State Einstein's photoelectric equation. Explain any two characteristics of photoelectric effect on the basis of this equation.

Explanation

Einstein’s explanation of photoelectric effect.
Photoelectric effect is the phenomenon of emission of electrons by certain substances, chiefly metals, when these are illuminated by radiations like X-rays, ultraviolet rays and even visible light. The electrons ejected from a. substance in this manner are called photoelectrons.

According to quantum theory, light consists of bundles of energy, called photons, each of energy hv, where h is the Planck’s constant and V is the frequency of the light.
When a photon of energy hv is incident on the surface of a photosensitive substance, a part of its energy `W_(0)` is used up in liberating the electrons from the surface and the rest of the energy is given to the ejected electron to impart it is a velocity v and hence a kinetic energy `1/2 mv^(2)`.
Work Function. The part of the incident photon WQ which is used up in liberating an electron from the surface is called the work function and depends upon the nature of the surface.
Einstein’s photoelectric equation
Einstein assumed that one incident photon can eject only one electron. The photon energy is utilised in two ways :
(i) A part of energy of photon is used for electron free from the atom and away from the metal surface. This energy is called photoelectric work function WQ.
(ii) The balance of the photon energy is used up in giving the electron a kinetic energy `1/2 mv^(2)`.
`therefore` Energy of incident photon = Work function + K.E. of electron
or `hv =W_(0) +1/2mv^(2)`...........(i)
If `v_(0)` is the threshold frequency which is just sufficient to eject an electron with zero velocity, i.e. v = 0.
So, `W_(0) =hv_(0)`...............(ii)
Putting (ii) in (i) we get
`hv = hv_(0) + 1/2mv^(2)`
or `1/2 mv^(2) = h(v-v_(0))`...........(iii)
This equation is called Einstein.s photoelectric equation.

From Eqn. (iii), it is clear that
(i) v depends only upon v, m and h are constants. Thus the velocity of the photoelectron ejected depends upon the frequency of light. From equation (iii), it is seen that greater is the frequency v, greater is the velocity of the photoelectrons ejected. This is the first law of photoelectric emission.
(ii) If the intensity of light is increased, the number of incident photons increases which results in an increase in the number of photoelectrons ejected. This is the second law.
(iii) If `v lt v_(0), v^(2)` is negative, i.e., v is imaginary. In other words, if the frequency of the incident photon is less than `v_(0)` no photoelectric effect is possible. This is the third law of photoelectric emission.
(iv) The phenomenon of photoelectric emission has been conceived as an effect of collision between a photon and an electron in metal. Hence there should be no time lag between the incidence of photon and ejection of the photoelectrons. This is the fourth law.