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Introduction to modern physics:Physics of the 20th and 21st centuries

Lectures: Quantum physics Nuclear and particle physics some condensed matter physics Relativity – special, general Cosmology

Lab experiments: some of the following: Earth’s magnetic field Geiger Müller counter, half life measurement operational amplifier mass of the K0 particle e/m of electron Franck-Hertz experiment Hall effect Planck’s constant from LED’s

Homework problems problem solving, modeling, simulations website http://www.physics.fsu.edu/courses/Summer13/YSP

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Quantum physics(quantum theory, quantum

mechanics)Part 1:

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Outline Introduction Problems of classical physics emission and absorption spectra Black-body Radiation

experimental observations Wien’s displacement law Stefan – Boltzmann law Rayleigh - Jeans Wien’s radiation law Planck’s radiation law

photoelectric effect observation studies Einstein’s explanation

Summary

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Question: What do these have in common? lasers solar cells transistors computer chips CCDs in digital cameras Ipods superconductors .........

Answer: They are all based on the quantum

physics discovered in the 20th century.

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Why Quantum Physics? “Classical Physics”:

developed in 15th to 20th century; provides very successful description of “every

day, ordinary objects”o motion of trains, cars, bullets,….o orbit of moon, planetso how an engine works,..

subfields: mechanics, thermodynamics, electrodynamics,

Quantum Physics:o developed early 20th century, in response to

shortcomings of classical physics in describing certain phenomena (blackbody radiation, photoelectric effect, emission and absorption spectra…)

o describes “small” objects (e.g. atoms and their constituents)

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“Classical” vs “modern” physics

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Quantum Physics QP is “weird and counterintuitive”

o“Those who are not shocked when they first come across quantum theory cannot possibly have understood it” (Niels Bohr)

o “Nobody feels perfectly comfortable with it “ (Murray Gell-Mann)

o“I can safely say that nobody understands quantum mechanics” (Richard Feynman)

But:oQM is the most successful theory ever

developed by humanityo underlies our understanding of atoms,

molecules, condensed matter, nuclei, elementary particles

oCrucial ingredient in understanding of stars, …

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Features of QP Quantum physics is basically the

recognition that there is less difference between waves and particles than was thought before

key insights:o light can behave like a particleo particles (e.g. electrons) are

indistinguishableo particles can behave like waves (or wave

packets)o waves gain or lose energy only in

"quantized amounts“o detection (measurement) of a particle

wave will change suddenly into a new wave

o quantum mechanical interference – amplitudes add

o QP is intrinsically probabilistic o what you can measure is what you can

know

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emission spectra

continuous spectrumosolid, liquid, or dense gas emits

continuous spectrum of electromagnetic radiation (“thermal radiation”);

o total intensity and frequency dependence of intensity change with temperature (Kirchhoff, Bunsen, Wien, Stefan, Boltzmann, Planck)

line spectrumorarefied gas which is “excited” by

heating, or by passing discharge through it, emits radiation consisting of discrete wavelengths (“line spectrum”)

o wavelengths of spectral lines are characteristic of atoms

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Emission spectra:

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Absorption spectra

first seen by Fraunhofer in light from Sun;

spectra of light from stars are absorption spectra (light emitted by hotter parts of star further inside passes through colder “atmosphere” of star)

dark lines in absorption spectra match bright lines in discrete emission spectra

Helium discovered by studying Sun's spectrum

light from continuous-spectrum source passes through colder rarefied gas before reaching observer;

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Fraunhofer spectra

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Spectroscopic studies

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Kinetic theory of heat

Molecules are in constant random motion, Average kinetic energy depends only on

temperature In thermal equilibrium, energy is equally shared

between all “degrees of freedom” of the possible motions, ave. kinetic energy per degree of freedom = <K> = ½kBT (kB = Boltzmann’s constant)

Degrees of freedom: translational motion in 3 dimensions has 3 degrees of freedom (dof);

Rotational and vibrational motion: nb. of dof depends on number of atoms and their configuration in molecule

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0th law of thermodynamics between bodies of different temperature (i.e. of

different average internal thermal energy), heat will flow from the body of higher temperature to the body of lower temperature until the temperatures of the two bodies are the same;

then the bodies are in “thermal equilibrium” two bodies are in thermal equilibrium (at same

temperature) if there is no heat flow between them; corollary: if two bodies are in thermal equilibrium with a

third body, then they are in thermal equilibrium with each other.

can use thermometer to compare temperature note:

o observation only shows that temperatures equalize - heat flow is hypothesis

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temperature Temperature:

was measured long before it was understood; Galilei (around 1592): “device to measure

degree of hotness”; inverted narrow-necked flask, warmed in hand, put upside down into liquid; liquid level indicates temperature; OK, but not calibrated.

