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

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

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

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

Apparatus

Simulations of Photoelectric Effect Photoelectric Effect

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

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

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

WRONG! Sorry Maxwell

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

Two Theories Animated Wave vs. Photon Model

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

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

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

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

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

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

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

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

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

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