ParticleWave Duality

1
Particle-Wave Duality

• Photoelectric Effect, Compton Effect, De Broglie

2
Planck

• Planck (1900s) idea of blackbody radiation.
• Radiation emitted is quantized.
• E0, h?, 2h?, 3h?, , nh?
• h 6.63E-34 Js
• Beginning of quantum theory

3
(No Transcript)
4
Photoelectric Effect

• Discovered by Heinrich Hertz (1887).
• Metal exposed to light ejects electrons.
• Compatible with the classical electromagnetic
  theory.

5
Photoelectric Effect (cont.)

• Plancks ideas extended by Einstein, who used
  Heinrichs discovery to explain the photoelectric
  effect.
• Intensity increases the number of electrons
  ejected, but does not change their kinetic
  energy.
• There is a critical frequency associated.

6

• 2nd electrode is kept at a higher potential.
• e are attracted, causing a current.
• 2nd electrode is instead kept at lower potential
• When light is incident, e escape, but only e with
  high enough K will overcome the retarding
  potential.

7
Photoelectric Effect (cont.)

• Vs(e) Kmax
• Kinetic Energy does not change, meaning light is
  not distributed continuouslybut consist of a
  finite number of energy quanta.
• h?0 ?
• ? is the work function. Energy needed to remove
  an electron from a metal.
• Kmax h? - ?
• Experiment carried out successfully by Robert
  Millikan.

8
Compton Effect

• Beam of light fired at a system of atoms, or
  electrons, beam and particle is scattered.
• Particle oscillates, and then radiate secondary
  wave.
• Classical ? ?0
• Observed with X-rays ?lt ?0

9
Compton Effect (cont.)

• Photons
• m0 Epc
• E2(pc)2 (mc2)2
• pE/c(h?)/ch/?

10
Compton Effect (cont.)

• Conservation of Energy
• Ee E mc2 E0
• pe p p0
• Ee mc2 E0 E
• (pec2 mc2)(1/2) mcp0-p
• pe2p02 - 2p0pcos?
• mc(p0 - p)p0p(1-cos?)
• (1/p)-(1/p0)1/(mc)(1-cos?)
• ??(h/mc)(1-cos?)

11
Photons

• Eh?
• Planck

• ph/?
• Compton

12
De Broglie Hypothesis

• Quantization of atomic energy levels, explained
  by the frequency of electron waves inside the
  atom.

13
De Broglie (cont.)

• Electron vibrating around the nucleus.
• Circumference 2pr n? n0,1,2
• ? h/p
• rp(nh)/(2p)
• Lnh n0,1,2
• Experimentally verified, but not seen due to
  extremely short wavelengths.

14
De Broglie (cont.)

• ? of e ranges from 100 to 1000 eV, comparable to
  X-rays, suggesting their use in to observe
  crystal structure.
• Clinton Davisson and Lester Germer (1927) used a
  54-eV beam of e for crystal of nickel.
• Consistent with ?h/p

15
De Broglie (cont.)

• Thomson and Davisson (1927) demonstrated electron
  diffraction transmission through thin metal
  foils.
• 1937 Noble Prize.