1Fri. Oct 29 Phy107 Lecture 22Quantum mechanics• At very small sizes the world is VERY different!– Energy not continuous,but can take on only particular discrete values.– Light has particle-like properties, so that photons canbounce off objects just like balls.– Particles also have wave-like properties, so that twoparticles can interfere just like light does.– Physics is not deterministic, but events occur with aprobability determined by quantum mechanics.HW8: Chap. 13 Concept 4, 8, 12, 14(Due 11/3) Problems 2, 8Fri. Oct 29 Phy107 Lecture 22The origin of quantum mechanics• The photoelectric effect• The Blackbody radiation spectrum• Both of these phenomena were impossible toexplain with classical physics• Only possible to understand them bypostulating that energy is quantized indiscrete units.Fri. Oct 29 Phy107 Lecture 22Energy quantizationExample of swinging pendulum.Larger amplitude, larger energySmall energyLarge energyQuantum mechanics:Not every swing amplitude is possibleenergy cannot change by arbitrarily small stepsFri. Oct 29 Phy107 Lecture 22Energy quantization• Energy can have only certain discrete values• Energy states are separated by ΔE = hf.f = frequencyh = Planck’s constant= 6.626 x 10-34 J-s• ΔE = hf=3.3x10-34 J for pendulum = spacing between energy levelsd• E=mgd=(1 kg)(9.8 m/s2)(0.2 m) ~ 2 Joules• ΔEmin=hf=3.3x10-34 J << 2 J• Quantization not noticeablePeriod = 2 secFreq = 0.5 cycles/secFri. Oct 29 Phy107 Lecture 22Light quantization• Quantization also applies to other physical systems– e.g. light– Classically, to change the energy, we change amplitude• Energy of light can change only in steps of hf.– f is the frequency of the lightFri. Oct 29 Phy107 Lecture 22Or could say…• Light comes in particles called photons.• Energy of one photon is E=hff = frequency of light• Photon is a particle, but moves at speed of light!– This is possible because it has zero mass.• Zero mass, but it does have momentum:– Photon momentum p=E/c2Fri. Oct 29 Phy107 Lecture 22Another way to think about light• Possible energies for 5000 green nm lightE=hfE=2hfE=3hfE=4hf– One quantum of energy:one photon– Two quanta of energytwo photons– etc• Think about light as aparticle rather than wave.Fri. Oct 29 Phy107 Lecture 22But light is a wave!• Light has wavelength, frequency, speed– Related by fλ = speed.• Light shows interference phenomena– Constructive and destructive interferenceLShorter pathLonger pathLightbeamFoil with twonarrow slitsRecordingplateFri. Oct 29 Phy107 Lecture 22Interference of sound waves• Interference arises when waves change their‘phase relationship’.• Can vary phase relationship of two waves bychanging physical location of speaker.ConstructiveDestructive‘in-phase’‘1/2 λ phase diff’Fri. Oct 29 Phy107 Lecture 22Interference of lightFri. Oct 29 Phy107 Lecture 22Neither wave nor particle• Light in some cases shows propertiestypical of waves• In other cases shows propertieswe associate with particles.• Conclusion:– Light is not a wave, or a particle, but somethingwe haven’t thought about before.– Reminds us in some ways of waves.– In some ways of particles.Fri. Oct 29 Phy107 Lecture 22No, really, it’s a particle• How do we know light showsparticle-like properties?• How can we tell it comes indiscrete pieces we callphotons?IncominglightEjectedelectronA metal is a container ofelectronsElectronsinside metal•Photoelectric effect–Incoming light knocks electronout of metal.–But only for short enoughwavelength!3Fri. Oct 29 Phy107 Lecture 22EjectedelectronPhotoelectric effect: WAVES• Electron held inside metal by someforce.• Light beam transfer energy to electron,and knocks it out of metal.• Wave picture:– Electromagnetic fields of light waveaccelerate charged electron– Electron gains ‘escape velocity’, and isejected from the metal.– Higher light intensities have largerelectric & magnetic fields.– Would expect high enough lightintensity to eject electron from metal.– No strong dependence on frequency.Fri. Oct 29 Phy107 Lecture 22Photoelectric effect: PARTICLES• Einstein says that light is made up of photons,individual ‘particles’, each with energy hf.• One photon collides with one electron- knocks it out of metal.• If photon doesn’t have enough energy,cannot knock electron out.• Intensity ( = # photons / sec)doesn’t change this.Minimum frequency(maximum wavelength)required to eject electronFri. Oct 29 Phy107 Lecture 22Photoelectric effect• Explained by quantized light.• Red light is low frequency, low energy.• (Ultra)violet is high frequency, high energy.• Red light will not eject electron from metal,no matter how intense.– Single photon energy hf is too low.• Need ultraviolet lightFri. Oct 29 Phy107 Lecture 22Photon EnergyA red and green laser are each rated at 2.5mW.Which one produces more photons/second?A. Red B. Green 3) SameRed light has less energy per photonso needs more photons!tonEnergy/phoPowersecondphotons #=hfPower=Fri. Oct 29 Phy107 Lecture 22Nobel TriviaFor which work did Einstein receive theNobel Prize?A. Special Relativity, E=mc2B. General Relativity Gravity bends LightC. Photoelectric Effect & PhotonsFri. Oct 29 Phy107 Lecture 22Why so important?Light hittingmetal• Makes behavior of light wave quite puzzling.• Said that one photon interacts withone electron, electron ejected.• If this wavefront represents onephoton, where is it?• Which electron does it interactwith?• How does it decide?4Fri. Oct 29 Phy107 Lecture 22Even more puzzling• Think about two-slit light interferencewe discussed earlier.• Turn down the intensity until only one photon per secondgoes through the slits.• Do we still get interference?Fri. Oct 29 Phy107 Lecture 22Single-photon interference1/30 secexposure1 secexposure100 secexposureFri. Oct 29 Phy107 Lecture 22• P.A.M. Dirac (early 20th century):– “… each photon interferes with itself.Interference between different photons never occurs.”We now can have ‘coherent’ photons in a laser,(Light Amplification by Stimulated Emission of Radiation)invented 40 years ago.These photons can in fact interfere.Fri. Oct 29 Phy107 Lecture 22Probabilities• We detect absorption of a photon at camera.• Cannot predict where on camera photon will arrive.• Position individual photon hits is determinedprobabilistically.• Photon has a probability amplitude through
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