Q. Describe Compton effect. Drive an expression for Compton shift. How does it support the particle nature of light. 

Compton Effect and Quantum Nature of Light

A.H. Compton in 1923, while studying the scattering of  X rays by a block of paraffin observed that the wavelength of the scattered radiation was greater than wavelength of incident radiation and this shift in wavelength was dependent on the angle of the scattering. The wavelength of scattered radiation is found maximum at right angles to the direction of incident beam. This effect is known as Compton Effect.

Classical theory is failed to explain this observed effect of increment in wavelength. According to classical theory the wavelength of incident radiation and scattered radiation must be same. Compton explain this effect by assuming that light is consist of a large number of oscillating particles vibrate with different frequencies known as Quanta having energy. Thus Compton effect gives us an experimental evidence of quantum nature of light.

Theory of Compton Effect

Let us consider the phenomenon of scattering as a elastic collision between the incident photon and electron. The conservation of energy and momentum will hold since collision is elastic.

Compton assumed the electron to be free and at rest before collision with the incident photon. After the collision has taken place, the relativistic mass of the electron to be electron to be considered instead of its rest mass. A small parts of energy of high energy photon is also being transferred to the electron is this process.

During the collision process some of the part of this energy is imparted to the electron, which in turn gain kinetic energy and so recoil. The direction of scattered photon is given by angle q, whereas the direction of recoil electron.