E4 1 Photoelectric Effect

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“Thus all of the earlier models have been superseded by QED, but the semiclassical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 Stopping potential

Contact potential Work function

Photoemission current Valence band

I-V characteristic curve Conduction band

Photoemission threshold Band-gap energy

Reverse current Electron affinity

Dark current 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,

obtain Einstein’s equation: asp

hV

e e

φν= − for the stopping potential of a metal

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.