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The Photoelectric Effect Einstein’s Triumph Graphics courtesy of Physics 2000, University of Colorado Presentation Text ©2001 Philip M. Dauber

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Do You Know How a Solar Cell Works? Light produces electricity, right? The Photoelectric Effect, first explained correctly by Einstein in 1905 How?

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Basic Info When light of high enough frequency strikes a metal, electrons are given off

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Apparatus

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Simulations of Photoelectric Effect Photoelectric Effect

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Planck’s E = hf Called quantum hypothesis Needed to explain spectrum of light given off by hot objects (black-body radiation) Main idea: energy of atomic oscillators is not continuous but finite number of discrete amounts (called photons) each related to frequency of oscillation by E = hf h = 6.63 x 10 -34 J-s (Planck’s Constant) Photons act like particles

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Photoelectric Effect Apparatus When light hits cathode(-) current flows Electrons move toward anode (+) If battery is reversed, electrons can be stopped KE max = qV 0 where V 0 is the stopping voltage o Light

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What Wave Theory Predicts If light made brighter –#electrons increases –Maximum KE increases If change frequency – No effect on KE of electrons – No minimum frequency required

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WRONG! Sorry Maxwell

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What Photon Theory Predicts Increasing brightness means more photons, not more energy per photon Increasing frequency increases KE max Decreasing frequency below “cutoff” could mean no electrons ejected

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Two Theories Animated Wave vs. Photon Model

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Now for the Math… Let hf be incoming energy of the photon Let W 0 be the minimum energy required to eject out through the surface(work function) KE max is the maximum energy of the ejected electron then hf = KE max + W 0 by conservation of energy in a collision

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How to Analyze KE max can be easily determined by measuring the stopping potential KE max =qV 0 So let’s plot KE max vs. f

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What Happens When Light Frequency Increases? KE max = hf - W 0 KE max f f0f0 W0W0 f 0 is called threshold frequency h is the slope

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Meaning of Threshold (Cutoff) Frequency When f is less than f 0 : KE max is negative. There can be no photocurrent The bigger f, the bigger is Ke max At cutoff frequency f 0 : hf 0 = W 0

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Problems 1.What stopping voltage is required to stop an electron with KE of 1 electron volt? 2.A stopping voltage of 2.5 volts is just enough to stop all photocurrent. What is KE max ? Ans. 1 volt Ans. 2.5 eV

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Finding Photon Energy What is the energy of a photon of blue light with = 450 nm ? HINT: First find f f = c/ E = hf = hc/ hc/ x10 -34 J-s)(3.0x10 8 m/s)/(4.5 x 10 -7 m) = 4.4x10 -19 J/(1.6)x10 -19 J/eV = 2.7 eV

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Finding KE max What is the maximum kinetic energy of electrons ejected from a sodium surface whose work function is W 0 = 2.28 eV when illuminated by light of wavelength 410nm? hf = hc/ = 4.85x10 -19 J or 3.03 eV (1243/410) KE max = hf - W 0 = 3.03 eV – 2.28 eV = 0.75 eV

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Finding Cutoff Frequency or Wavelength What is the cutoff frequency for sodium? What is the longest wavelength for a photo current to flow? hf 0 = W 0 = 2.28 eV = 3.65 x 10 -19 J f 0 = 3.65 x 10 -19 J / 6.63 x 10 -34 J-s = 5.5 x 10 14 Hz 0 = c/f 0 = 3.0 x 10 8 m/s /5.5 x 10 14 Hz = 545 nm ShortcutShortcut-click

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Using 1243 Rule The wavelength corresponding to the work function is just 1243/2.28 eV = 545 nm

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How Can We Measure h Using the Photoelectric Effect? Plot KE max as a function of frequency h is the slope KE max = hf - W 0

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