meas-urements recorded enable the diffe-rencial energy loss dE/dx to be cal-culated as a function of x.

Tasks:1. The spectrum of a covered 241Am

source is measured at a fixed dis-tance s as a function of the pres-sure p. The distance s is selectedin such a way as to correspond tothe maximum range at the highestpressure measurable with themanometer used. The energy cor-responding to the central points ofthe individual spectra are deter-mined (after calibration of themeasurement layout with an open241Am-emitter, see 3.) and plottedas a function of the distance xconverted to a 1013 hPa basis.Using this function, the differen-tial energy loss (–dE/dx) is thencalculated as a function of x andagain plotted on the graph.

2. The spectrum of the source usedin 1. is measured initially underthe same geometric conditionsunder vacuum and subsequentlywith the vessel filled with helium,nitrogen or carbon dioxide, ineach case under identical pres-sures. The different energy lossvalues are compared with theelectron concentration in the par-ticluar gas.

3. The mean energy with which the�-particles leave the coveredamericium source is determinedby calibration against the openamericium emitter (E = 5.485MeV). (This value is required forthe evaluation in 1.)


� Range� Range dispersion� Mean free path length� Mean ionization energy of

gas atoms� Mean energy loss of

�-particles per collision� Differencial energy loss� Bethe formula� Electron concentration in

gases

















Stopcock, 3-way, t-shaped. glass 36731.00 1


Compressded gas, helium, 12 l 41772.03 1

Compressed gas, nitrogen, 12 l 41772.04 1

Compressed gas, CO2, 12 l 41772.06 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedEnergy loss of �-particles in gaseswith Cobra3 P2522411

Influence of the type of gas on the energy loss of �-particles.

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:32 Uhr Seite 217



Principle:The attenuation of an electron parti-cle stream passing through a materi-al layer depends both on the thick-ness of the layer and on the masscoverage, resp. the “mass per unitarea”. It will be shown that the parti-cle flux consisting of electrons of aparticular energy distribution de-creases with the “mass per unit area”.As electron source, a radioactivesample of Sr90 is used.

Tasks:1. The �-counting rates are meas-

ured as a function of the absorberthickness using different absorb-ing materials such as aluminium(AL), glass (GL), hard paper (HP),and typing paper (TP).

Counting rate I as a function of absorber thickness.

2. The attenuation coefficients areevaluated for the four absorbingmaterials and plotted as a func-tion of the density.


Geiger-Müller Counter 13606.93 1




Base plate for radioactivity 09200.00 1

Supports f. base 09200.00, 2 pcs 09200.01 1

Counter tube holder on fix. magn. 09201.00 1


Source holder on fixing magnet 09202.00 1


Absorption plates f. beta-rays 09024.00 1

Cover glasses 22�40 mm, 50 p 64688.00 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedElectron absorption P2523100



� Density� Counter tube� Radioactive decay� Attenuation coefficient� Mass coverage

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:33 Uhr Seite 218


�-spectroscopy 5.2.32-00


Principle:The radiation of �-unstable atomicnuclei is selected on the basis of itspulses in a magnetic transverse field,using a diaphragm system. The rela-tionship between coil current andparticle energy is determined for cal-ibration of the spectrometer and thedecay energy of the �-transition isobtained in each case from the �–-spectra.

�-spectrum of 90Sr.

Tasks:1. Energy calibration of the magnet-

ic spectrometer.

2. Measurement of the �-spectra of90Sr and 22Na.

3. Determination of the decay energyof the two isotopes.


� �–-decay� �+-decay� Electron capture� Neutrino� Positron� Decay diagram� Decay energy� Resting energy� Relativistic Lorentz equation

Beta-spectroscope 09104.00 1

Iron core, solid, 25 mm long 06490.01 1




Coil, 600 turns 06514.01 1

Radioactive source, Na-22, 74 kBq 09047.52 1











What you need:

Complete Equipment Set, Manual on CD-ROM included�-spectroscopy P2523200

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:33 Uhr Seite 219



Principle:The inverse square law of distance isdemonstrated with the gamma radi-ation from a 60Co preparation, thehalf-value thickness and absorption

coefficient of various materialsdetermined with the narrow beamsystem and the corresponding massattenuation coefficient calculated.

Impulse counting rate N.

as a function of the thickness d of the absorber.

Tasks:1. To measure the impulse counting

rate as a function of the distancebetween the source and the coun-ter tube.

2. To determine the half-value thick-ness d1/2 and the absorption coef-ficient � of a number of materialsby measuring the impulse count-

Radioactive sources, set 09047.50 1

Absorption plates for �-radiation 09024.00 1


Counter holder, magnet held 09202.00 1


Plate holder for demonstration boardwith magnet 09204.00 1




Geiger-Müller Counter 13606.99 1

Absorption material, lead 09029.01 1

Absorption material, Plexiglas 09029.04 1

Absorption material, iron 09029.02 1

Absorption material, concrete 09029.05 1

Absorption material, aluminium 09029.03 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedLaw of distance and absorption of gammaor beta rays P2524101



� Radioactive radiation� Beta-decay� Conservation of parity� Antineutrino� Gamma quanta� Half-value thickness� Absorption coefficient� Term diagram� Pair formation� Compton effect� Photoelectric effect� Conservation of angular

momentum� Forbidden transition� Weak interaction� Dead time

ing rate as a function of the thick-ness of the irradiated material.Lead, iron, aluminium, concreteand Plexiglas are used as absorb-ers.

3. To calculate the mass attenuationcoefficient from the measuredvalues.

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:33 Uhr Seite 220


Law of distance and absorption of gamma or beta rays with Cobra3 5.2.41-11


Principle:The inverse square law of distance isdemonstrated with the gamma radi-ation from a 60Co preparation, thehalf-value thickness and absorption

coefficient of various materialsdetermined with the narrow beamsystem and the corresponding massattenuation coefficient calculated.

Tasks:1. To measure the impulse counting

rate as a function of the distancebetween the source and the coun-ter tube.

2. To determine the half-value thick-ness d1/2 and the absorption coef-ficient � of a number of materialsby measuring the impulse count-

Attenuation coefficient � of different materials as a function of the materi-al density � (from left to right: Plexiglas®, concrete, aluminium, iron, lead).

ing rate as a function of the thick-ness of the irradiated material.Lead, iron, aluminium, concreteand Plexiglas are used as absorb-ers.

3. To calculate the mass attenuationcoefficient from the measuredvalues.


� Radioactive radiation� Beta-decay� Conservation of parity� Antineutrino� Gamma quanta� Half-value thickness� Absorption coefficient� Term diagram� Pair formation� Compton effect� Photoelectric effect� Conservation of angular

momentum� Forbidden transition� Weak interaction� Dead time

Cobra3 BASIC-UNIT 12150.00 1






Counter tube, magnet held 09201.00 1


Plate holder for demonstration boardwith magnet 09204.00 1





Absorption plates for �-radiation 09024.00 1


Absorption material, iron 09029.02 1


Absorption material, Plexiglas® 09029.04 1

Absorption material, concrete 09029.05 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedLaw of distance and absorption of gammaor beta rays with Cobra3 P2524101

µcm

�

g cm

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:33 Uhr Seite 221


5.2.42-01 Energy Dependence of the �-absorption Coefficient

Principle:The intensity of �-radiation decreas-es when it passes through solid mat-ter. The attenuation can be the resultof Compton scattering, the photoeffect or the pair production. Anabsorption coefficient can be attrib-uted to each of the three phenome-na. These absorption coefficients, aswell as the total absorption, arehighly energy-dependent. The energydependence of the total absorptioncoefficient for aluminium in therange below 1.3 MeV is verified.

Tasks:1. For each of the emitting isotopes

Na22, Cs137 and Am241 the �-spec-trum is traced and a tresholdenergy, Ethres, just below thephoto-peak in the high energyrange determined.

2. Using the scintillation counter inconjunction with the pulse heightanalyser as a monochromator, the�-intensity is measured as a func-tion of the thickness of differentaluminium layers. The three �-emitting isotopes are used succes-sively as the source, assuming thatthe energy of the emitted �-radi-ation is known.

Gamma-intensity as a function of absorber thickness with the gamma ener-gy as parameter.



Source Cs-137, 37 kBq 09096.01 1


Gamma detector 09101.00 1

Operating unit f. gamma detector 09101.93 1




Lab jack 02074.00 1


High-voltage connecting cable 09101.10 1

Pulse height analyser 13725.93 1







Adapter,BNC-socket/4 mm plug pair 07542.27 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedEnergy Dependence of the �-absorptionCoefficient P2524201



� Compton scattering� Photo effect� Pair production� Absorption coefficient� Radioactive decay� �-spectroscopy

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:33 Uhr Seite 222


Energy Dependence of the �-absorption Coefficient with Cobra3 5.2.42-11


Principle:The intensity of �-radiation decreas-es when it passes through solid mat-ter. The attenuation can be the resultof Compton scattering, the photoeffect or the pair production. Anabsorption coefficient can be attrib-uted to each of the three phenome-na. These absorption coefficients, aswell as the total absorption, arehighly energy-dependent. The energydependence of the total absorptioncoefficient for aluminium in therange below 1.3 MeV is verified.

Total gamma-absorption coefficient as a function of the energy.

Tasks:1. For each of the emitting isotopes

Na22, Cs137 and Am241 the �-spec-trum is traced and a tresholdenergy, Ethres, just below thephoto-peak in the high energyrange determined.

2. Using the scintillation counter inconjunction with the pulse heightanalyser as a monochromator, the�-intensity is measured as a func-tion of the thickness of differentaluminium layers. The three �-emitting isotopes are used succes-sively as the source, assuming thatthe energy of the emitted �-radi-ation is known.


� Compton scattering� Photo effect� Pair production� Absorption coefficient� Radioactive decay� �-spectroscopy



Source Cs-137, 37 kBq 09096.01 1









Cobra3 Radioactivity software 14506.61 1





Lab jack 02074.00 1










What you need:

Complete Equipment Set, Manual on CD-ROM includedEnergy Dependence of the �-absorptionCoefficient with Cobra3 2524211

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:33 Uhr Seite 223



Principle:The energy of scattered �-radiationis measured as a function of theangle of scatter. The Compton wave-length is determined from the mea-sured values.

Calibration diagram; plot of peaks of known energy (x = height of pulses in mm).

Tasks:1. Calibrate the measuring set-up

with the aid of a Cs-137 calibrat-ing source (37 kBq), an Am-241source (370 kBq) and a Na-22source (74 kBq).

2. Measure the energy of the Cs-137661.6 keV peaks scattered at dif-ferent angles and calculate theCompton wavelength from thereadings taken.



Source CS-137, 37 kBq 09096.01 1

Radioact. source, Cs-137, 18.5 MBq 09096.20 1



Screen. cylinder f. gamma detector 09101.11 1


Rod, iron, d 25 mm, l = 200 mm 09101.13 1




Lead block, 200�100�50 mm 09029.11 1

Lead brick with hole 09021.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedCompton effect P2524401



� Corpuscle� Scattering� Compton wavelength� �-quanta� De Broglie wavelength� Klein-Nishina formula

LEP 5.1.01-00_5.2.44-01 12.10.2003 17:33 Uhr Seite 224


Compton effect with Cobra3 5.2.44-11

Radioactivity Physical structure of matter

Principle:The energy of scattered �-radiationis measured as a function of theangle of scatter. The Compton wave-length is determined from the mea-sured values.

Energy of known peaks as a function of the pulse height.

Tasks:1. Calibrate the measuring set-up

with the aid of a Cs-137 calibrat-ing source (37 kBq), an Am-241source (370 kBq) and a Na-22source (74 kBq).

2. Measure the energy of the Cs-137661.6 keV peaks scattered at dif-ferent angles and calculate theCompton wavelength from thereadings taken.


