The Photoelectric Effect
Einstein’s Triumph
Presentation Text ©2001 Philip M. Dauber
Graphics courtesy of Physics 2000, University of Colorado
Do You Know How a Solar Cell
Works?
Light produces electricity, right?
How?
The Photoelectric Effect, first explained
correctly by Einstein in 1905
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 (+)
o
Light
• If battery is reversed, electrons can be stopped
• KEmax = qV0 where V0 is the stopping voltage
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 KEmax
• 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 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
f0 is called
threshold
frequency
KEmax
h is the slope
W0
f0
f
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
Problems
1. What stopping voltage is required to stop
an electron with KE of 1 electron volt?
Ans. 1 volt
2. A stopping voltage of 2.5 volts is just
enough to stop all photocurrent. What is
KEmax?
Ans. 2.5 eV
Finding Photon Energy
• What is the energy of a photon of blue light
with l = 450 nm ?
HINT: First find f
f = c/l
E = hf = hc/l =
hc/l = (6.63x10-34 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/l = 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?
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
• What is the longest wavelength for a photo
current to flow?
l0 = c/f0 = 3.0 x 108 m/s /5.5 x 1014 Hz = 545 nm
Shortcut-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 KEmax as a function of frequency
• h is the slope
• KEmax = hf - W0