Max Planck put forward the quantum theory in 1900 to explain blackbody spectrum. In the theory, he proposed that the electromagnetic radiation emitted by the body consists of discrete concentrated bundles of energy, each equal to hv, where h is a universal constant (now called Planck’s constant) and v is the frequency of the radiation.

Einstein put forth (1905) that these energy quanta, called light quanta/later called photons, interact with matter much like a particle. When a photon collides with an electron in an atom, the electron absorbs whole of the photon energy hv in a single collision or nothing. The electron uses this energy (1) to liberate itself from the atom, (2) to overcome the potential energy barrier at the surface thus liberating itself from the metal, and (3) retains the remaining part as its kinetic energy. Different electrons need different energies in the first two processes. There are some electrons which use minimum energy in the two processes, and hence come out of the metal with maximum kinetic energy. The minimum energy required, in the form of electromagnetic radiation, to free an electron from a metal is called the photoelectric work function Φ of that metal.

Thus, for the most energetic photoelectrons at the time of emission,

maximum kinetic energy of the electron = photon energy – photoelectric work function

∴ \(\cfrac12\) mv²_max = hv – Φ 

∴ hv = Φ + \(\cfrac12\)mv²_max

The above equation is called Einstein’s photoelectric equation.

Light interacts with matter as concentrated bundles of energy rather than energy spread over a Huygens type wavefront. Even under weak irradiation, an electron absorbs a photon’s energy in a single collision. But the rate of incident photons in dim light being less, the chances of such absorption diminish and consequently the photoelectric current diminishes. However, a photoelectron is emitted as soon as a photon is absorbed.

[Note : Albert Einstein (1879-1955), German Swiss- US theoretical physicist, gave his photoelectric equation in 1905. In the period 1912-1916, Robert Andrews Millikan (1868 -1953), US physicist, was the first to obtain the precise experimental data from which the straight-line graphs, like the one shown in Fig. 14.6, were plotted for various metals. Einstein’s theoretically predicted equationclearly having the right form for a straight-line graph-was thus verified.]