Chapter 3

Light at Particles

Blackbody Radiation

Blackbody Radiation

• Light waves• Interference• Diffraction• Maxwell’s Equations• Ether?

Blackbody Radiation• Hot things radiate more energy (Stefan-Boltzmann

Law)– E = T4

– P = A T4

= emissivity (0-1, “how good of a blackbody”)• = 5.67 x 10-8 W/m2K4

• Hot things have a measureable spectrum• The spectrum shifts depending on temperature

– Wein’s Law (1893)max = b/T

– b = 0.002898 m K

Blackbody Radiationthought experiment

Radiation is absorbedthrough a hole and createsa long-lived standing wave.Eventually, a light waveescapes and can be detected.

A furnace at very high temperature

Blackbody Radiation

• Lord Rayleigh (John William Strutt) derived a classical expression based on standing waves

Lord Rayleigh’s Derivation

• Thermal Physics– Equipartition Theorem

Energy/wave = ½ kBT

• Ultraviolet Catastrophe

kBT

kBT

kBT

kBT

kBT

kBT

kBT...

.

.

.

Wilhelm Wien

• Spectrometers worked well at small wavelength (large frequency)

• Was able to derive a formula that worked in this range

• I f 3 e-af/T

– f : frequency– T : temperature– a : constant

Max Planck

• Quantized energies– E = 0, hf, 2hf, 3hf, … = nhf

•n: energy quantum number

Ludwig von Boltzmann

“… an act of desperation… a theoretical explanation had to be found at any cost, whatever the price…”

Distribution Comparison

Cosmic Background

• T = 2.727 K

• f = 160.2 GHz = 1.06 cm

Various EvaluationsWave Type Frequency (Hz) Wavelength T(K)

gamma 1021 0.3 pm 1.76 x 1010

X-Ray 1018 0.3 nm 1.76 x 107

UV 1015 300 nm 17,600

VIsible 6 x 1014 500 nm 11,000

IR 1014 3 µm 1760

microwave 1010 3cm 0.176

Photoelectric Effect• Wave description of light by Maxwell

– Light intensity should determine whether an electron is ejected

– Electric field vibrates the electron loose if there are enough waves (high intensity) to jiggle it loose.

Photoelectric Effect• James Clerk Maxwell

– EM waves traveling at c (1885)

• Heinrich Hertz– Sparks created from light hitting metal

electrodes (1886-87)

• Wilhelm Hallwachs• Clean charged metal surfaces (1888)

- - - - - - - - - - - - - - - - - - - - - - - -

Photoelectric Effect• J. J. Thomson

– Discovered that the particles ejectedwere electrons (1899)

– Cathode ray tube

• Philipp Lenard– Hertz assistant– Cathode tube (1902)

• Intensity• Wavelength

• Albert Einstein– Theory to describe photoelectric effect (1905)

Photoelectric Effect• Albert Einstein

– Theory to describe photoelectric effect (1905)– Photons are packets of kinetic energy– Nobel 1911

Photoelectric Effect• Robert Millikan

– Surface cleaning in-situ– Disagreed with Einstein’s theory– Experiments to verify Einstein’s eqn– Measured Planck’s constant, h, to within 0.5%

Metal Work Function ()

Cs 1.9 eV

K 2.2 eV

Na 2.3 eV

Mg 3.7 eV

Zn 4.3 eV

Cr 4.4 eV

W 4.5 eV

Conservation of energyKE = hf -

h = 6.626 x 10-34 J s

Photoelectric Effect• Einstein’s relationship gave a nice

linear way of determining Planck’sconstant

Metal Work Function ()

Cs 1.9 eV

K 2.2 eV

Na 2.3 eV

Mg 3.7 eV

Zn 4.3 eV

Cr 4.4 eV

W 4.5 eV

Conservation of energyKE = hc/ -

CsMgW

Photoelectric Effect• Einstein’s relationship gave a nice

linear way of determining Planck’sconstant

Metal Work Function ()

Cs 1.9 eV

K 2.2 eV

Na 2.3 eV

Mg 3.7 eV

Zn 4.3 eV

Cr 4.4 eV

W 4.5 eV

Conservation of energyKE = hf -

CsMgW

Multichannel Plate – Light Amplification by PE effect

-

+

lens

Phosphorescent screen

Incoming light

PE metal

Amplified electrons

photoelectron

X-Ray ProductionBremsstrahlung: “Braking Radiation”

X-Ray Production

Compton Effect – 1927 Nobel

Blackbody Radiation

Blackbody Radiation

Wien Distribution

Blackbody Radiation

Blackbody Radiation

Probability (a brief diversion)

Probability (a brief diversion)

Probability (a brief diversion)

P(2)

P(3)

P(4)

P(5)

P(6)

P(7)

Probability (a brief diversion)

P(12)

P(11)

P(10)

P(9)

P(8)

Probability (a brief diversion)

Planck Distribution

Planck Distribution

Planck Distribution

Solar Spectrum

2 4 6 8 10

51017

11018

1.51018

21018

Incorrect Solar Spectrum from only changing x-axis (=hc/)   

Photoelectric Effect

Photoelectric Effect

Photoelectric Effect

Photoelectric Effect

Compton Effect

Compton Effect

Compton Effect

Compton Effect

Compton Effect w/ long

Limiting Cases

Pair Production

• Carl D. Anderson (1905 -1991)– Nobel Prize for the discovery of positrons

• 1936

– Discovered the muon in 1936– Worked for Robert Millikan

Pair Production

)(

)(

BveF

BveF

Pair Production

Pair Production

Pair Production

Pair Production

Particle vs. Wave

Particle vs. Wave

Particle vs. Wave

Diffraction & Interference

Diffraction & Interference

Double Slit Experiment

10 (a), 200 (b), 6000 (c), 40000 (d), 140000 (e).

Matter Waves

• 1924 doctoral thesis– Approved by Einstein

• 1929 Nobel

Particle vs. Wave

Compton Effect

Compton Effect

1 2 3 4 5 6

0.5

1

1.5

2