The Birth of Modern Physics1895 - 1910

Thornton and Rex, Ch. 1

The Experimental Basis ofQuantum Theory

Thornton and Rex, Ch. 3

- Experimental discoveries:

Quantum Physics1895 X-rays

Relativity1896 Radioactivity

Atomic Physics1897 The electron

Nuclear Physics

Particle Physics

1907 Rutherford Scattering

- Theoretical insights:

1900 Planck (blackbody radiation)

1905 Einstein (relativity, brownian motion, photoelec. effect)

Important discoveries of 1895-1897(X-rays, radioactivity, the electron)

• Made while experimenting with cathoderay tubes

- +

Cathode Anode

• Plucker (1858-1859) - glow moves witha magnet.

• Hittorf (1869) - objects in front ofcathode cast shadows

• Goldstein (1876) coins term“cathode rays”

But what were cathode rays?

• Electromagnetic waves?

-conclusion of German establishment

(Hertz failed to bend rays withelectric field (1892).)

• Electrically-charged particles?

-prevailing view in England

J.J. Thomson (1856-1940)

- In 1897 he proved conclusively thatcathode rays were indeed streams ofnegatively-charged particles.

-obtained better vacuum

-deflected the rays by bothelectric and magnetic fields.

-able to calculate

Charge e = = 1.7 x 1011 Coulombs/kgMass m

(about 2000 times larger than that of Hydrogen atom)

Explanation of the “glow”:

• Electrons striking and exciting residualmolecules of air left in the tube (byinferior pumps).

- +

Cathode Anode

• Thomson (using techniques of Wilson)later measured charge and massseparately.

- Charges attach on water droplets

• Technique refined by Robert Millikan(1910).

The electron charge is

e = -1.6 x 10-19 Coulombs.

X-rays- Roentgen (1895) studying cathode raytube, noticed glass tubing glowing somedistance away.

- He covered the tube with black paper ina dark room. A flourescent screen lit up,even if faced away from the dischargetube.

-Then he placed his hand between thedischarge tube and the screen and saw theshadow of his bones!

fi X-Rays! (later shown to be high frequency electromagnetic waves)

Radioactivity- Becquerel (1896) was testing variousflourescent materials to see if theyemitted X-rays.

- He sealed a photographic plate in blackpaper and sprinkled a layer of UranylPotassium sulfate onto the paper.

- He wanted to expose the salt to sunlightin order to make it flouresce, but that dayParis was gray and overcast.

-Despite this images exposed with greatintensity.

-The new phenomenon was named“radioactivity” by Marie Curie.

The radiation from uranium was found toconsist of 3 distinct components --illustrated by its behavior in a magneticfield:

b-rays: electrons (Becquerel, 1900). Theyhave a range of energies and arefast and penetrating. Can beabsorbed by ~1 mm of lead.

a-rays: Helium nuclei (Rutherford, et al).They are heavy, slow, positively-charged particles. Absorbed by~few cm of air.

g-rays: Electromagnetic radiation, with ahigher frequency, lower wavelength,even than X-rays.

TransmutationPierre and Marie Curie found newradioactive elements, including Thorium,Polonium, and Radium.

A considerable amount of chemistrydetective work, especially by the Curies,Rutherford, and Soddy led to a remarkableconclusion:

Every Radioactive decay is a transmutationof the elements, a change from oneelement to another.

Blackbody RadiationAs an object gets hot, it radiates energy.

How does the radiation depend ontemperature?

What is the distribution amongfrequencies (or wavelengths)?

I(l,T) = Intensity as a function ofwavelength l and temperature T

Two experimental facts:

1) lmax T = 2.898 x 10-3 m˙K

(Wien’s displacement law)

2) Total Power (per unit Area)R(T) = ∫ I(l,T) dl

given by

R(T) = esT4

with e=1 for blackbody radiator (Stefan-Boltzmann law)

s = 5.67 x 10-8 W/ (m2 ˙K4)

0

∞

An ideal blackbody radiator can beconsidered as a black box with a tiny hole:

Any light that enters the hole is unlikely toescape; hence, a black body absorber (andemitter).

Lord Rayleigh and Sir James Jeans triedto explain the distribution usingequipartion of energy: the average energyin each mode of oscillation of the radiationis kT/2.

