History of Quantum Mechanics


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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.

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History of Quantum Mechanics

  1. 1. RelativityEinstein’s solution: Two principlesPrinciple of Relativity: All of the laws of physics are the same for any two observers moving at constant relative speedPrinciple 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. 2. Quantum MechanicsThe other great theory of modern physics Deals with very small objects  Electrons, atoms, moleculesGrew out of problems that seemed simple  Black-body radiation  Photoelectric Effect  Atomic SpectraProduces some very strange results…
  3. 3. Blackbody RadiationLight emitted by hot object Depends only on temperature Characteristic spectrum of light
  4. 4. Blackbody RadiationMax 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. 5. Blackbody ModelImagine 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. 6. Standing Waves
  7. 7. Ultraviolet CatastropheProblem: 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 wavelengthsNumber 60 40 20 0 0.0 0.2 0.4 0.6 0.8 1.0 Wavelength (box length)
  8. 8. Quantum HypothesisPlanck’s trick: Each mode has a minimum energy depending on frequency Can only contain an integer multiple of fundamental energyModes with very short wavelength would need more than their share of thermal energy  Amount of radiation drops off very sharply at short wavelength
  9. 9. Energy Partition6 quanta3 quanta2 quanta1 quanta0 quanta
  10. 10. Blackbody Spectrum
  11. 11. Photoelectric EffectShine light on some object, electrons come outDiscovered by Heinrich Hertz, 1887Simple 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. 12. Photoelectric Effect: ExperimentObservations: 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. 13. Photoelectric Effect: EinsteinEinstein, 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. 14. Photoelectric Effect: EinsteinObservations: 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. 15. Atomic SpectraAtoms emit light at discrete, characteristic frequenciesObserved in 1860’s, unexplained until 1913
  16. 16. Bohr Model1913: 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. 17. Matter WavesLouis 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. 18. Matter Waves de Broglie Waves: h  pWhy 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. 19. Electron DiffractionSend electrons at two slits in a barrier: Image and video from Hitachi: http://www.hitachi.com/rd/research/em/doubleslit.html
  20. 20. Fullerene Diffractionhttp://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. 21. Big Molecules430 ATOMS
  22. 22. Light as a ClockLight: Electromagnetic wave Extremely regular oscillation No moving partsUse atoms as a reference: Performance: Lose 1s in 100,000,000 years