Einstein Contribution to Planck Formula on the Quantum Nature of Radiation

While the existence of the photoelectric effect can be understood within the framework of classical electromagnetic theory since it was known that there were electrons in metals and one could envisage them to be accelerated by absorption of radiation, the frequency-dependence of the effect is not comprehensible within that framework. The energy carried out by an electromagnetic wave is proportional to the intensity of the source and frequency has nothing to do with it. Moreover, a classical explanation of the effect, which would have to involve the concentration of the energy deposited on single photoelectrons, would carry with it an implied time delay between the arrival of the radiation and the departure of the electron, the delay being longer when the intensity is decreased. As a matter of fact, no such time delays were ever observed, at least any longer than 10^-9 sec, even with incident radiation of very low intensity.

Albert Einstein considered the radiation to consist of a collection of quanta of energy hf, where h is the Planck’s constant (6.626 x 10^-34 J.s), and f is the frequency of the light. The absorption of a single quantum by an electron, a process that may take less time than the upper limit indicated above, increases the electron energy by an amount hf. Some of the energy must be expended to separate the electron from the metal. This amount, W (termed to as the work function), might be expected to vary from metal to metal, but should not depend on the electron energy. The rest is available for the electron kinetic energy, so that on this basis, we have the following relation between the electron velocity v and light frequency f.

½ mv² = hf – W

The threshold effect and the linear relation between electron kinetic energy and the frequency are contained in this formula. The proportionality of the current and the source intensity can also be understood in terms of these light quanta or photons i.e. a more intense light source emits more photons and these in turn can liberate more electrons.

Related: Basics Facts about Photons

Recommended Resource: Quantum Physics in Minutes