The Photoelectric Effect

1
The Photoelectric Effect

• Einsteins Triumph

Graphics courtesy of Physics 2000, University of
Colorado
2
Quantum Theory Early Experiments

• Cathode rays discovered in late 19th century
• Charge to mass ratio
• e/m measured E/B2r

End of tube near terminal(anode) glowed
evB mv2/r eE evB etc
3
Discovery of Electron

• Cathode rays became known as electrons
• Most believed they were atoms
• J.J. Thompson believed they were parts of atoms
• Millikin measured charge on electron

4
Millikin Oil Drop Experiment

• Shows that electron charge is quantized.
• qe integer x 1.6 x 10-19 C

5
Closer Look at Millikan Oil Drop
Millikan put a charge on a tiny drop of oil and
measured how strong an applied electric field had
to be in order to stop the oil drop from falling.
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Planck Distribution
Wavelength distribution of blackbody radiation
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Planck E hf

• Planck postulated that the radiators or
  oscillators can only emit electromagnetic
  radiation in finite amounts of energy.
• At a given temperature T, there is then not
  enough thermal energy available to create and
  emit many large radiation quanta. More large
  energy quanta can be emitted, however, when the
  temperature is raised.

8
Do You Know How a Solar Cell Works?
Light produces electricity, right?
How?
The Photoelectric Effect, first explained
correctly by Einstein in 1905
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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

• Link 1
• Link 2

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Plancks E hf

• Called quantum hypothesis
• Needed to explain spectrum of light given off by
  hot objects
• Main idea energy of atomic oscillators is not
  continuous but finite number of discrete amounts
  each related to frequency of oscillation by E
  nhf
• h 6.63 x 10-34 J-s (Plancks Constant)
• Photons act like particles

13
Photoelectric Effect Apparatus

• When light hits cathode(-) current flows
• Electrons move toward anode ()
• If battery is reversed, electrons can be stopped
• KEmax eV0 V0 is stopping voltage

Light
o
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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

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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 KEmax (Ehf)
• Decreasing frequency below cutoff could mean no
  electrons ejected

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Two Theories Animated

• Link

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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

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How to Analyze

• KEmax can be easily determined by measuring the
  stopping potential
• KEmax eV0 ( qeV)
• So lets plot KEmax vs. f

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What Happens When Light Frequency Increases?

• KEmax hf - W0

f0 is called threshold frequency
KEmax
h is the slope
f0
f
W0
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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

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Problems

• What stopping voltage is required to stop an
  electron with KE of 1electron volt?
• A stopping voltage of 2.5 volts is just enough to
  stop all photocurrent. What is KEmax?

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
  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)
4.42x10-19 J
/(1.6)x10-19 J/eV 2.76 eV
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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
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Finding Cutoff Frequency or Wavelength
h 6.63 x 10-34 J-s
W0 2.28 eV

• 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
l0 c/f0 3.0 x 108 m/s /5.5 x 1014 Hz 545 nm
Shortcut-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 KEmax as a function of frequency
• h is the slope
• KEmax hf - W0