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4.1.0. Overview
Typically in introductory level physics classes the photoelectric effect is trumpeted as a
shining example of the particle nature of light. Such unchallenged notions even survive
to the intermediate level. For example Thorton and Rex in Modern Physics for Scientists
and Engineers. 3rd ed., claim on page 103 “Perhaps the most compelling, and certainly the
simplest, evidence for the quantization of radiation energy comes from the only
acceptable explanation of the photoelectric effect.” Yet, as Kidd et al. (Am. J. Phys.,
Vol. 57, No. 1, January 1989) point out, “The photoelectric effect has received less
analysis and merits a more extended treatment. It is usually considered as simply and
interaction between a photon and an electron, but this cannot really be correct.” A
substantial fraction of this article goes on to explain why the “billiard ball” model of the
photon is incorrect and that convincing semi-classical explanations (light as a classical
wave and electron as a quantum particle) can account for the photoelectric data at the
advanced undergraduate level.
In fact, this was known as early as 1914. Kidd et al. state: “It is not necessary to assume
the photon in explaining the photoelectric effect. In 1914 Richardson derived Einstein’s
equation using a thermodynamic argument that considered photoemission as analogous to
evaporation from a liquid surface and the work function comparable to a latent heat of
vaporization. Richardson later specified that his conclusions were reached ‘without
making any definite hypothesis about the structure of the radiation.’” Yet, Richardson’s
results are the same as Einstein’s 1905 paper titled: “On a Heuristic Point of View
Concerning the Production and Transformation of Light.” Further on in their 1989 Am.
J. Phys. Article Kidd et al. quote Bunge (1973): “The optical duality is then a relic of the
1905-1927 interregnum, a remains serving mainly to mislead students into believing that
light is at the same time undulatory and non-undulatory.” Furthermore, Kidd et al. state,
“Thus all of the earlier models have been superseded by QED, but the semiclassical
model usually remains the most satisfactory approximation to it, . . .” So, what’s a
student to do?
We will approach the photoelectric effect, in part, from the point view of Kidd et al. as
articulated in the following statement: “Thus Einstein’s photoelectric equation is
essentially a mathematical model that eliminates unnecessary details about structure and
the extent of the radiation and focuses solely on energy transfer. As such, it is quite
reasonable and useful.”, without worrying about the semiclassical limit of QED.
4.1.1 The Big Ideas
Fermi - Dirac distribution
Contact potential
Photoemission current
I-V characteristic curve
Photoemission threshold
Reverse current
Dark current
Stopping potential
Work function
Valence band
Conduction band
Band-gap energy
Electron affinity
Fermi energy
THE FOLLOWING ARTICLES WILL HELP EXPLAIN THESE IDEAS.
The Art of Physics “Waves and Particles” by Dietz.
Experiments in Modern Physics “Photoelectric Effect” Melissinos.
“The Photoelectric Effect” MIT Physics Department.
Kidd et al. “Evolution of the modern photon” Am. J. Phys. 57(1), January 1989.
Planck's Constant and the Photoelectric effect by N. Morton and J Abraham
4.1.2. Modeling, Calculations, and Explanations
EXERCISE 1: What is the Photoelectric Effect?
EXERCISE 2: The energy of the photon is transferred to the electron (somehow!).
How is the momentum balanced?
EXERCISE 3: The excess energy of the photon appears as kinetic energy of the
electron. The potential applied and measured between the cathode and anode is NOT the
potential seen by the electron. Explain.
EXERCISE 4: Is the photoelectric effect consistent with the wave theory of light?
Justify your response. (See Kidd et al. 1989)
EXERCISE 5: The excess energy of the photon appears as kinetic energy of the
electron. The potential applied and measured between the cathode and anode is not the
potential seen by the electron. Explain.
EXERCISE 6: Complete exercise #4 from The Art of Experimental Physics. That is,
φ
h
obtain Einstein’s equation: Vsp = ν − a for the stopping potential of a metal
e
e
photocathode by using arguments similar to those used to obtain the stopping potential
for a semiconductor photocathode.
EXERCISE 7: Complete exercise #1 from The Photoelectric Effect handout from MIT:
If a certain metal with a work function of ¢ = 2.3e V is illuminated by monochromatic light
of wavelength 3500 A what is the maximum kinetic energy of the electrons ejected in
the photoelectric effect?
EXERCISE 8: Complete exercise #2 from The Photoelectric Effect handout from MIT.
a. What are the principal lines in the spectrum of a mercury discharge lamp.
(Hint: see A. Melissinos, Experiments in Modern Physics excerpt)?
b. Could you observe the photoelectric effect on a silver cathode?
EXERCISE 9: Read Planck’s Constatnt and the Photoelectric Effect by N. Morton and
J. Abraham. Interpret the meaning of the current “tail” and how to avoid its
complications. Justify a choice of I-V curve analysis (i.e curve-fitting) and the range
over which yours is valid.