1Fri. Mar. 18, 2007 Phy107 Lect. 231Today: Quantum mechanics• The quantum mechanical world is VERY different!– Energy not continuous,but can take on only particular discrete values.– Light has particle-like properties, so that light 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.Fri. Mar. 18, 2007 Phy107 Lect. 232Course essay• Wednesda y, March 28:Due in class — essay topicshort description• Friday, Apr. 13Due in class — essay outlinemain article reference• Wednesday, Apr. 26Due in class — final typed essay.Fri. Mar. 18, 2007 Phy107 Lect. 233Origins of quantum mechanicsPhotoelectric effect,Blackbody radiation spectrum,• Late 1800s:– Maxwell’s equations describe propagation of EM waves inexquisite detail.– Electricity and magnetism progress from basic science totechnological applications.say that energy is quantized in discrete units.• Early 1900s:— Further Investigations into light, and interaction of lightwith matter, hint at some scary ideasFri. Mar. 18, 2007 Phy107 Lect. 234Energy quantization in a pendulumSwinging pendulum.Larger amplitude, larger energySmall energyLarge energyQuantum mechanics:Not every swing amplitude is possibleenergy cannot change by arbitrarily small stepsFri. Mar. 18, 2007 Phy107 Lect. 235Energy quantization• Energy can have only certain discrete valuesEnergy states are separated by ΔE = hf.f = frequencyh = Planck’s constant= 6.626 x 10-34 J-sd• E=mgd=(1 kg)(9.8 m/s2)(0.2 m) ~ 2 Joules• ΔEmin=hf=3.3x10-34 J << 2 J• Quantization not noticeableSuppose the pendulum hasPeriod = 2 secFreq = 0.5 cycles/secΔE = hf=3.3x10-34 J for pendulum = spacing between energy levelsFri. Mar. 18, 2007 Phy107 Lect. 236Energy of light• Quantization also applies to other physical systems– In the classical picture of light (EM wave), we change thebrightness by changing the power (energy/sec).– This is the amplitude of the electric and magnetic fields.– Classically, these can be changed by arbitrarily smallamounts2Fri. Mar. 18, 2007 Phy107 Lect. 237Quantization of light• Possible energies for green light (λ=500 nm)E=hfE=2hfE=3hfE=4hf– One quantum of energy:one photon– Two quanta of energytwo photons– etc• Think about light as aparticle rather than wave.•Quantum mechanically, brightness can only bechanged in steps, with energy differences of hf.Fri. Mar. 18, 2007 Phy107 Lect. 238The particle perspective• 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/cFri. Mar. 18, 2007 Phy107 Lect. 239One quantum of green light• One quantum of energy for 500 nm light! E = hf =hc"=6.634 #10$34J $ s( )# 3 #108m / s( )500 #10$9m= 4 #10$19JQuite a small energy!Quantum mechanics uses new ‘convenience unit’ for energy:1 electron-volt = 1 eV = |charge on electron|x (1 volt) = (1.602x10-19 C)x(1 volt) 1 eV = 1.602x10-19 JIn these units,E(1 photon green) = (4x10-19 J)x(1 eV / 1.602x10-19 J) = 2.5 eVFri. Mar. 18, 2007 Phy107 Lect. 2310Simple relations• Translation between wavelength and energyhas simple form inelectron-volts and nano-meters ! E =hc"=constant [in eV # nm]wavelength [in nm]=1240 eV # nm500 nm= 2.5 eVGreen light example:Fri. Mar. 18, 2007 Phy107 Lect. 2311Photon energyWhat is the energy of a photon of red light(λ=635 nm)?A. 0.5 eVB. 1.0 eVC. 2.0 eVD. 3.0 eV! E =hc"=1240 eV # nm635 nm= 1.95 eVFri. Mar. 18, 2007 Phy107 Lect. 2312Photon properties of light• Photon of frequency f has energy hf• Red light made of ONLY red photons• The intensity of the beam can be increasedby increasing the number of photons/second.• Photons/second = energy/second = power.3Fri. Mar. 18, 2007 Phy107 Lect. 2313How many photons can you see?In a test of eye sensitivity, experimenters used1!milli-second (0.001 s) flashes of green light.The lowest power light that could be seen was4x10-14 Watt.How many green (500 nm, 2.5 eV) photons is this?A. 10 photonsB. 100 photonsC. 1,000 photonsD. 10,000 photonsFri. Mar. 18, 2007 Phy107 Lect. 2314But 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. Mar. 18, 2007 Phy107 Lect. 2315Wave behavior of light: interferenceFri. Mar. 18, 2007 Phy107 Lect. 2316Particle behavior of light:photoelectric effect• A metal is a bucket holding electrons• Electrons need some energy in order to jump outof the bucket.A metal is abucket of electrons.Energy transferred from the lightto the electrons.Electron uses some of the energyto break out of bucket.Remainder appears as energy ofmotion (kinetic energy).Light can supply this energy.Fri. Mar. 18, 2007 Phy107 Lect. 2317Unusual experimental results• Not all kinds of light work• Red light does not eject electronsMore red light doesn’t eitherNo matter how intense the red light,no electrons ever leave the metalUntil the light wavelength passes acertain threshold, no electrons areejected.Fri. Mar. 18, 2007 Phy107 Lect. 2318Wavelength dependenceLong wavelength:NO electrons ejectedShort wavelength:electrons ejectedHi-energy photonsLo-energy photonsThreshold depends onmaterial4Fri. Mar. 18, 2007 Phy107 Lect. 2319Einstein’s explanation• Einstein said 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. Mar. 18, 2007 Phy107 Lect. 2320Summary of Photoelectric 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. Mar. 18, 2007 Phy107 Lect. 2321Photon properties of light• Photon of frequency f has energy hf• Red light made of ONLY red photons• The
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