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?
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• KEmax = qV0 where V0 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
What Photon Theory Predicts
• Increasing brightness means more photons, not more energy per photon
• Increasing frequency increases KEmax
• Decreasing frequency below “cutoff” could mean no electrons ejected
Now for the Math…
• Let hf be incoming energy of the photon
• Let W0 be the minimum energy required to eject out through the surface(work function)
• KEmax is the maximum energy of the ejected electron
• then hf = KEmax + W0
by conservation of energy in a collision
How to Analyze
• KEmax can be easily determined by measuring the stopping potential
• KEmax =qV0
• So let’s plot KEmax vs. f
What Happens When Light Frequency Increases?
• KEmax = hf - W0
KEmax
ff0W0
f0 is called threshold frequency
h is the slope
Meaning of Threshold (Cutoff) Frequency
• When f is less than f0: KEmax is negative.
• There can be no photocurrent
• The bigger f, the bigger is Kemax
• At cutoff frequency f0: hf0 = W0
Problems1. 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 KEmax?
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)(3.0x108m/s)/(4.5 x 10-7 m)
= 4.4x10-19 J /(1.6)x10-19 J/eV = 2.7 eV
Finding KEmax
• What is the maximum kinetic energy of electrons ejected from a sodium surface whose work function is W0 = 2.28 eV when illuminated by light of wavelength 410nm?
hf = hc/ = 4.85x10-19 J or 3.03 eV (1243/410)
KEmax = hf - W0 = 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?
hf0 = W0 = 2.28 eV = 3.65 x 10-19 J
f0 = 3.65 x 10-19 J / 6.63 x 10-34 J-s = 5.5 x 1014 Hz
0 = c/f0 = 3.0 x 108 m/s /5.5 x 1014 Hz = 545 nm
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