We have to find the maximum wavelength shift for a Compton collision between a photon and a free electron.

Solution:             Click For PDF Version

The wavelength shift in scattering of a photon from a free electron is given by the Compton scattering equation

where is the angle from the incident photon direction in which the scattered photon wavelength is .

Therefore, the maximum wavelength shift will be when the photon is back scattered. That is The maximum change in wavelength of photon in Compton scattering is

.