# The Photoelectric Effect

Heinrich Hertz first observed this photoelectric effect in 1887. This, too, was one of those handful of phenomena that Classical Physics could not explain. Hertz had observed that, under the right conditions, when light is shined on a metal, electrons are released. Light falling on a metal can cause electrons to be ejected from the metal. This is known as the photoelectric effect.

In 1905 Albert Einstein provided a daring extension of Planck's quantum hypothesis and was able to explain the photoelectric effect in detail. It was officially for this explanation of the photoelectric effect that Einstein received the Nobel Prize in 1921. The figure below shows a circuit that can be used to analyze the photoelectric effect. Expanding on Planck's quantum idea, Einstein proposed that the energy in the light was not spread uniformly throughout the beam of light. Rather, the energy of the light is contained in "packets" or quanta (the plural of quantum, a single "packet") each with energy of

E = h f

where again h is Planck's constant and f is the frequency of the light. All of the energy in one quantum -- now called a photon -- is given to one electron. For light with a low frequency, the energy, E = h f, in one quantum of light would not be great enough to release an electron. For light with a higher frequency, a frequency greater than some particular threshold frequency, there would be enough energy and the electron would be ejected. From the conservation of energy, we would expect the electron to leave with kinetic energy KE given by

h f = KE + W

KE = h f - W

where W is the amount of work that must be done to separate an electron from the metal. For the least strongly bound electrons (the ones easiest to tear away from the metal) this amount of work is known as the "work function" and is labeled Wo. These electrons will leave with the greatest kinetic energy KEmax which is given by

h f = KEmax + Wo

KEmax = h f - Wo

Einstein's explanation of the photoelectric effect is quite different from that of Classical Physics. It makes the following predictions:

>> An increase in the intensity of the light means an increase in the number of photons (or "packets" or quanta of energy) so more electrons will be ejected. But each electron will have originated from a photon of the same energy so there will be no increase in the maximum energy of the electrons.

>> An increase in the frequency of the light will cause an increase in the maximum kinetic energy of the electrons according to our equation above,

KEmax = h f - Wo

>> Kinetic Energy can never be negative so this equation defines a threshold frequency, fo, from

h fo = Wo

>> If the frequency of the light is below this threshold frequency fo there will be no photoelectrons ejected from the metal.

The predictions of Classical Physics, using just the electromagnetic wave nature of light, are drastically different. In 1913 and 1914 Robert A Millikan (famous for measuring the charge on an electron with his "oil drop experiment") carried out careful experiments and measured precisely what Einstein's new theory predicted.    Planck's Hypothesis Compton Scattering Return to Ch 28, Quantum Mechanics