Question

A photon of energy E is scattered by a particle of rest energy Eo. Find the maximum kinetic energy of the recoiling particle in terms of E and Eo.

Answer 1

from crompton scatttering we get that :

$K=hf\frac{\Delta\lambda}{\lambda+\Delta\lambda}$

$K=hf\dfrac{2h}{m_oc(\lambda+\frac{2h}{m_oc})}$

$K=\dfrac{2hfhf}{m _oc(\lambda f+\frac{2hf}{m_oc})}$

$K=\dfrac{2hfhf}{m _oc^2(1+\frac{2hf}{m_oc^2})}$

now lets substitute the vale of E and E_o

E=hf and E_o=m_oc²

$K=\dfrac{2E^2}{E_o(1+\frac{E}{E_o})}$