Hooke, Huygens, Boyle (1665): “fixed points” -freezing or boiling point of water;

C. Renaldini (1694): use both freezing and boiling point

Modern point of view: temperature is measure of kinetic energy of random motion of molecules, atoms,..

http://en.wikipedia.org/wiki/Temperature http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html http://eo.ucar.edu/skymath/tmp2.html http://www.visionlearning.com/library/module_viewer.php?mid=48

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Thermal energy, heat, temperature observation of ”Brownian motion” (1827):

small seeds (e.g. burlap) suspended in liquid show erratic motion (“random motion”)

http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html http://www.aip.org/history/einstein/brownian.htm

kinetic theory of heat (Boltzmann, Maxwell,...) heat is a form of energy; internal energy = thermal energy of material bodies is

related to random motions of molecules or atoms temperature is a measure of this internal energy . explanation of Brownian motion: Albert Einstein

(1905): calculated speed of “diffusion” from kinetic theory of heat - found in agreement with experimental measurements

strong support for atomic picture of matter http://en.wikipedia.org/wiki/Theory_of_heat http://en.wikipedia.org/wiki/Kinetic_theory http://www.vias.org/physics/bk2_03_02.html http://www.youtube.com/watch?v=-n90pfbiBJE http://galileo.phys.virginia.edu/classes/252/kinetic_theory.html

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Fahrenheit, Celsius scale Fahrenheit scale:

Gabriel Daniel Fahrenheit (Danzig, 1686-1736), glassblower and physicist;

o reproducible thermometer using mercury (liquid throughout range) (around 1715)

o 0 point: lowest temperature of winter of 1709, (using mix of water, ice, salt  −17.8 °C )

o 96o= body temperature (96 divisible by 12, 8),o water freezes at 32oF, boils at 212oF o http://inventors.about.com/od/tstartinventions/a/History-Of-The-Thermometer.htm

Celsius scale: Anders Celsius (Swedish astronomer, 1701 -

1744) 0o C = ice point (mixture of water and ice at 1

atm) 100o C = boiling point of water at 1 atm. (1742)

relation between Fahrenheit and Celsius degrees: TC = (5/9)(TF - 32 ) , TF = (9/5)TC + 32

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Temperature (2) thermodynamic temperature scale

(absolute, Kelvin scale) pressure vs temperature of gas at constant

volume and volume vs temperature of gas at constant pressure extrapolate to zero at - 273.15o C

this is “absolute zero” unit: Kelvin Size of unit of Kelvin scale = that of Celsius scale,

only shift of zero-point This is the temperature scale which is used in

most of physics http://en.wikipedia.org/wiki/Kelvin http://abyss.uoregon.edu/~js/glossary/temperature_scale.html http://lamar.colostate.edu/~hillger/temps.htm

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Range of temperatures Universe 5×10−44 s after the Big Bang: T 1.4×1032 K core of hottest stars, 4109 K; seems maximum now hydrogen bomb ignites at , 4107K; interior of Sun , 1.5106K; plasma 105K; 105K : clouds of atoms, ions, e, occasional molecule; 5800 K: surface of the Sun; 5000 K: cool spots at surface of the

Sun; evidence for some molecules; 3000 K: water steam: about 1/4 of water molecules ruptured

into atoms; 2800 K: W light bulb filament; 2000 K: molten lava; 1520 oC: iron melts; 327 o C: lead melts; 100oC (373.15 K): water boils; 252 K (-21.1 o C = 5.8o F): temp. of salt-ice saltwater mix; 234 K: mercury freezes; 194 K: dry ice freezes; 77 K: nitrogen boils 4 K: helium boils. ;

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Thermal radiation thermal radiation = e.m. radiation emitted by a body by

virtue of its temperature spectrum is continuous, comprising all wavelengths thermal radiation formed inside body by random thermal

motions of its atoms and molecules, repeatedly absorbed and re-emitted on its way to surface original character of radiation obliterated spectrum of radiation depends only on temperature, not on identity of object

amount of radiation actually emitted or absorbed depends on nature of surface

good absorbers are also good emitters (why??) http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/absrad.html http://casswww.ucsd.edu/archive/public/tutorial/Planck.html http://panda.unm.edu/Courses/Finley/P262/ThermalRad/ThermalRad.html http://csep10.phys.utk.edu/astr162/lect/light/radiation.html http://www.youtube.com/watch?v=CDncSyDvpdQ http://www.enotes.com/topic/Kirchhoff's_law_of_thermal_radiation http://ip.anndannenberg.com/IPHandouts/Heattransfernotes.pdf

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warm bodies emit radiation

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Black-body radiation “Black body”

perfect absorber o ideal body which absorbs all e.m. radiation

that strikes it, any wavelength, any intensity

o such a body would appear black “black body”

must also be perfect emitteroable to emit radiation of any wavelength at

any intensity -- “black-body radiation” “Hollow cavity” (“Hohlraum”) kept at

constant To hollow cavity with small hole in wall is good

approximation to black bodyothermal equilibrium inside, radiation can

escape through hole, looks like black-body radiation

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Studies of radiation from hollow cavity

In 2nd half of 19th century, behavior of radiation within a heated cavity studied by many physicists, both theoretically and experimentally

Experimental findings: spectral density ρ(f,T)

(= energy per unit volume per unit frequency) of the heated cavity depends on the frequency f of the emitted light and the temperature T of the cavity and nothing else.

