1. Wave / Particle Duality
Electrons as discrete Particles.
Measurement of e (oil-drop expt.) and e/m (e-beam expt.).
Photons as discrete Particles.
Blackbody Radiation: Temp. Relations & Spectral Distribution.
Photoelectric Effect: Photon “kicks out” Electron.
Compton Effect: Photon “scatters” off Electron.
PART II
Wave Behavior: Diffraction and Interference.
Photons as Waves: l = hc / E
X-ray Diffraction (Bragg’s Law)
Electrons as Waves: l = h / p = hc / pc
Low-Energy Electron Diffraction (LEED)

2. Electrons: Quantized Charged Particles
In the late 1800’s, scientists discovered that electricity was composed of discrete or quantized particles (electrons) that had a measurable charge.
Found defined amounts of charge in electrolysis experiments, where F (or Farad) = NA e.
One Farad (96,500 C) always decomposes one mole (NA) of monovalent ions.
Found charge e using Millikan oil-drop experiment.
Found charge to mass ratio e/m using electron beams in cathode ray tubes.

3. Electrons: Millikan’s Oil-drop Expt.
Millikan measured quantized charge values for oil droplets, proving that charge consisted of quantized electrons.
Formula for charge q used terminal velocity of droplet’s fall between uncharged plates (v1) and during rise (v2) between charged plates.
Charged oil droplets
Charged Plates
Scope to measure droplet terminal velocity.

4. Electron Beam e/m : Motion in E and B Fields
Circular Motion of electron in B field:
 Larger e/m gives smaller r, or larger deflection.
Electron (left hand)
Proton (right hand)

5. Electron Beam e/m: Cathode Ray Tube (CRT)
Tube used to produce an electron beam, deflect it with electric/magnetic fields, and then measure e/m ratio.
Found in TV, computer monitor, oscilloscope, etc.
J.J. Thomson
Charged Plates
(deflect e-beam)
Deflection  e/m
(+) charge
Cathode
(hot filament produces electrons)
Slits
(collimate beam)
(–) charge
Fluorescent Screen (view e-beam)

6. Ionized Beam q/m: Mass Spectrometer
Mass spectrometer measures q/m for unknown elements. 1.
Ions accelerated by E field.
Ion path curved by B field. 2. 2. 1.

7. Photons: Quantized Energy Particle
Light comes in discrete energy “packets” called photons.
Energy of
Single Photon
From Relativity:
Rest mass
For a Photon (m = 0):
Momentum of
Single Photon

8. Photons: Electromagnetic Spectrum
400 nm
Gamma Rays
X-Rays
Ultraviolet
Visible Spectrum
Visible
Frequency
Wavelength
Infrared
Microwave
Short Radio Waves
TV and FM Radio
AM Radio
Long Radio Waves
700 nm

9. Photoelectric Effect: “Particle Behavior” of Photon
PHOTON IN  ELECTRON OUT
Photoelectric effect experiment shows quantum nature of light, or existence of energy packets called photons.
Theory by Einstein and experiments by Millikan.
A single photon can eject a single electron from a material only if it has the minimum energy necessary (or work function f).
For example, if 1 eV is necessary to remove an electron from a metal surface, then only a 1 eV (or higher energy) photon can eject the electron.

10. Photoelectric Effect: “Particle Behavior” of Photon
PHOTON IN  ELECTRON OUT
Electron ejection occurs instantaneously, indicating that photons cannot be “added up.”
If 1 eV is necessary to remove an electron from a metal surface, then two 0.5 eV photons cannot add together to eject the electron.
Extra energy from the photon is converted to kinetic energy of the outgoing electron.
For example above, a 2 eV photon would eject an electron having 1 eV kinetic energy.

11. Photoelectric Effect: Apparatus
Photons hit metal cathode and eject electrons with work function f.
Electrons travel from cathode to anode against retarding voltage VR (measures kinetic energy Ke of electrons).
Electrons collected as “photoelectric” current at anode.
Photocurrent becomes zero when retarding voltage VR equals stopping voltage Vstop, i.e. eVstop = Ke
Cathode
Anode
Light

12. Photoelectric Effect: Equations
Total photon energy = e– ejection energy + e– kinetic energy.
where hc/l = photon energy, f = work function, and eVstop = stopping energy.
Special Case: No kinetic energy (Vo = 0).
Minimum energy to eject electron.

13. Photoelectric Effect: IV Curve Dependence
Intensity I dependence
Vstop= Constant
f1 > f2 > f3
Frequency f dependence f1 f2 f3
Vstop f

14. Photoelectric Effect: Vstop vs. Frequency
hfmin
Slope = h = Planck’s constant -f

15. Photoelectric Effect: Threshold Energy Problem
If the work function for a metal is f = 2.0 eV, then find the threshold energy Et and wavelength lt for the photoelectric effect. Also, find the stopping potential Vo if the wavelength of the incident light equals 2t and t /2.
At threshold, Ek = eVo = 0 and the photoelectric equation reduces to:
For 2t, the incoming light has twice the threshold wavelength (or half the threshold energy) and therefore does not have sufficient energy to eject an electron. Therefore, the stopping potential Vo is meaningless because there are no photoelectrons to stop!
For t/2, the incoming light has half the threshold wavelength (or twice the threshold energy) and can therefore eject an electron with the following stopping potential:

16. Compton Scattering: “Particle-like” Behavior of Photon
An incoming photon (E1) can inelastically scatter from an electron and lose energy, resulting in an outgoing photon (E2) with lower energy (E2 < E1).
The resulting energy loss (or change in wavelength Dl) can be calculated from the scattering angle q.
Incoming X-ray
Scattered X-ray
Scattering
Crystal
Angle
measured

17. Compton Scattering: Schematic
PHOTON IN  PHOTON OUT (inelastic)