� Corpuscle� Scattering� Compton wavelength� �-quanta� De Broglie wavelength� Klein-Nishina formula



Source CS-137, 37 kBq 09096.01 1

Radioact. source, Cs-137, 18.5 MBq 09096.20 1



Screen. cylinder f. gamma detector 09101.11 1


Rod, iron, d = 25 mm, l = 200 mm 09101.13 1








Lead block, 200�100�50 mm 09029.11 1

Lead brick with hole 09021.00 1





What you need:

Complete Equipment Set, Manual on CD-ROM includedCompton effect with Cobra3 P2524411

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 225



Principle:The radiation emitted during thedecay of the 137Cs isotope is mea-sured with a scintillation detectorand the energy spectrum determinedwith a pulse height analyzer. Thespectrum contains fractions due to a

�-transition and fractions originat-ing from a characteristic X-ray radi-ation. The areas of the fractions inquestion are determined and theconversion factor obtained fromthem.

�-spectrum of 137Cs.

Tasks:1. Measurement of the �-spectrum

of 137Cs using a scintillation de-tector.

2. Determination of the conversionfactor of the 137mBa excited nu-cleus.

Source Cs-137, 37 kBq 09096.01 1














What you need:

Complete Equipment Set, Manual on CD-ROM includedInternal conversion in 137mBa P2544501

Physical structure of matter Radioactivity


� �-radiation� Nuclear transitions� Transition probability� Duration� Metastable states� Isotopic spin quantum

numbers� Rules governing selection� Multipole radiation� Isomeric nuclei� Photonuclear reaction� Conversion electron� Characteristic X-ray radiation� Scintillation detectors

N·

sec–1

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 226


Internal conversion in 137mBa with Cobra3 5.2.45-11


Principle:The radiation emitted during thedecay of the 137Cs isotope is mea-sured with a scintillation detectorand the energy spectrum determinedwith a pulse height analyzer. Thespectrum contains fractions due to a

�-transition and fractions originat-ing from a characteristic X-ray radi-ation. The areas of the fractions inquestion are determined and theconversion factor obtained fromthem.

�-spectrum of 137Cs. F_x corresponds to characteristic X-ray radiation causedby internal conversion in Ba-137. F_y1 and F_y2 corresponds to the transi-tion radiation.

Tasks:1. Measurement of the g-spectrum

of 137Cs using a scintillation de-tector.

2. Determination of the conversionfactor of the 137mBa excited nu-cleus.


� �-radiation� Nuclear transitions� Transition probability� Duration� Metastable states� Isotopic spin quantum

numbers� Rules governing selection� Multipole radiation� Isomeric nuclei� Photonuclear reaction� Conversion electron� Characteristic X-ray radiation� Scintillation detectors

Source Cs-137, 37 kBq 09096.01 1


















What you need:

PComplete Equipment Set, Manual on CD-ROM includedInternal conversion in 137mBa with Cobra3 P2524511

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 227



Principle:The radiation of 137Cs and 22Na ismeasured with a scintillation detec-tor and the energy spectrum deter-mined with a pulse height analyzer.The fractions of the spectra causedby Compton scattering and thosecaused by the photoelectric effectare determined on the basis of theirareas. The results are used for deter-mining the ratio of the effectivecross-sections and examining itsenergy dependence.

�-spectrum of 22Na.

Tasks:1. Measurement of the �-spectra of

22Na and 137Cs, using a scintilla-tion detector.

2. Determination of the ratio of thespecific effective cross-sectionsdue to the Compton effect and thephotoelectric effect in photonshaving energy values of 511, 662and 1275 keV.


Source Cs-137, 37 kBq 09096.01 1














What you need:

Complete Equipment Set, Manual on CD-ROM includedPhotonuclear cross-section /Compton scattering cross-section P2524601



� �-radiation� Interaction with material� Photoelectric effect� Compton effect� Pair formation� Detection probability� Scintillation detectors

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 228


Photonuclear cross-section / Compton scattering cross-section with Cobra3 5.2.46-11


Principle:The radiation of 137Cs and 22Na ismeasured with a scintillation detec-tor and the energy spectrum deter-mined with a pulse height analyzer.The fractions of the spectra causedby Compton scattering and thosecaused by the photoelectric effectare determined on the basis of theirareas. The results are used for deter-mining the ratio of the effectivecross-sections and examining itsenergy dependence.

�-spectrum of 22Na.

Tasks:1. Measurement of the g-spectra of

22Na and 137Cs, using a scintilla-tion detector.

2. Determination of the ratio of thespecific effective cross-sectionsdue to the Compton effect and thephotoelectric effect in photonshaving energy values of 511, 662and 1275 keV.


� �-radiation� Interaction with material� Photoelectric effect� Compton effect� Pair formation� Detection probability� Scintillation detectors


Source Cs-137, 37 kBq 09096.01 1









Support rod -PASS-, square, l =400 mm 02026.55 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedPhotonuclear cross-section / Comptonscattering cross-section with Cobra3 P2524611

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 229


5.2.47-01 X-ray fluorescence and Moseley’s law

Principle:The irradiation of strontinum (sul-phate), cadmium, indium, iodine andbarium (chloride) with soft �-radia-tions gives rise to Ka radiationscharacteristics of these elements.The X-ray spectra are recorded witha �-spectrometer consisting of ascintillation counter, a pulse heightanalyser and a recorder. After cali-bration of the spectrometer, the Ryd-berg constant is determined from theenergies of the X-ray lines, usingMoseley’s law.

X-ray fluorescence energy values versus (Z-1)2

Tasks:1. Calibration of the �-spectrometer

in the low energy range, using theBa-resonance line of a 137Cs emit-ter (32 keV) and the �-line of241Am at 59.6 keV.

2. Recording of the X-ray fluores-cence spectra (Ka-lines) of differ-ent elements and determinationof the corresponding energies.

3. Plotting of the measured X-rayenergies according to Moseley’slaw against (Z-1)2 and determi-nation of the Rydberg constantR∞ from the slope of the resultinglines.


Source Cs-137, 37 kBq 09096.01 1








Tin chloride, 250 g 31991.25 1

Silver plate 31839.04 1


Plastic bags, DIN A5, pack of 100 46444.01 1

Crocodile clips, pack of 10 07274.03 1

Support rod –PASS- , square, l = 250 mm 02025.55 3

Support base –PASS- 02005.55 1



Source holder, swivel-type 18461.88 1

Barium chloride, 250 g 30033.25 1

Iodine resublimed, 25 g 30093.04 1




What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray fluorescence and Moseley’s law P2524701



� Binding energy� Photoelectric eftect� Shell structure of electron

shells� Characteristic X-ray radiation� �-spectrometry� X-ray spectral analysis

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 230


X-ray fluorescence and Moseley’s law with Cobra3 5.2.47-11


Principle:The irradiation of strontinum (sul-phate), cadmium, indium, iodine andbarium (chloride) with soft �-radia-tions gives rise to Ka radiationscharacteristics of these elements.The X-ray spectra are recorded witha �-spectrometer consisting of ascintillation counter, a pulse heightanalyser and a recorder. After cali-bration of the spectrometer, the Ryd-berg constant is determined from theenergies of the X-ray lines, usingMoseley’s law.

Calibration lines of Cs-137 and Am-241

Tasks:1. Calibration of the �-spectrometer

in the low energy range, using theBa-resonance line of a 137Cs emit-ter (32 keV) and the �-line of241Am at 59.6 keV.

2. Recording of the X-ray fluores-cence spectra (Ka-lines) of differ-ent elements and determinationof the corresponding energies.

3. Plotting of the measured X-rayenergies according to Moseley’slaw against (Z-1)2 and determi-nation of the Rydberg constantR∞ from the slope of the resultinglines.


� Binding energy� Photoelectric eftect� Shell structure of electron

shells� Characteristic X-ray radiation� �-spectrometry� X-ray spectral analysis


Source Cs-137, 37 kBq 09096.01 1










Tin chloride, 250 g 31991.25 1

Silver plate 31839.04 1


Plastic bags, DIN A5, pack of 100 46444.01 1

Crocodile clips, pack of 10 07274.03 1

Support rod –PASS- , square, l = 250 mm 02025.55 3

Support base –PASS- 02005.55 1



Source holder, swivel-type 18461.88 1

Barium chloride, 250 g 30033.25 1

Iodine resublimed, 25 g 30093.04 1






What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray fluorescence and Moseley’s lawwith Cobra3 P2524711

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 231


5.3.01-01 Hall effect in p-germanium

Principle:The resistivity and Hall voltage of arectangular germanium sample aremeasured as a function of tempera-ture and magnetic field. The bandspacing, the specific conductivity,the type of charge carrier and themobility of the charge carriers aredetermined from the measurements.

2. The voltage across the sample ismeasured at room temperatureand constant control current as afunction of the magnetic induc-tion B.

3. The voltage across the sample ismeasured at constant controlcurrent as a function of the tem-

Hall voltage as a function of current.

Tasks:1. The Hall voltage is measured at

room temperature and constantmagnetic field as a function ofthe control current and plotted ona graph (measurement withoutcompensation for defect voltage).



Coil, 600 turns 06514.01 2


Pole pieces, plane, 30�30�48 mm, 2 06489.00 1













What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in p-germanium P2530101

Physical Structure of Matter Solid-state Physics


� Semiconductor� Band theory� Forbidden zone� Intrinsic conductivity� Extrinsic conductivity� Valence band� Conduction band� Lorentz force� Magnetic resistance� Mobility� Conductivity� Band spacing� Hall coefficient

Hall voltage as a function of magnetic induction.

perature. The band spacing of ger-manium is calculated from the mea-surements.

4. The Hall voltage UH is measuredas a function of the magnetic in-duction B, at room temperature.The sign of the charge carriersand the Hall constant RH togeth-

er with the Hall mobility mH and thecarrier concentration p are calculat-ed from the measurements.

5. The Hall voltage UH is measuredas a function of temperature atconstant magnetic induction Band the values are plotted on agraph.

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 232


Hall effect in p-germanium with Cobra3 5.3.01-11

Solid-state Physics Physical Structure of Matter

Principle:The resistivity and Hall voltage of arectangular germanium sample aremeasured as a function of tempera-ture and magnetic field. The bandspacing, the specific conductivity,the type of charge carrier and themobility of the charge carriers aredetermined from the measurements.

4. The Hall voltage UH is measuredas a function of the magnetic in-duction B, at room temperature.The sign of the charge carriersand the Hall constant RH togeth-er with the Hall mobility mH andthe carrier concentration p arecalculated from the measure-ments.

5. The Hall voltage UH is measuredas a function of temperature atconstant magnetic induction Band the values are plotted on agraph.

Hall voltage as a function of temperature.

Tasks:1. The Hall voltage is measured at

room temperature and constantmagnetic field as a function ofthe control current and plotted ona graph (measurement withoutcompensation for defect voltage).

2. The voltage across the sample ismeasured at room temperatureand constant control current as afunction of the magnetic induc-tion B.

3. The voltage across the sample ismeasured at constant controlcurrent as a function of the tem-perature. The band spacing ofgermanium is calculated from themeasurements.


� Semiconductor� Band theory� Forbidden zone� Intrinsic conductivity� Extrinsic conductivity� Valence band� Conduction band� Lorentz force� Magnetic resistance� Mobility� Conductivity� Band spacing� Hall coefficient



Coil, 600 turns 06514.01 2


Pole pieces, plane, 30�30�48mm, 2 06489.00 1















RS 232 data cable 14602.00 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in p-germanium with Cobra3 P2530111

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 233


5.3.02-01 Hall effect in n-germanium

Principle:The resistance and Hall voltage aremeasured on a rectangular strip ofgermanium as a function of the tem-perature and of the magnetic field.From the results obtained the energygap, specific conductivity, type ofcharge carrier and the carrier mobil-ity are determined.


Hall effect, n-Ge, carrier board 11802.01 1

Coil, 600 turns 06514.01 2















What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in n-germanium P2530201

Physical Structure of Matter Solid-state Physics


� Semiconductor� Band theory� Forbidden zone� Intrinsic conduction� Extrinsic conduction� Valence band� Conduction band� Lorentz force� Magneto resistance� Neyer-Neldel Rule

2. At room temperature and with aconstant control current, measurethe voltage across the specimenas a function of the magnetic fluxdensity B.

