Establish Einstein's relation 1 2 mu 2 = hv - hv 0 with respect to photoelectric emission.

The phenomenon of emission of electrons from a metal surface, when electromagnetic radiations of sufficiently high frequency are incident on it, is called the photoelectric effect. Einstein explained the photoelectric effect based on Planck's quantum theory according to which light radiation travels in the form of discrete photons. The energy of each photon is hv , where h is Planck's constant and v is the frequency of light. The main points of Einstein’s theory of the photoelectric effect are: The interaction between two particles results in photoelectric emission– one a photon of incident radiation and the other an electron of photosensitive metal. The free electrons are bound within the metal due to restraining forces on the surface. The minimum energy required to liberate an electron from the metal surface is called the work function W 0 of the metal. Each photon interacts with one electron. The energy hv of the incident photon is used up in two parts: A part of the energy of the photon is used in liberating the electron from the metal surface, which is equal to the work function W 0 of the metal, and The remaining energy of the photon is used in impairing kinetic energy to the ejected electron. Very few < 1 0 0 photons, whose energies are greater than W 0 , capable of ejecting the photons. By law of the conservation of energy, Energy of the incident photon = Maximum K . E . of photon + Work function hv = 1 2 mv 2 max + W 0 ∴ K max = 1 2 mv 2 max = hv - W 0 . . . . . . . ( 1 ) If the incident photon is threshold frequency v 0 , then its energy hv 0 is just sufficient to free the electron from the metal surface and does not give it any kinetic energy. So hv 0 = W 0 . Hence K max = 1 2 mv 2 max = hv - hv 0 = h v - v 0 . . . . . . ( 2 ) Equations (1) and (2) are called Einstein’s photoelectric equations.A