Lecture slides for a class giving a historical overview of quantum mechanics, including black-body radiation, the photoelectric effect, and the Bohr model of hydrogen. Used in a class for non-majors titled "A Brief History of Timekeeping," as a lead-in to talking about atomic clocks.

1. Relativity
Einstein’s solution: Two principles
Principle of Relativity:
All of the laws of physics are the
same for any two observers
moving at constant relative speed
Principle of Constancy of Speed of Light:
All observers see the same speed of light, no matter their relative
velocities.
Requires re-thinking of basic physics from the ground up
Requires re-thinking of nature of time and space
Time moves at different rates for different observers

2. Quantum Mechanics
The other great theory of modern physics
Deals with very small objects
 Electrons, atoms, molecules
Grew out of problems that seemed simple
 Black-body radiation
 Photoelectric Effect
 Atomic Spectra
Produces some very strange results…

3. Blackbody Radiation
Light emitted by hot object
Depends only on temperature
Characteristic spectrum of light

4. Blackbody Radiation
Max Planck, 1900
 Developed mathematical formula for spectrum
Problem: Derivation of formula required a mathematical trick
Introduced idea of “quantum” of energy
Completely overturned classical physics

5. Blackbody Model
Imagine object as box with “oscillators” in walls
Small amount of light leaks out blackbody spectrum
What radiation exists in box?
“Standing wave”  integer number of half-wavelengths
fit across the length of the box
Divide thermal energy of object among possible modes
 Add up all allowed modes to get total spectrum
(Rayleigh-Jeans approach; slightly different than Planck, but simpler)

6. Standing Waves

7. Ultraviolet Catastrophe
Problem: Lots and lots of ways to get short wavelengths
120
200 modes, 0.02L bins
 Predicts huge
100
80 amount of light at very
short wavelengths
Number
60
40
20
0
0.0 0.2 0.4 0.6 0.8 1.0
Wavelength (box length)

8. Quantum Hypothesis
Planck’s trick:
Each mode has a minimum energy depending on frequency
Can only contain an integer multiple of fundamental energy
Modes with very short wavelength would need more than their
share of thermal energy
 Amount of radiation drops off very sharply at short wavelength

9. Energy Partition
6 quanta
3 quanta
2 quanta
1 quanta
0 quanta

10. Blackbody Spectrum

11. Photoelectric Effect
Shine light on some object,
electrons come out
Discovered by Heinrich Hertz, 1887
Simple model: Shaking electrons
Predict: 1) Number of ejected electrons depends on intensity
2) Energy of ejected electrons depends on intensity
3) No obvious dependence on frequency

12. Photoelectric Effect: Experiment
Observations:
1) Number of electrons
depends on intensity
2) Energy of electrons DOES
NOT depend on intensity
3) Cut-off frequency:
minimum frequency to get
any emission
4) Above cut-off, energy increases linearly
with frequency

13. Photoelectric Effect: Einstein
Einstein, 1905: “Heuristic Model” of PE Effect
Particle model: “Light quanta” with energy
Some minimum energy to remove electron:
“Work Function”
Energy of emitted electron:
Take’s Planck’s “trick” seriously, runs with the idea

14. Photoelectric Effect: Einstein
Observations:
1) Number of electrons depends on intensity
Higher intensity More quanta
2) Energy of electrons DOES NOT depend
on intensity
Only one photon to eject
3) Cut-off frequency: minimum frequency
to get any emission
Einstein in 1921
Nobel Prize portrait
4) Above cut-off, energy increases linearly Cited for PE Effect
with frequency

15. Atomic Spectra
Atoms emit light at discrete, characteristic frequencies
Observed in 1860’s, unexplained until 1913

16. Bohr Model
1913: Neils Bohr comes up with “solar system” model
1) Electrons orbit nucleus in certain “allowed states”
2) Electrons radiate only when moving between allowed states
3) Frequency of emitted/absorbed light determined by Planck rule
 Works great for hydrogen, but no reason for ad hoc assumptions

17. Matter Waves
Louis de Broglie: Particles are Waves
Electrons occupy standing wave orbits
Orbit allowed only if integral number of
electron wavelengths
h
Wavelength determined by momentum 
p
 Same rule as for light…

18. Matter Waves
de Broglie Waves:
h

p
Why don’t we see this?
Planck’s Constant is tiny
h = 6.626  10 –34 J-s
More significant for single atoms
145 g baseball, 40 m/s 87Rb, 200 m/s
 = 1.1  10 –34 m  = 0.02 nm
Insignificant for macroscopic objects Still small, but can
start to see effects

19. Electron Diffraction
Send electrons at two slits in a barrier:
Image and video from Hitachi:
http://www.hitachi.com/rd/research/em/doubleslit.html

20. Fullerene Diffraction
http://commons.wikimedia.org/wiki/
File:Fullerene-C60.png
Fig. 7 in the paper, "Quantum interference experiments with large molecules,"
by Nairz, Arndt, and Zeilinger (Am. J. Phys 71, 319 (2003)).

21. Big Molecules
430 ATOMS

22. Light as a Clock
Light: Electromagnetic wave
Extremely regular oscillation
No moving parts
Use atoms as a reference:
Performance: Lose 1s in 100,000,000 years