3. Keeping the control current con-stant measure the voltage acrossthe specimen as a function of

Hall voltage as a function of current.

Tasks:1. At constant room temperature

and with a uniform magnetic fieldmeasure the Hall voltage as afunction of the control currentand plot the values on a graph(measurement without compensa-tion for error voltage).

Hall voltage as a function of the magnetic flux density.

temperature. From the readingstaken, calculate the energy gap ofgermanium.

4. At room temperature measure theHall Voltage UH as a function ofthe magnetic flux density B. Fromthe readings taken, determine theHall coefficient RH and the sign of

the charge carriers. Also calculatethe Hall mobility mH and the carrierdensity n.

5. Measure the Hall voltage UH as afunction of temperature at uni-form magnetic flux density B, andplot the readings on a graph.

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 234


Hall effect in n-germanium with Cobra3 5.3.02-11

Solid-state Physics Physical Structure of Matter

Principle:The resistance and Hall voltage aremeasured on a rectangular strip ofgermanium as a function of the tem-perature and of the magnetic field.From the results obtained the energygap, specific conductivity, type ofcharge carrier and the carrier mobil-ity are determined.

4. At room temperature measure theHall Voltage UH as a function ofthe magnetic flux density B. Fromthe readings taken, determine theHall coefficient RH and the sign ofthe charge carriers. Also calculatethe Hall mobility mH and the carri-er density n.

5. Measure the Hall voltage UH as afunction of temperature at uni-form magnetic flux density B, andplot the readings on a graph.

Tasks:1. At constant room temperature

and with a uniform magnetic fieldmeasure the Hall voltage as afunction of the control currentand plot the values on a graph(measurement without compensa-tion for error voltage).

2. At room temperature and with aconstant control current, measurethe voltage across the specimenas a function of the magnetic fluxdensity B.

3. Keeping the control current con-stant measure the voltage acrossthe specimen as a function oftemperature. From the readingstaken, calculate the energy gap ofgermanium.


� Semiconductor� Band theory� Forbidden zone� Intrinsic conduction� Extrinsic conduction� Valence band� Conduction band� Lorentz force� Magneto resistance� Neyer-Neldel Rule


Hall effect, n-Ge, carrier board 11802.01 1

Coil, 600 turns 06514.01 2

















RS 232 data cable 14602.00 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in n-germanium with Cobra3 P2530211

Hall voltage as a function of temperature.

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 235


5.3.03-00 Hall effect in metals

Principle:The Hall effect in thin zinc and cop-per foils is studied and the Hall coef-ficient determined. The effect oftemperature on the Hall voltage isinvestigated.

Hall voltage as a function of magnetic induction B, using a copper sample.

Tasks:1. The Hall voltage is measured in

thin copper and zinc foils.

2. The Hall coefficient is determinedfrom measurements of the currentand the magnetic induction.

3. The temperature dependence ofthe Hall voltage is investigated onthe copper sample.

Hall effect, Cu, carrier board 11803.00 1

Hall effect, zinc, carrier board 11804.01 1

Coil, 300 turns 06513.01 2


Pole pieces, plane, 30�30�48 mm, 2 06489.00 1

Power supply 0-30 VDC/20 A, stabil 13536.93 1






Meter, 10/30 mV, 200 °C 07019.00 1

Universal clamp with join 37716.00 1







What you need:

Complete Equipment Set, Manual on CD-ROM includedHall effect in metals P2530300

Physical structure of matter Solid-state Physics


� Normal Hall effect� Anomalous Hall effect� Charge carriers� Hall mobility� Electrons� Defect electrons

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 236


Band gap of germanium 5.3.04-01

Solid-state Physics Physical structure of matter

Principle:The conductivity of a germaniumtestpiece is measured as a functionof temperature. The energy gap isdetermined from the measured val-ues.

Regression of the conductivity versus the reciprocal of the absolute temper-ature.

Tasks:1. The current and voltage are to be

measured across a germaniumtest-piece as a function of tem-perature.

2. From the measurements, the con-ductivity � is to be calculated andplotted against the reciprocal ofthe temperature T. A linear plot isobtained, from whose slope theenergy gap of germanium can bedetermined.


� Semiconductor� Band theory� Forbidden band� Intrinsic conduction� Extrinsic conduction� Impurity depletion� Valence band� Conduction band


Hall effect, undot.-Ge, carrier board 11807.01 1









What you need:

Complete Equipment Set, Manual on CD-ROM includedBand gap of germanium P2530401

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 237


5.3.04-11 Band gap of germanium with Cobra3

Principle:The conductivity of a germaniumtestpiece is measured as a functionof temperature. The energy gap isdetermined from the measured val-ues.

Typical measurement of the probe-voltage as a function of the temperature.

Tasks:1. The current and voltage are to be

measured across a germaniumtest-piece as a function of tem-perature.

2. From the measurements, the con-ductivity � is to be calculated andplotted against the reciprocal ofthe temperature T. A linear plot isobtained, from whose slope theenergy gap of germanium can bedetermined.


Hall effect, undot.-Ge, carrier board 11807.01 1









RS 232 data cable 14602.00 2


What you need:

Complete Equipment Set, Manual on CD-ROM includedBand gap of germanium with Cobra3 P2530411

Physical structure of matter Solid-state Physics


� Semiconductor� Band theory� Forbidden band� Intrinsic conduction� Extrinsic conduction� Impurity depletion� Valence band� Conduction band

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:01 Uhr Seite 238


Characteristic X-rays of copper 5.4.01-00

X-ray Physics Physical structure of matter

Principle:Spectra of X-rays from a copperanode are to be analyzed by meansof different monocrystals and theresults plotted graphically. The ener-gies of the characteristic lines arethen to be determined from thepositions of the glancing angles forthe various orders of diffraction.

X-ray intensity of copper as a function of the glancing angle; LiF (100) mono-crystal as Bragg analyzer.


� Bremsstrahlung� Characteristic radiation� Energy levels� Crystal structures� Lattice constant� Absorption� Absorption edges� Interference� The Bragg equation� Order of diffraction

Tasks:1. The intensity of the X-rays emit-

ted by the copper anode at maxi-mum anode voltage and anodecurrent is to be recorded as afunction of the Bragg angle, usingan LiF monocrystal as analyzer.

2. Step 1 is to be repeated using theKBr monocrystal as analyzer.

3. The energy values of the charac-teristic copper lines are to be cal-culated and compared with theenergy differences of the copperenergy terms.

X-ray basic unit, 35 kV 09058.99 1

Goniometer for x-ray unit, 35 kV 09058.10 1

Plug-in module with Cu x-ray tube 09058.50 1

Counter tube, type B 09005.00 1

Lithium fluoride crystal, mounted 09056.05 1

Potassium bromide crystal, mounted 09056.01 1

Recording equipment:XYt recorder 11416.97 1

Connecting cable, l = 100 cm, red 07363.01 2

Connecting cable, l = 100 cm, blue 07363.04 2

or

Software x-ray unit, 35 kV 14407.61 1

Data cable, plug/socket, 9 pole 14602.00 1


What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristic X-rays of copper P2540100

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 239


5.4.02-00 Characteristic X-rays of molybdenum

Principle:Spectra of X-rays from a molybde-num anode are to be analyzed bymeans of different monocrystals andthe results plotted graphically. Theenergies of the characteristic linesare then to be determined from thepositions of the glancing angles forthe various orders of diffraction.

X-ray intensity of molybdenum as a function of the glancing angle; LiF (100)monocrystal as Bragg analyzer.



Plug-in module with Mo x-ray tube 09058.60 1







or




What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristik X-rays of molybdenum P2540200

Physical structure of matter X-ray Physics


� X-ray tube� Bremsstrahlung� Characteristic radiation� Energy levels� Crystal structures� Lattice constant� Absorption� Absorption edges� Interference� The Bragg equation� Order of diffraction


ted by the molybdenum anode atmaximum anode voltage andanode current is to be recorded asa function of the Bragg angle,using an LiF monocrystal as ana-lyzer.


3. The energy values of the charac-teristic molybdenum lines are tobe calculated and compared withthe energy differences of themolybdenum energy terms.

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 240


Characteristic X-rays of iron 5.4.03-00


Principle:Spectra of X-rays from a iron anodeare to be analyzed by means of dif-ferent monocrystals and the resultsplotted graphically. The energies ofthe characteristic lines are then to bedetermined from the positions of theglancing angles for the various or-ders of diffraction.

X-ray intensity of iron as a function of the glancing angle; LiF (100)monocrystal as Bragg analyzer.


� X-ray tube� Bremsstrahlung� Characteristic radiation� Energy levels� Crystal structures� Lattice constant� Absorption� Absorption edges� Interference� The Bragg equation� Order of diffraction


ted by the iron anode at maximumanode voltage and anode currentis to be recorded as a function ofthe Bragg angle, using an LiFmonocrystal as analyzer.


3. The energy values of the charac-teristic iron lines are to be calcu-lated and compared with the en-ergy differences of the iron energyterms.



Plug-in module with Fe x-ray tube 09058.70 1







or




What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristik X-rays of iron P2540300

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 241


5.4.04-00 The intensity of characteristic X-rays as a function of anode current and anode voltage

100 120 14020 40 60 80

7000

8000

9000

10000

1000

2000

3000

4000

5000

6000

Principle:Polychromatic X-radiation from acopper anode is to be directedagainst an LiF monocrystal so thatthe wavelengths can be analyzed ac-cording to Bragg. The dependency ofthe characteristic Ka and Kb radia-tion on the anode current and anodevoltage are to be determined.

Ka and Kb intensities as a function of (UA - UK)1.5 (IA = const.).

Tasks:1. The intensity spectrum of poly-

chromatic radiation from an X-raytube is to be recorded with thehelp of an LiF monocrystal.

2. The intensities of the characteris-tic Ka and Kb radiations are to bedetermined as a function of boththe anode current and the anodevoltage, and be plotted graphical-ly.

3. The results of the measurementare to be compared with the the-oretical intensity formula.









or




What you need:

Complete Equipment Set, Manual on CD-ROM includedThe intensity of characteristic X-rays as a function ofanode current and anode voltage P2540400



� Characteristic X-ray radiation� Energy levels� The Bragg equation� Intensity of characteristic

X-rays

(UA - UK)3/2/kV3/2

Kb

Ka

N

Imp s-1

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 242


Monochromatization of molybdenum X-rays 5.4.05-00


Principle:Polychromatic X-rays are to be ener-gy analyzed using various monocrys-tals and a suitably selected thinmetal foil having an absorption edgewhich drastically reduces the inten-sity of an unwanted line.

3. The LiF monocrystal is to be usedto filter out a characteristic lineand the appertaining monochrom-atization graphically recorded.

4. Step 1 is to be repeated, using azirconium filter.

Molybdenum X-ray monochromatization with Zr filter; LiF (100) monocrystalas analyzer.


� Bremsstrahlung� Characteristic radiation� Energy levels� Absorption� Absorption edges� Interference� Diffraction� Bragg scattering


ted by the molybdenum anode isto be graphically recorded as afunction of the Bragg angle, usingLiF and KBr monocrystals succes-sively as analyzers.

2. The energy values of the charac-teristic molybdenum lines are tobe calculated.







Diaphragm tube with zirconium foil 09058.03 1





or




What you need:

Complete Equipment Set, Manual on CD-ROM includedMonochromatization of molybdenum X-rays P2540500

Molybdenum X-ray intensity as a function of the glancing angle q; LiF (100)monocrystal as analyzer

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 243

244 PHYWE Systeme GmbH & Co. KG · 37070 GöttingenLaboratory Experiments Physics

5.4.06-00 Monochromatization of copper X-rays


Principle:Polychromatic X-rays are to be ener-gy analyzed using various monocrys-tals and a suitably selected thinmetal foil having an absorption edgewhich drastically reduces the inten-sity of an unwanted line.

Copper X-ray monochromatization with Ni filter; LiF (100) monocrystal as an-alyzer (Diameter of diaphragm tube d = 2 mm).


What you need:


ted by the copper anode is to begraphically recorded as a functionof the Bragg angle, using LiF andKBr monocrystals successively asanalyzers.

