PHOTOELECTIC EFFECT

When light of sufficiently small wavelength is incident on a metal surface, electrons ejected from the metal. This phenomenon is known as photoelectric effect. The electrons ejected from the metal surface are called photoelectrons. Let us try to understand photoelectric effect on the basis of  the photon theory of light.

We know that there are large number of free electrons in a metal which wander throughout the body of the metal. However, these electrons are not free to leave the surface of the metal. as they try to come out of the metal attracts them back. A minimum energy, equal to work function (φ), must be given to an electron so as to bring out of the metal.

When light is incident on a metal surface, the photons collide with free electrons. In a particular collision, the photons may give all of it's energy to the free electron. If this energy is more than the work function (φ), it will come out. The electron after receiving the energy, may lose energy to the metal in course of collisions with the atoms of the metal. Only if an electron near the surface gets extra energy and heads towards the outside, it is able to come out. If it is given energy E which greater than φ, and it makes the most economical use of it, it will have the kinetic energy (E - φ) after coming out. If it makes some collisions before coming out, kinetic energy would be less than (E - φ). The actual kinetic energy of such an electron will depend on the total energy lost in collisions. It is possible that the electrons makes several collisions inside the metal and losses so much energy that it fails to come out. So, the kinetic energy of the photoelectron coming out may be may anything between zero and 

(E - φ), where E is the energy supplied to the individual electron. We can, therefore write,

K.E. max = E - φ

Metal	Work function	Metal	Work function
Cesium	1.9 e.v.	Calcium	3.2 e.v.
Potassium	2.2 e.v.	Copper	4.5 e.v.
Sodium	2.3 e.v.	Platinum	5.6 e.v.

Work functions of some photosensitive metals 

Let monochromatic light of wavelength (λ) be incident on the metal surface. In a particle picture photons of energy hc/λ fall on the surface. Suppose, a particular photon collides with a free electron and supplies all its energy to the electron. The electron gets an extra energy E=hc/λ and may come out of the metal. The maximum kinetic energy of this electron is therefore,

K max = hc/λ - φ

The above equation is known as Einstein's photoelectric equation. Einstein, after an average academic career, put forward this theory in 1905 while working as a grade Ⅲ technical officer in a patent office. He was awarded the Nobel prize in physics for 1921 for this work.