Q. Explain how Compton scattering confirms the quantum nature of radiation.

OR

What is "Compton Effect"? Deduce an expression for shift in wavelength of scattered X rays by Compton Scattering.

Ans.

In 1921, A. H. Compton discovered that when a monochromatic beam of high frequency radiation scattered by substance, the scattered radiation contains two components.

(i)     Unmodified Radiation - The radiation of unchanged frequency in scattered beam as incident beam.

(ii)    Modified Radiation - The radiation having lower frequency or greater wavelength then incident radiation. This phenomenon is known as Compton effect.

Theory - According to quantum theory, primary x rays beam is made up of photons of energy hv, where v is the frequency of the primary x rays. These photons travel with speed of light C and  possess momentum given by hv/c and also obey all the laws of conservation of energy and momentum when these photons strike the electrons of a scattering substance. The phenomenon of scattering is due to an elastic collision between the photon and the electron.

When the photon of energy hv collides with the electron of the scattered at rest, it transfers some energy to the electron i.e., it lessees energy. The scattered photon will therefore have a smaller energy than hv and consequently a lower frequency then the primary x ray. The observed change in frequency or wavelength of the scattering radiation is known as Compton effect.

In scattering process, the electron gains kinetic \energy and thus recoil with velocity v. as the work function of substance is negligibly small as compared to the energy of photon, the recoil electron is treated practically free,. Thus, during the collision, photon gives a fraction of its energy to the free electron and its relativistic mass is considered after collision.

Let a photon of energy hv collides with a free electron and after collision scattered photon of energy hv' is found at the scattering angle q while recoil electron is found at the recoil angle f as shown in Fig.

(i)            Energy Conservation Law - it states that before collision and after collision energy should remain same i.e. constant.

(ii)       Momentum Conservation Law - It states that before collision and after collision momentum should be same i.e. constant. Since momentum is a vector quantity taking component of momentum in horizontal and perpendicular direction