2. The energy values of the charac-teristic copper lines are to be cal-culated.

3. The LiF monocrystal is to be usedto filter out a characteristic lineand the appertaining monochrom-atization graphically recorded.

4. Step 1 is to be repeated, using anickel filter.

� Bremsstrahlung� Characteristic radiation� Energy levels� Absorption� Absorption edges� Interference� Diffraction� Bragg scattering







Diaphragm tube with nickel foil 09056.03 1


Connecting cable, 100 cm, red 07363.01 2

Connecting cable, 100 cm, blue 07363.04 2

or


Data cable, 2� SUB-D, plug/socket, 9 pole 14602.00 1


Complete Equipment Set, Manual on CD-ROM includedMonochromatization of copper X-rays P2540600

Copper X-ray intensity as a function of the glancing angle q; LiF (100)monocrystal as analyzer (Diameter of diaphragm tube d = 1 mm).

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 244

L

What you need:

Complete Equipment Set, Manual on CD-ROM included20000

245PHYWE Systeme GmbH & Co. KG · 37070 Göttingen Laboratory Experiments Physics


Ka doublet splitting of molybdenum X-rays / fine structure 5.4.07-00


Principle:The polychromatic molybdenum X-rayspectrum is to analyzed by means ofa monocrystal. The energy of thecharacteristic lines is to be deter-mined from the positions of theglancing angles at various orders ofdiffraction. The separation of the Kadoublet in higher order diffraction isto be examined.

X-ray spectrum of molybdenum; separation of the Ka1 and Ka2 lines in 5th

order diffraction.


ted by the molybdenum anode atmaximum anode voltage is to berecorded as a function of theBragg angle, using an LiFmonocrystal as analyzer.

2. The wavelengths and ratio of theintensities of the two Ka lines areto be determined in high orderdiffraction, and a comparisonmade with the theoretical predic-tions.

� Characteristic X-ray radiation� Energy levels� Selection rules� The Bragg equation� Energy term symbols









or




What you need:

Complete Equipment Set, Manual on CD-ROM includedKa doublet splitting of molybdenum X-rays / fine structure P2540700

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 245


5.4.08-00 Ka doublet splitting of iron X-rays / fine structure

Principle:The polychromatic iron X-ray spec-trum is to analyzed by means of amonocrystal. The energy of the char-acteristic lines is to be determinedfrom the positions of the glancingangles for various orders of diffrac-tion. The separation of the Ka dou-blet in higher order diffraction is tobe examined.

X-ray spectrum of iron; separation of the Ka1 and Ka2 lines in 2nd orderdiffraction.


ted by the iron anode at maximumanode voltage is to be recorded asa function of the Bragg angleusing an LiF monocrystal as ana-lyzer.

2. The wavelengths and ratio of theintensities of the two Ka lines areto be determined in high orderdiffraction, and a comparisonmade with the theoretical predic-tions.









or




What you need:

Complete Equipment Set, Manual on CD-ROM includedKa doublet splitting of iron X-rays /fine structure P2540800



� Characteristic X-ray radiation� Energy levels� Selection rules� The Bragg equation� Energy term symbols

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 246


Duane-Hunt displacement law and Planck's “quantum of action” 5.4.09-00


Principle:X-ray spectra are to be recorded as afunction of the anode voltage. Theshort wavelength limit of thebremsspectrum is to be used to de-termine the agreement with theDuane-Hunt displacement law, andto determine Planck's “quantum ofaction”.

Bremsstrahlung as function of two anode voltages; Glancing angle q as x-axis in degree.


ted by the copper anode at variousanode voltages is to be recordedas a function of the Bragg angle,using an LiF monocrystal.

2. The short wavelength limit(=maximum energy) of the brems-spectrum is to be determined forthe spectra obtained in (1).

3. The results are to be used to veri-fy the Duane-Hunt displacementlaw, and to determine Planck's“quantum of action”.


� X-ray tube� Bremsstrahlung� Characteristic X-ray radiation� Energy levels� Crystal structures� Lattice constant� Interference� The Bragg equation









or




What you need:

Complete Equipment Set, Manual on CD-ROM includedDuane-Hunt displacement law andPlanck’s “quantum of action” P2540900

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 247


5.4.10-00 Characteristic X-ray lines of different anode materials/Moseley's Law;Rydberg frequency and screening constant

20 30 40

10

15

20

Principle:The X-rays emanating from three X-ray tubes, each with a differentanode material, are to be analyzedand the wavelengths of the charac-teristic X-ray lines from each are tobe determined, so that Moseley'sLaw can be verified.

Moseley straight linesCurve a: Transition n2 —>n1 (Ka line)Curve b: Transition n3 —>n1 (Kb line)

Tasks:1. The X-ray spectra emanated from

Fe, Cu and Mo X-ray tubes are tobe recorded.

2. The Bragg angles of the character-istic lines are to be determinedfrom the spectra, and then be usedto determine their wavelengthsand frequencies.

3. The Rydberg constants and thescreening constants are to bedetermined from the Moseleystraight lines.











or




What you need:

Complete Equipment Set, Manual on CD-ROM includedCharacteristik X-ray lines of different anode materials / Moseley’s Law; Rydberg frequency and screening constant P2541000



� Characteristic X-ray radiation� Bohr's atomic model� Energy levels� Binding energy� Bragg scattering� Moseley's law; Rydberg

frequency and screeningconstant

Z

2 f

108 s�1>2a

b

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 248


Absorption of X-rays 5.4.11-00


1 0

10

8

8

7

2

1

3

7

6

6

9

9

4

4

3

3

2

2

1

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

5

5

Principle:Polychromatic X-rays are to be ener-gy selected using a monocrystal an-alyzer. The monochromatic radiationobtained is to serve as the primaryradiation source for examination ofthe absorption behaviour of variousmetals as a function of the absorberthickness and the wavelength of theprimary radiation.

3. The absorption coefficients forcopper and nickel are to be deter-mined as a function of the wave-length and the measured valuesplotted. The energies of the K lev-els are to be calculated.

4. The validity of m/r = f(Z3) is tobe proved.

Semi-logarithmic representation of the pulse rates as a function of the ab-sorber thickness.

Ua = 35 kV, Ia = 1 mA.

Curve 1: Al (Z = 13); l = 139 pm

Curve 2: Al (Z = 13); l = 70 pm

Curve 3: Zn (Z = 30); l = 139 pm.

Tasks:1. The intensity attenuation of the

primary radiation is to be mea-sured for aluminium and zinc as afunction of the material thicknessand at two different wavelengths.The mass absorption coefficientsare to be determined from thegraphical representation of themeasured values.

2. The mass absorption coefficientsfor aluminium, zinc and tin foils ofconstant thickness are to be de-termined as a function of thewavelength. It is to be shown fromthe graphical representation thatm/r = f(l3).


� Bremsstrahlung� Characteristic radiation� Bragg scattering� Law of absorption� Mass absorption coefficient� Absorption edges� Half-value thickness� Photoelectric effect� Compton scattering� Pair production






Absorption set for x-rays 09056.02 1

Recommended accessories:Software x-ray unit, 35 kV 14407.61 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedAbsorption of X-rays P2541100

d/mm

I/I0

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 249


5.4.12-00 K- and L-absorption edges of X-rays / Moseley's Law and the Rydberg constant

Principle:Samples of various elements of dif-ferent atomic numbers are to be irra-diated with X-rays of a known spec-tral distribution, and the energy ofthe transmitted intensities analyzedusing a monocrystal analyzer. TheRydberg constant and screeningconstants are to be found by deter-mining the energy at which absorp-tion edges occur.

3. The Rydberg and screening con-stants are to be calculated fromthe energy values of the K ab-sorption edges.

4. The L absorption edges of differ-ent absorber materials are to befound.

5. The Rydberg constant is to be cal-culated from the energy values ofthe L absorption edges.

X-ray spectra of copper without absorber and with K absorption edges forvarious absorbers.


ted from the copper anode is to berecorded as a function of theBragg angle using an LiFmonocrystal as analyzer.

2. The K absorption edges of differ-ent absorber materials are to befound.

X-ray basic unit, 35 kV 09058.99 1Goniometer for x-ray unit, 35 kV 09058.10 1Plug-in module with Cu X-ray tube 09058.50 1Counter tube, type B 09005.00 1Lithium fluoride crystal, mounted 09056.05 1Chemicals for edge absorption 09056.04 1Silver nitrate, crst., 15 g 30222.00 1Mortar and pestle, 90 mm, porcelain 32603.00 1Spoon with spatula end, l = 150 mm, steel, micro 33393.00 1

Recording equipment:XYt recorder 11416.97 1Connecting cable, 100 cm, red 07363.01 2Connecting cable, 100 cm, blue 07363.04 2orSoftware x-ray unit, 35 kV 14407.61 1Data cable, 2� SUB-D, plug/socket, 9 pole 14602.00 1PC, Windows® 95 or higher

What you need:

Complete Equipment Set, Manual on CD-ROM includedK- and L-absorption edges of X-rays /Moseley’s Law and Rydberg constant P2541200



� X-ray bremsstrahlung� Characteristic radiation� Bragg equation� Bohr's atomic model� Atomic energy level scheme� Moseley's law� Rydberg constant� Screening constant

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 250


Examination of the structure of NaCl monocrystals with different orientations 5.4.13-00


Principle:Polychromatic X-rays are to bedirected against NaCl monocrystalswith different orientations. Thespacing between the lattice planesof each monocrystals then to bedetermined by analyzing the wave-length-dependent intensity of thereflected radiation.

3. The planes of reflection and theirMiller indices are to be found.

X-ray intensity of copper as afunction of the glancing angle:

NaCl monocrystal with differentorientations as Bragg-analyzer:

1-(100); 2-(110); 3-(111)

Tasks:1. NaCl monocrystals with the orien-

tations (100), (110) and (111) areeach to be separately used torecord an intensity spectrum ofthe polychromatic radiation em-anated by the X-ray tube.

2. The Bragg angles of the character-istic radiations are to be deter-mined from the spectra, and thedistances between lattice planescalculated for each orientation.


� Characteristic X-ray radiation� Energy levels� Crystal structures� Reciprocal lattice� Miller indices� Bragg scattering� Atomic form factor� Structure factor



Plug-in module with Cu X-ray tube 09058.50 1


Universal crystal holder 09058.02 1

Sodium chloride monocrystals, set of 3 09058.01 1




or




What you need:

Complete Equipment Set, Manual on CD-ROM includedExamination of the structure of NaCl monocrystalswith different orientations P2541300

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:02 Uhr Seite 251


5.4.14-00 X-ray investigation of cubic crystal structures / Debye-Scherrer powder method

Principle:Polycrystalline samples are to beirradiated by an X-ray beam and theresulting diffraction patterns record-ed on film and evaluated.

3. The lattice constants of the sam-ple materials are to be deter-mined.

4. The number of atoms in the unitcells of each sample are to be de-termined.

Debye-Scherrer pattern of a powdered sample of CsCl. Thickness of the sam-ple, 0.4 mm. Exposure time, 2.0 h. Mo X-ray tube: UA = 35 kV; IA = 1 mA.

Tasks:1. Debye-Scherrer photographs are

to be taken of powdered samplesof sodium chloride and caesiumchloride.

2. The Debye-Scherrer rings are to beevaluated and assigned to the cor-responding lattice planes.



Mortar and pestle, d = 90 mm 32603.00 1

Spoon with spatula end, l = 150 mm, steel, micro 33393.00 1


Film holder 09058.08 1


Caesium chloride, 5 g 31171.02 1

Polaroid film, (ISO 3000), (9�12) cm, 20 sheets 09058.20 1

Polaroid film adapter 09058.21 1

or

X-ray-film, (90�120) mm, 10 sheets 06696.03 1

X-ray-film developer for 4.5 l 06696.20 1

X-ray-film fixing for 4.5 l 06696.30 1

Laboratory tray, PP, 18�24 cm 47481.00 3

What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray investigation of cubic crystal structures /Debye-Scherrer powder method P2541400



� Crystal lattices� Crystal systems� Reciprocal lattice� Miller indices� Structure amplitude� Atomic form factor� Bragg scattering

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:03 Uhr Seite 252


X-ray investigation of hexagonal crystal structures / Debye-Scherrer powder method 5.4.15-00


Principle:A polycrystalline sample of zirconi-um is to be irradiated by an X-raybeam and the resulting diffractionpatterns recorded on film and evalu-ated.

