From Last Time…Exam 3 is Tuesday Nov. 25Origin of Malus’ lawCircular and elliptical polarizationEnergy of lightThe photoelectric effectThe experimentAnalyzing the dataUnusual experimental resultsEinstein’s explanationEinstein’s analysisWavelength dependenceQuestionQuantization and photonsThe particle perspectiveCompton scatteringOne quantum of green lightSimple relationsPhoton energyHow many photons can you see?Photon properties of lightSlide 22Nobel TriviaBut light is a waveNeither wave nor particleParticle-wave dualityThurs. Nov. 12, 2008 Phy208 Lect. 221From Last Time…Energy and power in an EM wavePolarization of an EM wave: oscillation plane of E-fieldThurs. Nov. 12, 2008 Phy208 Lect. 222Exam 3 is Tuesday Nov. 25Students w / scheduled academic conflict please stay after class Tues. Nov. 18 to arrange alternate time.5:30-7 pm, 2103 Ch (here)Covers: all material since exam 2.Bring: CalculatorOne (double-sided) 8 1/2 x 11 note sheetExam review: Thursday, Nov. 20, in classThurs. Nov. 12, 2008 Phy208 Lect. 223Origin of Malus’ lawPolarizer transmits component of E-field parallel to transmission axis absorbs component of E-field perpendicular to transmission axisTransmitted intensity: I = I0cos2 I0 = intensity of polarized beam on analyzer (Malus’ law)Allowed componentparallel to analyzer axisPolaroid sheetsThurs. Nov. 12, 2008 Phy208 Lect. 224Circular and elliptical polarizationCircularly polarized light is a superposition of two waves with orthogonal linear polarizations, and 90˚ out of phase.The electric field rotates in time with constant magnitude.Thurs. Nov. 12, 2008 Phy208 Lect. 225Energy of lightQuantization also applies to other physical systemsIn the classical picture of light (EM wave), we change the brightness by changing the power (energy/sec).This is the amplitude of the electric and magnetic fields.Classically, these can be changed by arbitrarily small amountsThurs. Nov. 12, 2008 Phy208 Lect. 226The photoelectric effectA metal is a bucket holding electronsElectrons need some energy in order to jump out of the bucket.A metal is a bucket of electrons.Energy transferred from the light to the electrons.Electron uses some of the energy to break out of bucket.Remainder appears as energy of motion (kinetic energy).Light can supply this energy.Thurs. Nov. 12, 2008 Phy208 Lect. 227The experimentLight ejects electrons from cathode with range of velocitiesReverse potential: applies electric force opposing electron motionStopping potential: voltage at which highest kinetic energy (Kmax) electrons turned back€ Vstop=KmaxeThurs. Nov. 12, 2008 Phy208 Lect. 228Analyzing the dataElectrons absorb fixed energy Eabsorb from lightHighest KE electronLowest KE electronBound in solidEscaped from solidEo€ Kmax= Eabsorb− EoEnergyKmax€ Vstop=Kmaxe=Eabsorbe−EoeEabsorbRange of electron energies in solidThurs. Nov. 12, 2008 Phy208 Lect. 229Unusual experimental resultsNot all kinds of light workRed 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 a certain threshold, no electrons are ejected.Thurs. Nov. 12, 2008 Phy208 Lect. 2210Einstein’s explanationEinstein 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 electronThurs. Nov. 12, 2008 Phy208 Lect. 2211Einstein’s analysisElectron absorbs energy of one photon € Eabsorb= Ephoton= hf€ Vstop=Kmaxe=Eabsorbe−Eoe=hfe−Eoe€ Vstop=hef − fo( )Slope of line =h/eMinimim frequency€ hfo= Eo=Work functionThurs. Nov. 12, 2008 Phy208 Lect. 2212Wavelength dependenceLong wavelength: NO electrons ejectedShort wavelength: electrons ejectedHi-energy photonsLo-energy photonsThreshold depends on materialThurs. Nov. 12, 2008 Phy208 Lect. 2213QuestionPotassium has a work function of 2.3 eV for photoelectric emission. Which of the following wavelengths is the longest wavelength for which photoemission occurs?a. 400 nmb. 450 nmc. 500 nmd. 550 nme. 600 nmKmax = hf – Φ = hc/λ – ΦThe maximum wavelength is when Kmax =0: λ = hc/Φ = 539.1 nm.Thurs. Nov. 12, 2008 Phy208 Lect. 2214Quantization and photonsPossible energies for green light (=500 nm) E=hfE=2hfE=3hfE=4hfOne quantum of energy:one photonTwo quanta of energytwo photonsetcThink about light as a particle rather than wave.•Quantum mechanically, brightness can only be changed in steps, with energy differences of hf.Thurs. Nov. 12, 2008 Phy208 Lect. 2215The particle perspectiveLight comes in particles called photons.Energy of one photon is E=hff = frequency of lightPhoton 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/cThurs. Nov. 12, 2008 Phy208 Lect. 2216Compton scatteringPhoton loses energy, transfers it to electronPhoton loses momentum transfers it to electronTotal energy and momentum conservedBefore collisionAfter collisionPhoton energy E=hfPhoton mass = 0Photon momentum p=E/cThurs. Nov. 12, 2008 Phy208 Lect. 2217One quantum of green lightOne quantum of energy for 500 nm light€ E = hf =hcλ=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 eVThurs. Nov. 12, 2008 Phy208 Lect. 2218Simple relationsTranslation between wavelength and energyhas simple form in electron-volts and nano-meters € E =hcλ=constant [in eV − nm]wavelength [in nm]=1240 eV − nm500 nm= 2.5 eVGreen light example:Thurs. Nov. 12, 2008 Phy208 Lect. 2219Photon energyWhat is the energy of a photon of red light (=635 nm)?A. 0.5 eVB. 1.0 eVC. 2.0 eVD. 3.0 eV€ E =hcλ=1240 eV − nm635 nm=1.95 eVThurs. Nov. 12, 2008 Phy208 Lect. 2220How many photons can you see?In a test of eye sensitivity, experimenters used 1 milli-second (0.001 s) flashes of green light. The lowest power light that could be
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