When a high energy X-ray photon or γ-ray photon is scattered by an electron that is (almost) free, the photon loses energy and the electron gains energy shown in figure. This effect was discovered by A.H. Compton in 1923. It is now known as the Compton effect. This effect exhibits particle nature of electromagnetic radiation.
compton effect
If X is the wavelength of the incident photon, λ is the wavelength of the scattered photon, θ is the angle through which the photon is scattered, m0 is the rest mass of an electron, c is the speed of light in free space and h is Plank’s constant, then, the wavelength shift, called the Compton shift is given by
[Note : In a collision between a low energy photon and a high energy electron, scattering results in loss in the energy of the electron and gain in the energy of the photon. This effect is known as the inverse Compton effect.]