3. The lattice constants of the sam-ple material are to be determined.

4. The number of atoms in a unit cellof the sample is to be determined.

Debye-Scherrer pattern of a zirconium foil. Thickness of the sample, 0.05 mm.Exposure time, 2.5 h. Mo X-ray tube: UA = 35 kV; IA = 1 mA

Tasks:1. Debye-Scherrer photographs are

to be taken of the zirconium sam-ple.

2. The Debye-Scherrer rings are to beevaluated and assigned to the cor-responding lattice planes.


� Crystal lattices� Crystal systems� Reciprocal lattice� Miller indices� Structure amplitude� Atomic form factor� Bragg scattering



Diaphragm tube with Zr foil 09058.03 1





or





What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray investigation of hexagonal crystalstructures / Debye-Scherrer powder method P2541500

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:03 Uhr Seite 253


5.4.16-00 X-ray investigation of crystal structures / Laue method

Principle:A monocrystal is to be irradiated by apolychromatic X-ray beam and theresulting diffraction patterns record-ed on film and evaluated.

Laue pattern of an LiF (100) crystal.

Cu X-ray tube: UA = 35 kV; IA = 1 mADistance between sample and film: D = 19 mmExposure time: t = 120 min

Tasks:1. The Laue diffraction of an LiF

monocrystal is to be recorded on afilm.

2. The Miller indices of the corre-sponding crystal surfaces are to beassigned to the Laue reflections.


Plug-in module with Mo X-ray tube 09058.60 1

Lithium fluoride monocrystal, mounted 09056.05 1

Crystal holder for Laue diffraction 09058.11 1





or





What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray investigation of crystal structures /Laue method P2541600



� Crystal lattices� Crystal systems� Crystal classes� Bravais lattice� Reciprocal lattice� Miller indices� Structure amplitude� Atomic form factor� The Bragg equation

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:03 Uhr Seite 254


Compton scattering of X-rays 5.4.17-00


55 60 65

0.35

0.4

0.3

0.25

0.2

Principle:Compton scattering is to be achievedby directing an X-ray beam against apiece of plastic. The portions of thescattered X-rays at various angles isto be measured with a counter tube.Measurements are to be made withan absorber positioned in front ofand behind the scatterer, so that theCompton wavelength can be deter-mined from the varying intensity at-tenuation of the X-rays at differentwavelengths, using a premeasuredtransmission curve.

for the same angles as previously,and the different transmission coef-ficients then calculated.

3. The different transmission coeffi-cients and the transmission curveare to be used to determine thechanges in wavelengths.

4. The Compton wavelength for 90°scattering is to be determined andcompared with the theoreticalvalue.

Transmission curve of aluminium.Experimental set-up for 90° Compton scattering.

Tasks:1. The transmission of an aluminium

absorber is to be determined as afunction of the wavelength of theX-rays by means of Bragg scatter-ing and the measured values plot-ted graphically.

2. A scatterer is to be used and theintensity of the X-rays scatteredat different angles determined.The intensity attenuation whichoccurs on placing an aluminiumabsorber in front of, and behind,the scatterer is to be determined


� Compton effect� Compton wavelength� Rest energy� Absorption� Transmission� Conservation of energy and

momentum� X-rays� The Bragg equation






Compton attachment for x-ray unit, 35 kV 09058.04 1

Recommended accessories:Software x-ray unit, 35 kV 14407.61 1



What you need:

Complete Equipment Set, Manual on CD-ROM includedCompton scattering of X-rays P2541700

∆l

l/pm

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:03 Uhr Seite 255


5.4.18-00 X-ray dosimetry

3.0

2.0

1.0

100 200 300 400 500

Principle:The molecules of air within a platecapacitor are to be ionized by X-rays.The ion dose, ion dose rate and localion dose rate are to be calculatedfrom the ionization current and theradiated mass of air.

ous anode currents but with maxi-mum anode and capacitor voltages.

5. The saturation current is to beplotted as a function of the anodevoltage.

6. Using the d = 5 mm aperture, theion current is to be determinedand graphically recorded at vari-ous anode currents but with max-imum anode and capacitor volt-ages.

7. Using the two different diaphragmtubes and the fluorescent screen,the given distance between theaperture and the radiation sourceat maximum anode coltage andcurrent is to be verified.

Ionization current IC as a function of capacitor voltage UC for various anodevoltages UA. Diaphragm tube d = 5 mm; IA = 1 mA.

Tasks:1. The ion current at maximum

anode voltage is to be measuredand graphically recorded as afunction of the capacitor voltageby using two different beam limit-ing apertures.

2. The ion dose rate is to be deter-mined from the saturation currentvalues and the air masses pene-trated by radiation are to be cal-culated.

3. The energy dose rate and variouslocal ion dose rates are to be cal-culated.

4. Using the d = 5 mm aperture, theion current is to be determinedand graphically recorded at vari-



Capacitor plate for x-ray unit, 35 kV 09058.05 1

Power supply, regulated, 0...600 V- 13672.93 1

DC measuring amplifier 13620.93 1


High value resistor, 50 MW 07159.00 1

Adapter, BNC socket / 4 mm plug pin 07542.20 1

Screened cable, BNC, l = 30 cm 07542.10 1

Connecting cable, blue, l = 10 cm 07359.04 2

Connecting cable, red, l = 50 cm 07361.01 2

Connecting cable, blue, l = 50 cm 07361.04 2

Connecting cable, red, l = 75 cm 07362.01 2

What you need:

Complete Equipment Set, Manual on CD-ROM includedX-ray dosimetry P2541800



� X-rays� Absorption inverse square law� Ionizing energy� Energy dose� Equivalent dose and ion dose

and their rates� Q factor� Local ion dose rate� Dosimeter

IC/nA

UC/V

UA= 35 kV

UA= 30 kV

UA= 25 kV

UA= 20 kV

UA= 15 kV

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:03 Uhr Seite 256


Contrast medium experiment with a blood vessel model 5.4.19-00


Principle:A liquid contrast medium is to be in-jected into a model of a blood vessel,which is hidden from sight and ex-posed to X-ray radiation, to enablethe inner structure of the model tobe examined on a fluorescent screen.

Figure shows the model filled to different extents with contrast medium.

Experimental steps:1. A 50% potassium iodide solution

is to be injected into the bloodvessel model.

2. The fluorescent screen of the X-ray basic unit is to be observedto follow the course taken by theinjected solution in the blood ves-sel model.


� X-ray radiation� Bremsstrahlung� Characteristic radiation� Law of absorption� Mass absorption coefficient� Contrast medium



Blood vessel model for contrast medium 09058.06 1

Potassium iodide, 50 g 30104.05 1


Reagent bottle, brown, 250 ml 46223.00 1

Glass rod, l = 200 mm, d = 6 mm 40485.04 1

What you need:

Complete Equipment Set, Manual on CD-ROM includedContrast medium experiment with a bood vessel model P2541900

LEP 5.2.44-11_5.4.20-00 12.10.2003 22:43 Uhr Seite 257


5.4.20-00 Determination of the length and position of an object which cannot be seen

Principle:The length and the spatial position ofa metal pin which cannot be seen areto be determined from radiograms oftwo different planes which are atright angles to each other.

Projection fotos of the implant model in the xz-plane (left) and in the yz-plane (right).

Tasks:1. The length of a metal pin which

cannot be seen is to be deter-mined from radiograms of twodifferent planes which are at rightangles to each other.

2. The true length of the pin is tobe determined by taking themagnification which results fromthe divergence of the X-rays intoaccount.

3. The spatial position of the pin is tobe determined.

X-ray basic unit. 35 kV 09058.99 1

Plug-in module with Cu-X-ray tube 09058.50 1


Implant model for X-ray photography 09058.07 1


Polaroid film, (9�12) cm, 20 sheets 09058.20 1

Polaroid film holder chassis 09058.21 1

or

X-ray-film, (9�12) cm, 10 sheets 06696.03 1



Tray (PP), (18�24) cm , white 47481.00 3

What you need:

Complete Equipment Set, Manual on CD-ROM includedDetermination of the length and position of an object which cannot be seen P2542000



� X-ray radiation� Bremsstrahlung� Characteristic radiation� Law of absorption� Mass absorption coefficient� Stereographic projection

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:03 Uhr Seite 258


Handbooks Physical structure of matter

1 (25401)Characteristic X-rays of copper

2 (25402)Characteristic X-rays ofmolybdenum

3 (25403)Characteristic X-rays of iron

4 (25404)The intensity of characteristic X-rays as a function of anodecurrent and anode voltage

5 (25405)Monochromatization of molybdenum X-rays

6 (25406)Monochromatization of copper X-rays

7 (25407)K� doublet splitting of molybdenumX-rays / fine structure

8 (25408)K� doublet splitting of iron X-rays / fine structure

9 (25409)Duane-Hunt displacement law andPlanck's “quantum of action”

10 (25410)Characteristic X-ray lines of differ-ent anode materials/ Moseley's Law;Rydberg frequency and screeningconstant

11 (25411)Absorption of X-rays

12 (25412)K and L absorption edges of X-rays / Moseley's law and theRydberg constant

13 (25413)Examination of the structure ofNaCl monocrystals with differentorientations

14 (25414)X-ray investigation of cubic crystalstructures / Debye-Scherrer powdermethod

15 (25415)X-ray investigation of hexagonalcrystal structures / Debye-Scherrerpowder method

16 (25416)X-ray investigation of crystalstructures / Laue method

17 (25417)Compton scattering of X-rays

18 (25418)X-ray dosimetry

19 (25419)Contrast medium experiment with ablood vessel model

20 (25420)Determination of the length andposition of an object which cannotbe seen

A unique feature:3 different X-ray tubes with anodes made of copper or molybdenum or iron to beplugged into the unit.Due to their anode material, the tubes show different characteristic X-ray lines (Moseleylaw). They can thus be used for fundamental measurements concerning the formation of X-rays and also for experiments on the basis of radiation of different hardness levels (wavelength). The X-ray tubes are separately available and easy to exchange:

The tubes are completely adjusted and come supplied in separate plug-in modules which aresimply to be plugged into the basic unit. Exchanging the tubes takes only seconds and theX-ray unit is immediately ready to operate.