It didn’t work.(To be precise, it failed for small l,large n.)

Max Planck, prof. at University of Berlin,attempted an explanation in 1900, addingone new and strange assumption:

Each oscillation mode can not absorb justany amount of energy. Each mode can onlyabsorb energy in packets of fixed size.

It described the data perfectly!

The size of each energy packet (nowtermed a quantum) is proportional to thefrequency of the mode:

E = h n

The proportionality factor (Planck’sconstant) is

h = 6.63 x 10-34 J s.

The above formula was first presented ata meeting of the German Physical Societyon Dec. 14, 1900.The birthday of Quantum Physics!

Max Planck derived:

Planck’s Radiation Law

Important new assumption:

The energy in each frequency mode ncan only come in integer multiples ofsome fundamental unit (quanta):

E = h n

with h = 6.6261 x 10-34 J˙s = 4.1357 x 10-15 eV ˙s

The S-B law and Wien’s law both followfrom Planck’s formula.

†

I(l,T) =2pc 2h

l51

ehc / lkT -1

In a cathode ray tube, the change inpotential energy of the electron is eV,where V is the voltage difference betweencathode and anode.

Thus, eV is the Kinetic Energy of theelectron when it hits the anode.

If all of this energy is converted into asingle quantum of X-ray radiation (called aphoton), then the photon would have afrequency given by

n = eV/h, l = c/n

This is the maximum frequency X-ray thatcould be emitted in the process.

For example, 2000 V l = 0.621 nm

X-Ray Spectra

The wavelength distribution of X-raysproduced by bombarding electrons on ahigh-Z target (fig. 3.17):

Sharp peaks: due to atomic excitations atspecific frequencies.

Continuum: due to sudden deceleration ofelectron by heavy nucleus in the anode.The deceleration causes the electronto radiate. Called Bremsstrahlung(German for Braking radiation).

The smallest possible wavelengthcorresponds to maximum energy lossby the electron (i.e. it loses all of itsenergy).

h c 1243 eV ˙nmlmin = =

KE KE

The Photoelectric Effect

1887 - Hertz:

Visible or UV light on metal surface mayrelease electrons

photon electron

Classical theory says energy of electronsshould increase with intensity of light.

However, this was not the case.

Experiments (Lenard) showed:

1) KE of photoelectrons depends only on n(frequency) of light, independent ofI (its intensity).

2) # of photoelectrons is proportionalto I

3) For a given metal, there is a minimum n,below which no photoelectrons areemitted.

4) The photoelectrons are emittedinstantaneously, independent of I.

Classical theory could not explain theseobservations.

1905 - Einstein explained:

Electromagnetic radiation transferred indiscrete bundles of energy (“photons”).The energy of each photon is

E = h n

The KE of an emitted photoelectron is

KE = h n - f

• hn is Energy of the incident photon• f is the binding energy of electron to

the metal surface (the work function).

The KE of the electrons can be measuredby applying a positive voltage to thesurface and noting when the photoelectriccurrent stops. This voltage is called thestopping potential.

Spectral Lines

• 1814-1824: Von Fraunhofer discoveredabsorption lines in sun.

• 1850’s: Kirchhoff discoveredcharacteristic emission lines of elements

• 1859: Kirchoff and Bunsen discoverednew elements, Cesium and Rubidium, byfirst observing their spectral lines.

• 1885: Balmer found a formula for thewavelengths of the spectral lines inHydrogen:

1 1 1 = RH ( - ) l 4 n2

where n=3,4,5,...

The constant RH is Rydberg’s constant:

RH = 1.096776 x 107 m-1

• 1890: Rydberg found a more generalformula for the spectral lines ofHydrogen:.

1 1 1 = RH ( - ) l m2 n2

where both n and m are integers with n>m.

Visible light is in the approximate range 400 nm < l < 700 nm

m=1: Lyman series => Ultraviolet (UV) (l < 122 nm)

m=2: Balmer seriesn=3: l = 657 nmn=4: l = 486 nmn=5: l = 434 nmn=6: l = 410 nmn>7: Ultraviolet (l < 397.1 nm)

m=3: Paschen series => Infrared (IR) (l > 820 nm)