1Thurs. Nov. 12, 2008 Phy208 Lect. 221From Last Time…Energy and power inan 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 classTues. 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’ law Polarizer transmits component of E-field parallel to transmission axis absorbs component of E-field perpendicular to transmission axis Transmitted intensity: I = I0cos2θ I0 = intensity of polarizedbeam on analyzer (Malus’ law)Allowed componentparallel to analyzer axisPolaroid sheetsThurs. Nov. 12, 2008 Phy208 Lect. 224Circular and elliptical polarization Circularly polarized light is a superpositionof two waves with orthogonal linearpolarizations, and 90˚ out of phase. The electric fieldrotates in time withconstant magnitude.Thurs. Nov. 12, 2008 Phy208 Lect. 225Energy 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 smallamountsThurs. Nov. 12, 2008 Phy208 Lect. 226The photoelectric effect A metal is a bucket holding electrons Electrons need some energy in order tojump out of 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.2Thurs. Nov. 12, 2008 Phy208 Lect. 227The experiment Light ejects electrons fromcathode with range of velocities Reverse potential: applieselectric force opposing electronmotion Stopping potential: voltage atwhich highest kinetic energy(Kmax) electrons turned back! Vstop=KmaxeThurs. Nov. 12, 2008 Phy208 Lect. 228Analyzing the data Electrons absorb fixedenergy Eabsorb from lightHighest KEelectronLowest KEelectronBoundin solidEscapedfrom solidEo! Kmax= Eabsorb" EoEnergyKmax! Vstop=Kmaxe=Eabsorbe"EoeEabsorbRange of electronenergies in solidThurs. Nov. 12, 2008 Phy208 Lect. 229Unusual 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.Thurs. Nov. 12, 2008 Phy208 Lect. 2210Einstein’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 electronThurs. Nov. 12, 2008 Phy208 Lect. 2211Einstein’s analysis Electron 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 onmaterial3Thurs. Nov. 12, 2008 Phy208 Lect. 2213QuestionPotassium has a work function of 2.3 eV forphotoelectric emission. Which of the followingwavelengths is the longest wavelength for whichphotoemission occurs?a. 400 nmb. 450 nmc. 500 nmd. 550 nme. 600 nmKmax = hf – Φ = hc/λ – ΦThe maximum wavelength is whenKmax =0: λ = hc/Φ = 539.1 nm.Thurs. Nov. 12, 2008 Phy208 Lect. 2214Quantization and photons 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 be changed insteps, with energy differences of hf.Thurs. Nov. 12, 2008 Phy208 Lect. 2215The 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/cThurs. Nov. 12, 2008 Phy208 Lect. 2216Compton scattering Photon loses energy, transfers it to electron Photon loses momentum transfers it to electron Total energy and momentum conservedBefore collisionAfter collisionPhoton energy E=hfPhoton mass = 0Photon momentum p=E/cThurs. Nov. 12, 2008 Phy208 Lect. 2217One 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 eVThurs. Nov. 12, 2008 Phy208 Lect. 2218Simple 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:4Thurs. Nov. 12, 2008 Phy208 Lect. 2219Photon 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 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 lowestpower light that could be seen was 4x10-14 Watt.How many green (500 nm, 2.5 eV) photons is this?A. 10 photonsB. 100 photonsC. 1,000 photonsD. 10,000 photons! 4 " 10#14J / s( )0.001s( )= 4 "10#17J4 " 10#17J( )1eV /1.6 " 10#19J( )= 250eV250eV( )1photon /2.5eV( )= 100 photonsThurs. Nov. 12, 2008 Phy208 Lect. 2221Photon 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 = powerThurs. Nov. 12, 2008 Phy208 Lect. 2222QuestionA red and green laser
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