Further new features:● RS232 interface for computer-assisted control, measuring and evaluation purposes

● X-ray tube visible during operation

● integrated rate meter with counter

X-Ray Experiments

X-Ray Experiments • No. 01189.02 • 20 described ExperimentsPlease ask for a complete equipment list Ref. No. 25421

Contrast medium experiment with a blood vessel model

Models for two different extent with contrast medium

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:03 Uhr Seite 259


Handbooks


Please ask for a completeequipment list Ref. No.25422

1. Mechanics1.1 (13301)Frequency of a spring pendulum1.2 (13302)Frequency of a thread pendulum1.3 (13369)Free fall with a screen1.4 (13370)The path-time law for free fallwith the falling sphere apparatus1.5 (13371)Uniform, linear, unacceleratedmotion1.6 (13372)Force-free, linear motion1.7 (13373)Uniformly accelerated, linear mo-tion, Newton`s 2nd law1.8 (13374)The elastic collision1.9 (13375)The inelastic collision1.10 (13376)Frequency of a thread pendulum1.11 (13377)Pendulum oscillations-variable g pendulum1.12 (13378)The harmonic oscillation of heli-cal springs-parallel and seriesconnection of spring1.13 (13379)Dependence of the oscillation pe-riod of a leaf spring on the pen-dulum length & pendulum mass1.14 (13380)Moment of inertia of differentbodies:disc,solid and hollowcylinder - Steiner`s law1.15 (13381)Uniform rotary motion1.16 (13382)Uniform, accelerated rotationalmotion, moment of inertia

2. Acoustics2.1 (13360)Measurement of frequency oftuning forks, detuning of tuningforks2.2 (13361)Investigation of the naturaloscillation of columns of air2.3 (13362)Measurement of the speed ofsound in air2.4 (13363)Measurement of the speed ofsound in diffent gases2.5 (13364)Measurement of the speed inmetal rods2.6 (13365)Acoustical Doppler effect2.7 (13615)Investigation of beats2.8 (13619)Influence of damping on thespectrum of the characteristicoscillations of air columns2.9 (13620)Characteristic oscillations in cavityresonators - Hemholtz's resonators2.10 (13621)Tone analysis

2.11 (13622)Oscillations in metal plates2.12 (13623)Speech analysis2.13 (13628)Signal filtration - elimination ofbackground noises2.14 (13629)Determination of the speed ofsound in air - travel time measure-ment between two microphones2.15 (13630)Acoustic spacial orientation

3. Thermodynamics3.1 (13491)Specific heat capacity of water3.2 (13492)Specific evaporation heat ofwater3.3 (13493)Specific heat capacity of liquids3.4 (13494)Specific heat capacity of solidbodies3.5 (13495)Specific condensation heat ofwater3.6 (13496)Specific melting heat of ice3.7 (13497)Specific dissolution heat of salts3.8 (13498)Specific heat value of fuels3.9 (13499)Volume expansion of gases3.10 (13500)Gay-Lussas Law3.11 (13501)Amontons Law3.12 (13502)Boyle's and Mariotte's Law3.13 (13641)Gay-Lussac's law3.14 (13642)Charles' (Amontons') law - variant A3.15 (13643)Charles' (Amontons') law - variant B3.16 (13644)Boyle and Mariotte's law

4 Electricity4.1 (13303)Ohm's Law4.2 (13304)Temperature dependence of theresistance of pure metals4.3 (13305)Characteristics of semi-conductordiodes4.4 (13306)Collector current-collector voltagecharacteristic of an NPN-transistor4.5 (13307)Second order conductors4.6 (13308)Switch-on current of aincandescent bulb4.7 (13309)Measurement of the work andpower of an incandescent bulb4.8 (13310)Switch-on behaviour of acapacitance4.9 (13311)Switch-on behaviour of aninductivity4.10 (13312)Induction impulse



1. Food Chemistry1.1 (13705)The manual titration of citric acid1.2 (13706)The automatic titration of ordinary vinegar1.3 (13707)Determination of the phosporic acid contentof a soft drink1.4 (13708)The pH and degree of acidity of coffee1.5 (13709)Determination of the content of fruit acidin juices and wine1.6 (13710)Titration curves of fresh milk and sour milk1.7 (13711)Changes in pH during the aging of milk(souring)1.8 (13712)The buffering properties of foods1.9 (13713)Determination of the calcium carbonatecontent of egg shell1.10 (13714)Determination of the common salt contentof meat broth1.11 (13715)Chloride in mineral water

2 Ecology and Environment2.1 (13701)The conductivity of various water samples2.2 (13702)The pH of various water samples2.3 (13703)The origin of acid rain2.4 (13704)The twenty-four hour rhythm of an aquaticplant2.5 (13509)Comparison of the heat capacities of waterand land2.6 (13510)The Bergman rule: heat loss in dependenceon body surface area and volume2.7 (13511)The isolating effect of body coverage2.8 (13325)Daily course of luminosity2.9 (13325)Daily course of luminosity

3. Biochemistry3.1 (13696)Determination of the isoelectric point of anamino acid (glycine)3.2 (13697)The ionic permeability of the cell membrane3.3 (13698)Determination of the Michaelis constant3.4 (13699)Substrate inhibition of enzymes3.5 (13700)Enzyme inhibition (poisoning of enzymes

4. Nerves Physiology4.1 (13600)Neuro-simulator (membrane time constantand low-pass filtering)4.2 (13601)Neuro-simulator (how an exciting synapsefunctions)4.3 (13602)Mechanical stimulation of the rear end ofan earthworm4.4 (13603)Mechanical stimulation of the front end ofan earthworm4.5 (13604)Electrical stimulation of an anaesthesizedearthworm

5. Human Physiology5.1 (13326)Cardiac and vasular sonic measurement(Phonocardiography)5.2 (13327)Electrocardiography5.3 (13327)Electrocardiography5.4 (13503)Electromyography5.5 (13605)Muscle stretch reflex and determination ofconducting velocity5.6 (13504)Electro-oculography5.7 (13326)Cardiac and vascular sonic measurement(Phonocardiography)5.8 (13606)Acoustic orientation in space5.9 (13607)The enzymatic activity of catalase5.10 (13505)Blood pressure measurement5.11 (13506)Measurement of the respiratory rate5.12 (13507)Changes in the blood flow during smoking5.13 (13508)Regulation of body temperature

6. Plant Physiology6.1 (13608)Photosynthesis (bubble-counting method)6.2 (13513)Photosynthesis (measurement of oxygenpressure)6.3 (13512)Transpiration of leaves6.4 (13609)Glycolysis (measurement of pressure)6.5 (13514)Glycolysis (measurement of temperature6.6 (13515)Calorimetry of foods

7. Electrochemistry7.1 (13318)Electrolysis of copper sulphate solutions7.2 (13319)The electrochemical series of metals7.3 (13320)Electric potential of a concentrationelement

8. Chemical equilibrium8.1 (13321)Chromatographic seperation processes: gas chromatography

9. Gas laws9.1 (13499)Volume expansion of gases (with Software Pressure)9.2 (13500)Gay-Lussas Law (with Software Pressure)9.3 (13501)Amontons Law (with Software Pressure)9.4 (13502)Boyle's and Mariotte's Law (with Software Pressure)9.5 (13641)Gay-Lussac's law (with Software Gas Laws)9.6 (13642)Charles' (Amontons') law - variant A (with Software Gas Laws)9.7 (13643)Charles' (Amontons') law - variant B (with Software Gas Laws)9.8 (13644)Boyle and Mariotte's law (with Software Gas Laws)

Cobra3 Physics, Chemistry /Biology

Cobra3 Physics • No. 01310.02

Cobra3 Chemistry/Biology • No. 01320.02

4.11 (13313)Generation of an alternating cur-rent, rectification and filtration4.12 (13314)Efficiency of motor and generator4.13 (13366)Measurement of the reboundtime of a switch4.14 (13367)Current-voltage characteristic ofa solar cell4.15 (13611)Single-valued and multiple-valued Fourier spectra4.16 (13612)Analysis of simple and compositesinusoidal signals4.17 (13613)Spectral analysis of differentsignal forms - sinusoidal, rectan-gular, triangular signals4.18 (13614)Spectral analysis of periodic spikepulses4.19 (13616)Determination of the non-lineardistortion factor from the Fourierspectrum of distorted sinusoidaloscillations4.20 (13617)The Fourier spectrum of rectified,non-smoothed alternating currents4.21 (13618)Investigation of the characteristicoscillations of air columns4.22 (13624)Coupled electrical resonant cir-cuits4.23 (13625)Forced oscillations of a non-linearelectrical series resonance circuit- chaotic oscillation4.24 (13626)Analysis of Fourier series4.25 (13627)High-pass, low-pass, bandpassfilters4.26 (13631)Switch rebound4.27 (13632)Phase relationships in a seriesresonant circuit4.28 (13633)Free damped oscillation

5. Optics5.1 (13315)Dependence of the luminousintensity on the distance

6. Physical Structure of Matter6.1 (13368)Franck-Hertz Experiment6.2 (13634)Range of alpha particles in the air6.3 (13635)Mean range of beta radiation in air6.4 (13636)Absorption of electrons (orpositrons) in thin layers of matter6.5 (13637)The quantal flux of gammaradiation in air6.6 (13638)Absorption of gamma quanta (or electrons) as a function ofmaterial density6.7 (13639)Law of radioactive decay6.8 (13640)Radioactive equilibrium

