Section 5.2: Light as a Particle: Photoelectric and Compton Effects

photon energy = eV

cesium | sodium | calcium | magnesium | zinc | tin | copper

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The photoelectric effect, discovered by Hertz in 1887, occurs when light impinges on certain metals and electrons are ejected. These electrons are often called photoelectrons. The kinetic energy of the exiting electrons is measured by applying a stopping potential, V0, that repels electrons with kinetic energy less than qV0. Restart.  In this animation, you may change the incident photon's energy by using the text box and the "enter energy" button. In addition you may change the substance upon which the light impinges by selecting one of the radio buttons.

What was found experimentally was that the kinetic energy of the ejected electrons had a correlation with the frequency (particle behavior) of the light and no correlation with the intensity (wave behavior) of the light. Even with low intensity light, if the frequency is above a certain threshold, ν0, photoelectrons are emitted from the metal. However, if the frequency is below ν0, there are no emitted electrons. In 1905, Einstein asserts Planck's hypothesis, Eγ = , outside of the realm of the blackbody radiation, postulating that this assumption of Planck was actually a general property of light. Applying it to the photoelectric effect yields

Eγ = hν = Φ + eV0. (5.1)

From Einstein's point of view, quanta of light (photons) were incident on the electrons of a metal and only when the photons had enough energy to overcome the metal's work function, Φ, photoelectrons were produced. Thus, if the light acted like particles of energy hν, photoelectrons would be produced only if the light had a frequency high enough so that hν was bigger than Φ, the work function of the metal.

| wavelength of incident photon = nm

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Compton used the idea that light behaves like a particle to explain light-electron (photon-electron) scattering. Compton used the relation for the energy, Eγ = hν, momentum, p = E/c or p = h/λ, and the relativistic expression for the conservation of  energy and momentum,

Ee = γmec2 = (p2c2 + me2c4)1/2, (5.2)

to describe the scattering of light off of an electron.

In this animation, a photon scatters off of an electron, which is initially at rest. You may vary the wavelength of the photon between 0.5 nm and 1.0 nm using the text box and the "fire photon" button. The scattered photon is collected and analyzed at the end of the experiment. Its wavelength and angle from the forward direction are reported. Firing repeatedly allows you to see photons scatter at different angles. How does the wavelength shift depend on the angle of the scattered photon (and the electron)?  Observe the change in wavelength of the light. It is given by

λ' − λ = (h/mec) (1 − cos(θ)), (5.3)

where λ' is the scattered photon's wavelength and θ is the photon's scattering angle.1

While the work of Einstein and Compton is convincing, treating light as a particle is not the only explanation for the photoelectric and Compton effects. In 1969 Lamb and Scully2 showed that they could explain the photoelectric effect semi-classically (treating light as a classical electromagnetic wave). Therefore Einstein did not prove the particle-like behavior of light, he only came up with one possible explanation. It was not until 1986 when Grangier, Roger, and Aspect (the so-called Aspect anti-coincidence experiment) experimentally showed that light can indeed behave like a particle. In their experiment, they used a beam splitter and two detectors that were separated by a large distance. For light to display particle-like behavior, the detectors should not detect the same photon. Grangier et al. were never able to measure the same photon arriving at the two different detectors. Each photon was measured only at one detector or the other, a perfect anti-coincidence.3

1For more details on the derivation of the Compton scattering formula, see Chapter 3 of K. Krane, Modern Physics, John Wiley and Sons (1996).
2W. E. Lamb, Jr. and M. O. Scully, "The Photoelectric Effect without Photons," in Polarisation, Matierer et Rayonnement, Presses University de France (1969).
3For more details on this fascinating experiment, see Chapter 2 of G. Greenstein and A. G. Zajonc, The Quantum Challenge, Jones and Bartlett (1997); J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, "Observing the Quantum Behavior of Light in an Undergraduate Laboratory," Am. J. Phys. 72, 1210-1219 (2004).

Exploration written by Steve Mellema, Chuck Niederriter, Mario Belloni, and Wolfgang Christian.