# Compton scattering explanation using non relativistic relation between electron kinetic energy and momentum

On basic Physcis textbooks Compton scattering is explained considering the conservation of momentum of the photon and the electron, and the conservation of their energies.

For the total electron energy $U_e$ a relativistic expression is used to link kinetic energy $K_e$ and momentum $p_e$ $$U_{e}=\sqrt{p_e^2c^2+m_e^2 c^4}=K_e+m_ec^2$$

But I wonder if the explanation of the Compton scattering can be given also considering an unrelativistic approximation for the relation between $K_e$ and $p_e$, which is

$$K_e=\frac{p_e^2}{2m_e}$$

Is this possible? If so, what does change in that case?

• The analysis can be done. The question is, does the result of the analysis match experimental data? Do the calculation yourself then see if it gives about 175 keV for the maximum electron kinetic energy ($\theta=\pi$ radians) if the original gamma is 511 keV. – Bill N Apr 7 '17 at 2:05
• One would expect the answers to be pretty much indistinguishable so long as the speed of the outgoing electron is much less than $c$, since in that case the final kinetic energy of the electron would be close to the classical value (and the rest energy of the electron would cancel from both sides.) – Michael Seifert Apr 12 '17 at 17:28