LEP 5.2.44-11_5.4.20-00 12.10.2003 18:03 Uhr Seite 260

Index



Index

AAlpha-, beta-, gamma-particles 210

Absorption 136, 189, 197, 239240, 241, 243, 244, 255

Absorption coefficient of ultrasonic waves 71

Absorption coefficient 220, 221222, 223

Absorption edges 239, 240, 241243, 244, 249

Absorption inversesquare law 256

AC impedance 173, 174, 175

Acceleration 19, 20

Acceleration due to gravity 24

Acceleration of gravity 19

Acceptors 152

Acoustic resonant circuit 65

Acoustic waves 66

Adhesion 55

Adsorption 198

Aerofoil 58

Airy disk 93

Airy ring 93

Amount of substance 154

Amplitude holograms 106

Amplitude 36, 64

Analyzer 100, 103

Angle of incidence 58

Angle of scattering 211

Angular acceleration 30, 33, 40, 41

Angular frequency 43, 44

Angular momentum 27, 34, 35199, 201

Angular restoring force 45, 46

Angular restoring moment 48

Angular restoring torque 47

Angular velocity 28, 29, 30, 31, 3233, 40, 41, 47, 52

Anode 197

Anomalous Hall effect 236

Antineutrino 220, 221

Aperiodic case 43, 44

Apparent force 31, 32

Atomic beam 203

Atomic energy level scheme 250

Atomic form factor 251, 252253, 254

Atomic model accordingto Bohr 200

Attenuation coefficient 218

Avalanche effect 148, 178

Average velocity 123

Avogadro’s number 154

Axis of rotation 45, 46, 48

BBabinet’s theorem 74, 93, 96

Ballistics 26

Band-pass filter 184

Band spacing 232, 233

Band theory 232, 233, 234235, 237, 238

Band-width 176, 177, 184

Barrier layer 214, 215

Beat 40, 41

Beat frequency 61

Bernoulli equation 58

Bessel function 74, 93

Beta deflection 210

Beta+-decay 219

Beta–-decay 219

Beta-decay 220, 221

Bethe formula 216, 217

Binding energy 200, 230, 231, 248

Biot-Savart’s law 162, 163

Birefraction 105

Birefringence 109

Black body radiation 134

Bode diagram 180

Bohr magneton 202, 203

Bohr’s atomic model 202, 248, 250

Boiling point 127, 128, 130

Bounding surface 56

Boyle and Mariotte’s law 120

Boyle temperature 124

Bragg equation 239, 240, 241242, 245, 246

247, 250, 254, 255

Bragg reflection 205

Bragg scattering 243, 244, 248249, 251, 252

253

Bravais lattice 254

Bremsstrahlung 239, 240, 241243, 244, 247249, 257, 258

Brewster angle 107, 109

Brewster’s law 102, 103

Broadening of lines due toDoppler effect and pressurebroadening 89

CCapacitance 157, 159, 175, 176

177, 180, 182

Capacitance of a platecapacitor 160

Capacitor 155, 157, 176, 177, 180

Carbon film resistor 148

Carnot cycle 130

Cathode 197

Cathode rays 194

Cavity resonator

Central force 211

Centre of gravity 45, 46

Centrifugal force 32, 52

Centripetal force 31, 32

Characteristic frequency 40, 4143, 44

Characteristic impedance 184

Characteristic radiation 239, 240241, 243

244, 249, 250257, 258

CharacteristicX-ray radiation 226, 227, 230

231, 242, 245, 246247, 248, 251

Charge 154, 157

Charge carrier generation 148

Charge carriers 236

Charging 156

Charging capacitor 178

Charles’ (Amontons’) law 120

Chemical potential 132, 133

Circuit 146, 180

Circular motion 30

Circularly and ellipticallypolarised light 100

Circularly and ellipticallypolarized waves 187

Circulation 58

Clausius-Clapeyronequation 130, 131

Coefficient of cubiccompressibility 120

Coefficient of thermalexpansion 120

Coefficient of thermal tension 120

Coercive field strength 167

Coherence conditions 89

Coherence length fornon punctual light sources 89

Coherence time 89

Coherence 87, 93, 94, 95, 96, 106

Coherent light 85

Coil 169, 170, 176, 177, 180

Collector equations 136

Collision of second type 109

Compressibility 69

Compressor 137

Compton effect 220, 221228, 229, 255

Compton scattering 222, 223249

Compton wavelength 224, 225255

Concave lens 82

Concentration ratio 132, 133

Condensation 137

Conduction band 152, 232, 233234, 235, 237

238



Diffraction at the slit 186

Diffraction imageof a diffraction grating 200

Diffraction index 168

Diffraction spectrometer 199

Diffraction uncertainty 91

Diffusion 135

Diffusion potential 152

Diode and Zener diode 178

Diode laser 110, 112

Direct energy conversion 150

Directional characteristicpattern 188

Directional quantization 203

Directivity 188

Discharging 156

Disintegrationor decay constant 206, 207, 208

Disintegration product 206, 207208

Dispersion 83

Dissipation factor 184

Donors 152

Doppler effect 108

Doppler shift of frequency 61, 62

Dosimeter 256

Double refraction 100

Doublets 199

Drag coefficient 58

Droplet method 193

Dulong Petit’s law 127, 128

Duration 226, 227

Duration of oscillation 36

Dynamic and kinematicviscosity 54

Dynamic pressure 58

EEbullioscopic constants 132

Efficiency 136, 139, 150, 152

Efficiency rating 151

Elastic after-effect 17

Elastic collision 21

Elastic hysteresis 17

Elastic loss 21, 22

Elasticity 16

Electric charge 159

Electric constant 158, 160

Electric discharge 107

Electric field 155, 157, 158159, 193

Electric field constant 81

Electric field strenght 158

Electric flow 159

Electric flux 158

Electric theory of light 103

Electrical conductivity 135

Electrical eddy field 170

Electrode polarisation 153

Electrolysis 153, 154

Electromagnetic fieldinteraction 104

Electromagnetic theoryof light 102

Electromagnetism 104

Electromotive force (e.m.f.) 147

Electron capture 219

Electron charge 193, 194

Electron collision 195, 196

Electron concentrationin gases 216, 217

Electron in crossed fields 194

Electron mass 194

Electron oscillation 104

Electron spin 202, 203

Electrons 236

Electro-optical modulator 105

Electrostatic induction 157, 158

Electrostatic inductionconstant 157

Electrostatic potential 158, 159

Energy-band diagram 152

Energy ceiling 136

Energy dose 256

Conduction of heat 136

Conductivity 145, 232, 233

Conductor 146, 166

Connection between the finestructure of the �-spectrumand the accompanying�-spectrum 212, 213

Conservation of angularmomentum 220, 221

Conservation of energyand momentum 255

Conservation of energy 20, 21, 22

Conservation of momentum 21, 22

Conservation of parity 220, 221

Constructive and destructive interference 187

Contact resistance 145

Contrast medium 257

Convection 136, 151

Conversion electron 226, 227

Conversion of heat 139

Convex lens 82

Cooling capacity 151

Coplanar forces 14

Corpuscle 224, 225

Cosmic radiation 210

Coulomb field 211

Coulomb forces 211

Coulometry 154

Counter tube 218

Counting rate 206, 207, 208

Couple 14

Creeping 43, 44

Critical or optimum coupling 184

Critical point 55, 124

Cryoscopic constants 133

Cryoscopy 133

Crystal classes 254

Crystal lattices 252, 253, 254

Crystal structures 239, 240, 24147, 251

Crystal systems 252, 253, 254

Current 149

Current density 166

Curvature 13

Cycle 137

DDamped oscillation 171, 172

Damped/undampedfree oscillation 43, 44

Damping 176, 177

Damping constant 43, 44

Damping of waves 49

Daughter substance 206, 207, 208

De Broglie equation 205

De Broglie relationship 91

De Broglie wavelength 224, 225

Dead time 209, 220, 221

Debye temperature 127, 128

Debye-Scherrer method 205

Debye-Sears-effect 114

Decay diagram 219

Decay energy 214, 215, 219

Decay series 210, 214, 215

Decomposition of force 38, 39

Decomposition voltage 153

Defect electrons 236

Deformation 15

Degree of dissociation 132, 133

Degree of freedom 121

Density 69, 218

Detection probability 228, 229

Developing of film 106

Diameter 13

Dielectric constant 160

Dielectric displacement 158, 160

Dielectric polarisation 160

Dielectrics 157

Differencial energy loss 216, 217

Differentiating network 179

Different symmetriesof distributions 209

Diffraction 66, 91, 106187, 243, 244

Index



Energy level diagram(decay diagram) 212, 213

Energy levels 199, 200, 201, 239240, 241, 242, 243244, 245, 246, 247

248, 251

Energy of rotation 33

Energy of translation 33

Energy quantum 195, 196, 204

Energy term symbols 245, 246

Eötvös equation 55

Equation of adiabatic changeof slate 125

Equation of state 57, 124

Equation of state forideal gases 121, 122

Equilibrium 14, 52

Equilibrium spacing 119

Equipotential lines 155

Equivalent dose and ion doseand their rates 256

Evaporation 51

Exchange energy 199, 201

Excitation energy 195, 196199, 201

Excited nuclear states 212, 213

Exitation of molecularvibration 107

Expected value of pulse rate 209

Exponential function 156

Extension and compression 18

External photoelectriceffect 197, 198

Extrinsic conduction 234, 235237, 238

Extrinsic conductivity 232, 233

FFabry Perot Etalon 109

Fabry-Perot interferometer 202

Faraday’s contant 154

Faraday’s law 153, 154

Fermi characteristic energylevel 152

Ferromagnetic material 168

Field intensity 159

Field strength 166

Filter 180

First and second lawof thermodynamics 139

First law ofthermodynamics 121, 122, 129

Flat coils 163

Fluidity 54

Focal length 82

Focal point 187

Forbidden band 237, 238

Forbidden transition 220, 221199, 201

Forbidden zone 232, 233234, 235

Force 19

Forced cooling 151

Forced oscillation 43, 44

Fourier transform 113, 114

Four-point measurement 135

Four-wire method ofmeasurement 145

Fraunhofer andFresnel diffraction 72, 73, 74, 75

89, 93, 94, 9596

Fraunhofer diffraction 92, 113114, 186

Free and fixed end 49

Free charges 160

Free path 148

Free, damped, forced andtorsional oscillations 25

Frequency 49, 63, 6467, 68, 69, 81

Frequency doubling 111

Fresnel and Fraunhoferdiffraction 87

Fresnel biprism 84

Fresnel integrals 92

Fresnel mirror 84

Fresnel’s zone construction 74, 7587, 93

Fresnel zones 186

Frictional resistance 58

Frustrated total reflection 189

Full-wave rectifier 178

Gg-factor 203, 204

G-modulus 47

Gamma-emission 212, 213

Gamma-quanta 220, 221224, 225

Gamma-radiation 226, 227228, 229

Gamma-spectrometry 230, 231

Gamma-spectroscopy 222, 223

Galvanic elements 153

Gas 123

Gas constant 57

Gas discharge tube 109

Gas jaws 139

Gaussian beam 112

Gaussian distribution 209

Gaussian rule 159

Gay-Lussac theory 126

Gay-Lussac’s law 120

Geiger-Nuttal law 214, 215

General equationof state for ideal gases 120, 154

Gibbs-Helmholtzequation 132, 133

Gradient 159

Graetz rectifier 178

Graphite structure 205

Gravitational acceleration 23

Gravitational force 39

Gravity pendulum 40, 41

Greenhouse effect 136

Group velocity 50

Grüneisen equation 119

Gyroscope 33

HH2O anomaly 51

Half life 156, 206, 207, 208

Half-shade principle 101

Half-value thickness 220, 221249

Half-wave rectifier 178

Hall coefficient 232, 233

Hall effect 104, 162, 163

Hall mobility 236

Harmonic oscillation 36, 38, 39

Harmonic sound intervals 59

Harmonic wave 50

Heat conduction 151

Heat conductivity 138

Heat of vaporisation 130

Heat pipe 151

Heat radiation 136

Heat transfer 138

Heat transition 138

Heat transport 135

Heating capacity 151

Helmholtz coils 161, 164

Henry’s law 132

High- and low-pass filters 108

High-pass 179

Hooke’s law 15, 16, 17

Hooke’s law oscillations 42

Horn antenna 188

Hothouse effect 138

Huygens’ principle 72, 73, 74, 7576, 93, 94, 95

96, 113, 114, 186

Huygens-Fresnel principle 66, 87

Hydrogen bond 51

IIdeal gas 124

Identity of atomic numberand charge on the nucleus 211

Index



Index

Illuminance 97, 98, 99

Image charge 159

Impact parameter 211

Impedance 181, 182

Impurity depletion 237, 238

Inclinometer 161

Index of refraction 113, 114

Induced emission 107, 110, 111

Induced resistance 58

Induced voltage 170

Inductance 173, 174, 176177, 180

Induction 159, 162, 165166, 167, 169

Induction constant 159

Inductive and capacitivereactance 181

Inelastic collision 27

Inside diameter thickness 13

Instantaneous velocity 33

Integrating network 179

Intensity of characteristicX-rays 242

Intensity 92

Interaction potential 124

Interaction with material 228, 229

Interface 55

Interference 64, 66, 72, 73, 74, 7576, 87, 88, 89, 90, 93

94, 95, 96, 106, 108, 168239, 240, 241, 244, 247

Interference in thin films 85

Interference ofelectromagnetic waves 202

Interference of equal inclination 86

Interference of thin layers 86

Internal energy 127, 128

Internal friction 53

Internal resistance 152, 178

Intrinsic conduction 234, 235237, 238

Intrinsic conductivity 232, 233

Intrinsic energy 126

Inverse Joule-Thomson effect 126

Inversion 107, 109, 110, 111

Inversion temperature 126

Ionising particles 210

Ionizing energy 256

Isobars 121, 122

Isochoric and isothermalchanges 139

Isochors and adiabaticchanges of slate 121, 122

Isoclinic lines 161

Isogenic lines 161

Isomeric nuclei 226, 227

Isotherms 121, 122

Isotopic properties 214, 215

Isotopic spin quantumnumbers 226, 227

JJoule effect 151

KKinetic gas theory

Kinetic theory of gases 123

Kirchhoff’s diffraction formula 91

Kirchhoff’s laws 146, 147, 173174, 175, 180, 181

Klein-Nishina formula 224, 225

LLaminar flow 58

Landé factor 204

Laser 93, 94, 95, 96

Lattice constant 239, 240241, 247

Lattice planes 205

Lattice potential 119

Lattice vibration 127, 128

Law of absorption 71, 249257, 258

Law of distance 188

Law of inductance 171

Law of induction 183

Law of gravitation 25

Law of lenses 82

Law of refraction 102

Laws governing falling bodies 24

Laws of falling bodies 23

Length 13

Lenses 113, 114

Lenz’s law 171, 172

Lever 14

Light intensity 99

Light quantity 99

Light velocity 90

Limit of elasticity 17, 18, 42

Linearity 187

Linear expansion 119

Linear motion 20, 21, 22

Linear motion due toconstant acceleration 23, 24

Linear relationship betweenthe propagation time of soundand its respective path 60

