Question

In the Compton scattering, the photon of energy E₀ = hν₀ and momentum P₀ = hν₀/c is scattered from a free electron of rest mass m. Show that 

(a) the scattered photon will have energy E = E₀/[1 + α(1 − cos θ)], where θ is the angle through which the photon is scattered and α = h ν₀/mc² 

(b) the kinetic energy acquired by the electron is T = α E₀(1 − cos θ)/[1 + α(1 − cosθ)] 

(c) tan (θ/2) = (1 + α) tanϕ, where ϕ is the recoil angle of the electron.

Answer 1

(a) Let E = hν be the energy of the scattered photon and hν/c be its momentum (Fig. 7.15). 

Energy conservation gives 

hν₀ = hν + T ...(1) 

where T is the electron’s kinetic energy. 

Balancing momentum along and perpendicular to the direction of incidence