Distribution of the compton scattering due to the direction change of X-ray

The Compton scattering of x-rays can be interpreted as the result of elastic collisions between x-ray photons and free electrons. According to quantum theory, a photon of wavelength λ has a kinetic energy hc/λ and a linear momentum of magnitude h/λ where h is Planck's constant and is the speed of light. In the Compton effect. An incident beam of x-rays of known wavelength λ in a known is scattered in passing through matter, and the scattered radiation at an angle θ to the incident beam is found to have a longer wavelength λ' which is a function of the angle. Assuming an elastic collision between an incident photon and as electron of mass at rest, set up the equations expressing conservation of energy and momentum. Use the relativistic expressions for the energy and momentum of the electron. Show that the change in x-ray wavelength is and that the abjected electron appears at an angle given by