Liquid 54

Littrow prism 109

Loaded transformer 169

Local ion dose rate 256

Logarithmic decrement 43, 44171, 172

Longitudinal waves 60, 63, 6870, 71, 7272, 73, 74

75, 76

Lorentz force 149, 194, 210, 232233, 234, 235

Lorenz number 135

Loudness 64

Loss resistance 176, 177

Low-pass 179

Luminance 97, 98, 99

Luminous flux 97, 98, 99

Luminous intensity 97, 98

Lyman-, Paschen-, Brackett-and Pfund-Series 200

MMagnetic field 162

Magnetic field constant 81

Magnetic field of coils 167, 170

Magnetic field strength 167

Magnetic flow density 161

Magnetic flux 164, 165, 166169, 170, 183

Magnetic flux, coil 167

Magnetic flux density 162

Magnetic inclination anddeclination 161

Magnetic induction (formerlymagnetic-flux densitiy) 149

Magnetic moment 203

Magnetic resistance 232, 233234

Magneto resistance 235

Magnification 82, 89

Malus’ law 103

Mass absorptioncoefficient 249, 257, 258

Mass coverage 218

Mass-spring system 59

Material waves 205

Mathematical pendulum 38, 39

Mathies rule 148

Maxwell disk 33

Maxwell relationship 83

Maxwell’s equations 160, 163, 165166, 170, 173174, 175, 183

Maxwellian velocitydistribution 203

Mean energy loss of�-particles per collision 216, 217

Mean free path length 216, 217

Mean ionization energyof gas atoms 216, 217

Mean lifetime of ametastable state 110

Measurement accuracy 91

Measurement of projectilevelocities 27


Mechanical equivalent of heat 129

Mechanical hysteresis 16

Mechanical work 129

Melting 51

Mesons 210

Metallic film resistor 148

Metastable states 201, 226, 227

Michelson interferometer 89, 185

Microscope 82

Miller indices 251, 252253, 254

Mixture temperature 127, 128

Mobility 232, 233

Model kinetic energy 123

Modulation 81

Modulation of light 105

Modulus of elasticity 15, 47

Mohr balance 51

Mole volumes 121, 122

Molecular vibration 107

Molecule radius 124

Molecules 123

Moment 14, 28, 29

Moment of inertia 27, 29, 3033, 35, 37, 3845, 46, 47, 48

Moment of inertia of2 point masses 48

Moment of inertia of a bar 28, 48

Moment of inertia of acylinder 48

Moment of inertia of adisc 28, 48

Moment of inertia of amass point 28

Moment of inertia of a sphere 48

Moment of inertia of spheresand rods 25

Momentum of inertia 34

Monomode and multimodefibre 112

Moseley’s law 250

Moseley’s law;Rydberg frequency and screening constant 248

Motion involving uniformacceleration 26

Moving charges 149

Multiplicity 199, 201

Multipole radiation 226, 227

NNatural frequency 49

Natural vibrations 59, 63

Neutrino 219

Newton’s Laws 30

Newton’s ring apparatus 85

Newtonian liquid 54

Neyer-Neldel Rule 234, 235

No-load operation 147

Normal Hall effect 236

NTC 148

Nuclear transitions 226, 227

Numerical aperture 112

Nutation 34, 35

OObject beam 106

Object distance 82

Ohm’s law 145, 147

Ohmic resistance 181

Optic axis 100

Optical activity 101

Optical anisotropy 105

Optical path difference 86

Optical pumping 111

Optical resonator 107, 111

Optical rotatory power 101

Order of diffraction 239240, 241

Ordinary andextraordinary ray 100

Orthohelium 199, 201

Oscillation period 38, 39

Oscillatory circuit 171, 172

Pp-n junction 152

Pair formation 220, 221, 228, 229

Pair production 222, 223, 249

Paraboloid of rotation 52

Parahelium 199, 201

Parallel conductance 184

Parallel connection 175

Parallel springs 42

Parallel-T filters 179

Parallel-tuned circuit 176, 177

Parent substance 206, 207, 208

Particle energy 214, 215

Particle velocity 210

Path difference 85

Path of a ray 82

Pauli method 184

Peltier coefficient 150, 151

Peltier effect 151

Period 36

Periodic motion 49

Phase 81, 84, 88, 90, 168

Phase center 188

Phase displacement 173, 174, 175176, 177, 180

Phase holograms 106

Phase relationship 85

Phase shift 64, 182

Phase velocity 49, 50, 189

Phasor diagram 182

Photo-conductive effect 152

Photo effect 222, 223

Photoelectric effect 220, 221, 228229, 249, 230

231

Photon energy 197, 198

Photonuclear reaction 226, 227

Physical pendulum 37, 38, 39

Piezoelectric effect 68, 69

Piezoelectric ultrasonictransducer 69

Piezoelectric ultrasonicstransformer 68

Planck’s constant 200

Plane 100

Plane of polarisation 100

Plane parallel plate 86

Plastic flow 16

Plasticity 16, 53

PLZT-element 105

Poisson’s distribution 209

Poisson’s ratio 15

Poisson’s spot 74, 93, 96

Polar diagram 58

Polariser 100

Polarizability 83

Polarization level 102

Polarization of light 105

Polarization 102, 103, 104107, 111

Polarizer 103

Polarizer and Analyzer 187

Polytropic equation 125

Positron 219

Potential 155, 157

Potential and kinetic energy 27

Potential difference 159

Potential energy 33

Potential well model ofthe atomic nucleus 214, 215

Power matching 147

Precession 34, 35

Pressure 57, 131

Pressure and temperature 120

Principle of conservationof momentum 27

Prism 83

Propagation of soundwaves 61, 62, 71

PTC 148


Index



Index

QQ factor 171, 172, 176

177, 184, 256

Quantisation of energy levels 202

Quantity of light 97, 98

Quantum leap 196

Quantum number 204

Rr.m.s. value 178

Radioactive decay 210, 218222, 223

Radioactive equilibrium 214, 215

Radioactive radiation 220, 221

Range 216, 217

Range dispersion 216, 217

Raoult’s law 132, 133

Rate of decay 206, 207, 208

Ratio of attenuation/decrement 43, 44

Reaction rate 101

Real and virtual image 106

Real charges 160

Real gas 124, 126

Real image 82

Reciprocal lattice 251, 252253, 254

Recovering time and resolutiontime of a counter tube 209

Reduced length of pendulum 37

Reference beam 106

Reflection 66, 86, 185, 189

Reflection coefficient 102

Reflection factor 102

Reflection of longitudinalwaves 70

Refraction 86, 189

Refraction index 90

Refractive index 81, 83, 88

Refrigerator 137

Relativistic Lorentz equation 219

Relaxation 16, 110, 111

Remanence 167

Resistance 146, 176, 177, 180

Resistance to pressure 58

Resistivity 145

Resolution of opticalinstruments 93

Resonance 171, 172, 184, 204

Resonance frequency 43, 44, 65

Resonator cavity 109

Resonator modes 111

Rest energy 255

Resting energy 219

Restrictor valve 137

Reversible cycles 139

Reversible pendulum 37

Reynolds number 58

Rigid body 45, 46, 48

Ripple 178

Ripple voltage 178

Rotary motion 28, 31, 32, 52

Rotation 29, 30

Rotation niveau 107

Rotational energy 27, 29

Rowland grating 83

Rüchardt’s experiment 125

Rules governing selection 226, 227

Rutherford atomic model 211

Rydberg constant 250

Rydberg series 201

SSaccharimetry 101

Sampling theorem 108

Scattering 211, 224 ,225

Scattering of light by smallparticles (Mie scattering) 108

Scintillation detectors 226, 227228, 229

Screening constant 250

Seebeck coefficient 150, 151

Seebeck effect (thermoelectric effect) 150

Selection rules 199, 201, 245, 246

Self-inductance 171, 172, 182

Semiconductor 152, 214, 215232, 233, 234235, 237, 238

Serial springs 42

Series connection 146, 175

Series-tuned circuit 176, 177

Shear modulus 25, 47

Shear stress 53

Shell structure of electronshells 230, 231

Short circuit 147

Single electron atom 200

Singlet and triplet series 199, 201

Slope efficiency 112

Smoothing factor 178

Solenoids 171, 172

Sound pressure 67

Sound velocity 67

Sound velocity in gasesand solids 63

Spatial and time coherence 89

Specific heat 135

Specific rotation 101

Specific thermal capacity 129

Spectral lines(shape and half width value) 89

Spectral power density 108

Spectrometer-goniometer 83

Spectrum of emission 107

Speed of light 168

Spin 199, 201

Spinorbit interaction 201

Spin-orbital angularmomentum interaction 199

Spin-orbit coupling 168

Spiral spring 40, 41

Spontaneous and stimulatedlight emission 109

Spontaneous emission 107, 110111

Spring constant 17, 18, 40, 4142, 45, 46, 48

Square wave 179

Standard deviation 209

Standing waves 49, 185

Statics 14

Stationary longitudinal waves 70

Stationary waves 63, 66, 67

Steiner’s law 37

Steiner’s theorem 25

Step response 179

Stereographic projection 258

Stirling engine 139

Stokes’ law 54, 193

Stress 15

Structure amplitude 252, 253, 254

Structure factor 251

Superimpositionof magnetic fields 165

Superimpositionof sound waves 61

Superposition of waves 70

Surface adhesion 56

Surface charge density 158, 159

Surface energy 55, 56

Surface tension 55, 56

Surface waves 189

Sweep 184

TTelescope 82

Temperature 57, 123, 131

Temperature amplitudeattenuation 138

Temperature dependenceof resistances 134

Temperature gradient 135

Term diagram 220, 221


Terminal voltage 147

Terrestrial gravitationalacceleration 37

Testoring torque 44

The Bragg equation 239, 240, 241242, 245, 246

247, 250, 254, 255

Thermal capacity 119, 129, 138

Thermal capacity of gases 125

Thermal energy 129

Thermal pump 139

Thermal radiation 138

Thermoelectric e. m. f. 134150, 151

Thomson coefficient 150, 151

Thomson equations 150, 151

Threshold energy 112

Throttling 126

Time constant 156

Time measurement 13

Torque 16, 29, 34, 35, 4041, 44, 47, 164

Torque and Restoring torque 43

Torsion molulus 16

Torsion pendulum 43, 44

Torsional vibration 40, 41, 4344, 45, 46, 48

Total reflection 112, 189

Trajectory parabola 26

Transfer function 179

Transformer 171, 172

Transit time 112

Transition probability 212, 213226, 227

Transmission 185, 189, 255

Transverse and longitudinalmodes 112

Transverse and longitudinalresonator modes 109

Transverse and longitudinalwaves 64

Transverse waves 187

Tuned circuit 176, 177

Tunnel effect 189, 214, 215

Turbulence 108

Turbulent flow 58

Two-wire field 203

UUltrasonics 67, 69

Uncertainty of location 91

Uncertainty of momentum 91

Uniform magnetic field 149, 164

Universal gas constant degreeof freedom 122

Universal gas constant 120, 121

Unloaded transformer 169

Use of an interface 42, 66

VValence band 152, 232, 233, 234

235, 237, 238

Van der Waals equation 124, 126

Van der Waals force 126

Van’t Hoff law 130

Van’t Hoff factor 133

Vaporisation enthalpy 137

Vaporization 131, 137

Vapour pressure 131, 137

Variable g-pendulum 39

Velocity 19, 20, 21, 22

Velocity distribution 123

Velocity gradient 53

Velocity of light 88, 112

Velocity of sound 60

Velocity of sound in air 64

Velocity of sound in liquids 68, 69

Verdet’s constant 104

Vernier 13

Vibration niveau 107

Virtual image 82

Virtual light source 84, 88, 90168

Viscosity 53, 193

Viscosity measurements 54

Visible spectral range 200

Voltage 146, 155, 157

Voltage doubling 178

Voltage source 147

Voltage stabilisation 178

Volume 120, 131

Volume expansion 51

Volume expansion of liquids 119

WWave equation 50

Wavelength 49, 50, 63, 64, 6768, 69, 81, 84, 88

90, 168, 185

Wave-particle dualism 91

Weak interaction 220, 221

Weber-Fechner law 64, 101

Weight resolution 13

Weiss molecular magneticfields 168

Wheatstone bridge 181

Wiedmann-Franz law 135

Wien-Robinson bridge 179

Wire loop 162, 163

Work function 197, 198

XX-ray bremsstrahlung 250

X-ray radiation 257, 258

X-ray spectral analysis 230, 231

X-ray tube 240, 241, 247

X-rays 255, 256

YYoung’s modulus 15

ZZ diode 148

Zeeman effect 204

Zener effect 148

Zone plates 75, 87


Index


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PHYSICS – CHEMISTRY – BIOLOGYThe comprehensive catalogue for physics, chemistry

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PHYSICS - accueil › iso... · 1 About Phywe Founded in Göttingen, Germany in 1913 by Dr. Gotthelf Leimbach, Phywe Systeme GmbH & Co. KG quickly advanced to one of the leading manufacturers