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Thermal radiation “Global description”, i.e without frequency dependence:

Descriptions successful, i.e. in agreement with observations

total power output of black body: Stefan-Boltzmann law: For an “ideal” radiator (“black body”),

total emitted power (per unit emitting area), P/A P/A = σ·T4 σ = 5.672 · 10-8 W m-2 K-4

(Josef Stefan, Ludwig Boltzmann 1879, 1884)

http://csep10.phys.utk.edu/astr162/lect/light/radiation.html http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html http://scienceworld.wolfram.com/physics/Stefan-BoltzmannLaw.html

Wien’s displacement law (1893) peak vs temperature:

max ·T = C, C= 2.898 · 10-3 mK inverse relationship between the wavelength of the peak of the emission of a black body and its temperature when expressed as a function of wavelength

http://en.wikipedia.org/wiki/Wien's_displacement_law hyperphysics.phy-astr.gsu.edu/hbase/quantum/wien2.html http://scienceworld.wolfram.com/physics/WiensDisplacementLaw.html http://webphysics.davidson.edu/faculty/dmb/blackbody/Wiendemo.html

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Intensity vs frequency

Wilhelm Wien (1896) r(f, T) = af3 exp(-bf/T),

(a and b constants).

OK for high frequency but fails for low frequencies http://en.wikipedia.org/wiki/Wien_approximation http://theochem.kuchem.kyoto-u.ac.jp/Ando/planck1901.pdf http://bado-shanai.net/map%20of%20physics/mopWienslaws.htm

http://physics.info/planck/

Rayleigh-Jeans Law (1900)r(f,T) = af2T (a = constant)

(constant found to be = 8pk/c3 by James Jeans, in 1906) OK for low frequencies, but “ultra – violet catastrophe” at

high frequencies, i.e. intensity grows f2 for f (corresponding to limit of wavelength 0)

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html

http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html http://scienceworld.wolfram.com/physics/Rayleigh-JeansLaw.html

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Ultraviolet catastrophe

(Rayleigh-Jeans)

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Planck’s quantum hypothesis Max Planck (Oct 1900) found formula that

reproduced the experimental results

derivation from classical thermodynamics, but required assumption that oscillator energies can only take specific values E = 0, hf, 2hf, 3hf, …

for a multi-state system of particles in thermal equilibrium, probability for particle to be in state with energy E,

P(E) = (1/Z)e-E/kT (“Boltzmann factor” )

2

3

/

8( , )

1

osc

osc hf kT

ff T E

chf

Ee

<Eosc> is the averageenergy of a cavity “oscillator”

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Black-body radiation spectrum Measurements of

Lummer and Pringsheim (1900)

calculationschematisch

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Consequences of Planck’s hypothesis

oscillator energies E = nhf, n = 0,1,…; h = 6.626 10-34 Js = 4.13 10-15 eV·s

now called Planck’s constant

oscillator’s energy can only change by discrete amounts, absorb or emit energy in small packets – “quanta”;

Equantum = hf average energy of oscillator

<Eosc> = hf/(ex – 1) with x = hf/kT; for low frequencies get classical result <Eosc> = kT, k = 1.38 · 10-23 J·K-1

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Frequencies in cavity radiation

cavity radiation = system of standing waves produced by interference of e.m. waves reflected between cavity walls

many more “modes” per wavelength band at high frequencies (short wavelengths)

than at low frequencies for cavity of volume V, n = (8πV/4)

or n = (8πV/c3) f2 f

if energy continuous, get equipartition, <E> = kT all modes have same energy spectral density grows beyond bounds as f

If energy related to frequency and not continous (E = nhf), the “Boltzmann factor” e-E/kT leads to a suppression of high frequencies

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Problems

estimate Sun’s surface temperature assuming: Earth and Sun are black bodies Stefan-Boltzmann law Earth in energetic equilibrium

(i.e. rad. power absorbed = rad. power emitted) , mean temperature T = 290K

Sun’s angular size Sun = 32’ show that for small frequencies, Planck’s average

oscillator energy yields classical equipartition result <Eosc> = kT

show that for standing waves on a string, number of waves in band between and + is n = (2L/2)

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Summary

classical physics explanation of black-body radiation failed

Planck’s ad-hoc assumption of “energy quanta” of energy Equantum = h, modifying Wien’s

radiation law, leads to a radiation spectrum which agrees with experiment.

old generally accepted principle of “natura non facit saltus” violated

Opens path to further developments