We have to show that (a) when a photon of energy E scatters from a free electron, the maximum recoil kinetic energy of the electron is given by

(b) We have to find the maximum kinetic energy of the Compton scattered electron knocked out of a thin copper foil by an incident beam of 17.5-keV x rays.

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(a)

The Compton scattering on change of wavelength of a photon when it is scattered from a free electron at rest is

,

where and are the wavelengths corresponding to the incident and the scattered photons, respectively.

The wavelength of the photon is back scattered is obtained by using the scattering angle of in the Compton scattering equation. We have

The energy of the incident photon is

.

The energy of the back scattered photon will be

Therefore, the recoil energy of the electron on back scattering of photon will be

The maximum recoil kinetic energy of the electron will therefore be

(b)