- 1. RelativityEinsteins solution: Two principlesPrinciple of
Relativity:All of the laws of physics are thesame for any two
observersmoving at constant relative speedPrinciple of Constancy of
Speed of Light:All observers see the same speed of light, no matter
their relativevelocities. Requires re-thinking of basic physics
from the ground up Requires re-thinking of nature of time and
spaceTime moves at different rates for different observers
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.
Blackbody RadiationLight emitted by hot objectDepends only on
temperatureCharacteristic spectrum of light 4. Blackbody
RadiationMax Planck, 1900 Developed mathematical formula for
spectrumProblem: Derivation of formula required a mathematical
trick Introduced idea of quantum of energy Completely overturned
classical physics 5. Blackbody ModelImagine object as box with
oscillators in wallsSmall 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 boxDivide 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
CatastropheProblem: Lots and lots of ways to get short wavelengths
120200 modes, 0.02L bins Predicts huge 100 80amount of light at
very short wavelengthsNumber 60 40 200 0.0 0.20.40.6 0.8 1.0
Wavelength (box length) 8. Quantum HypothesisPlancks trick: Each
mode has a minimum energy depending on frequencyCan only contain an
integer multiple of fundamental energyModes with very short
wavelength would need more than theirshare of thermal energy Amount
of radiation drops off very sharply at short wavelength 9. Energy
Partition6 quanta3 quanta2 quanta1 quanta0 quanta 10. Blackbody
Spectrum 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 intensity2) Energy of ejected electrons depends on
intensity3) No obvious dependence on frequency 12. Photoelectric
Effect: ExperimentObservations:1) Number of electronsdepends on
intensity2) Energy of electrons DOESNOT depend on intensity3)
Cut-off frequency:minimum frequency to getany emission4) Above
cut-off, energy increases linearly with frequency 13. Photoelectric
Effect: EinsteinEinstein, 1905: Heuristic Model of PE
EffectParticle model: Light quanta with energySome minimum energy
to remove electron:Work FunctionEnergy of emitted electron:Takes
Plancks trick seriously, runs with the idea 14. Photoelectric
Effect: EinsteinObservations:1) Number of electrons depends on
intensity Higher intensity More quanta2) Energy of electrons DOES
NOT dependon intensity Only one photon to eject3) Cut-off
frequency: minimum frequencyto get any emissionEinstein in
1921Nobel Prize portrait4) Above cut-off, energy increases linearly
Cited for PE Effectwith frequency 15. Atomic SpectraAtoms emit
light at discrete, characteristic frequenciesObserved in 1860s,
unexplained until 1913 16. Bohr Model1913: Neils Bohr comes up with
solar system model1) Electrons orbit nucleus in certain allowed
states2) Electrons radiate only when moving between allowed
states3) Frequency of emitted/absorbed light determined by Planck
rule Works great for hydrogen, but no reason for ad hoc assumptions
17. Matter WavesLouis de Broglie: Particles are WavesElectrons
occupy standing wave orbitsOrbit allowed only if integral number
ofelectron wavelengthsh Wavelength determined by momentum p Same
rule as for light 18. Matter Waves de Broglie Waves: h pWhy dont we
see this?Plancks Constant is tinyh = 6.626 10 34 J-s More
significant for single atoms145 g baseball, 40 m/s 87Rb, 200 m/s =
1.1 10 34 m = 0.02 nm Insignificant for macroscopic objects Still
small, but canstart to see effects 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.
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. Big Molecules430 ATOMS 22. Light as a ClockLight:
Electromagnetic waveExtremely regular oscillationNo moving partsUse
atoms as a reference: Performance: Lose 1s in 100,000,000 years