Photoelectric Effect

In 1905, Albert Einstein proposed a radical new theory of light in order to
account for the photoelectric effect. According to this theory, light
of fixed angular frequency
consists of a collection of indivisible discrete packages, called
*quanta*,^{C.1} whose energy is

Here, is a new constant of nature, known as

Suppose that the electrons at the surface of a piece of metal lie in a potential well
of depth
. In other words, the electrons have to acquire an energy
in order to be emitted from the surface. Here,
is generally called
the *workfunction* of the surface, and is a property of the
metal. Suppose that an electron absorbs a single quantum of light, otherwise known as a *photon*. Its energy
therefore increases by
. If
is greater than
then the
electron is emitted from the surface with the residual kinetic energy

(C.2) |

Otherwise, the electron remains trapped in the potential well, and is not emitted. Here, we are assuming that the probability of an electron absorbing two or more photons is negligibly small compared to the probability of it absorbing a single photon (as is, indeed, the case for relatively low-intensity illumination). Incidentally, we can determine Planck's constant, as well as the workfunction of the metal, by plotting the kinetic energy of the emitted photoelectrons as a function of the wave frequency. This plot is a straight-line whose slope is , and whose intercept with the axis is . Finally, the number of emitted electrons increases with the intensity of the light because, the more intense the light, the larger the flux of photons onto the surface. Thus, Einstein's quantum theory of light is capable of accounting for all three of the previously mentioned observational facts regarding the photoelectric effect. In the following, we shall assume that the central component of Einstein's theory--namely, Equation (C.1)--is a general result that applies to all particles, not just photons.