We can consider photons to carry momentum. As in any collision involving particles with non zero mass, collisions involving photons and matter particles will result in the overall conservation of momentum and energy.

A photon with wavelengthcan be considered as a particle with mass zero and momentumwhere h = Planck's constant. When the photon collides with a stationary electron, it is scattered elastically and its wavelength increases fromto

Conservation of momentum gives

(1)

(2)

Multiplying (1) and (2) bythroughout and usinggives(3) and(4)

Rewriting (3) as(5), squaring and adding (4) and (5) gives

(6)

Conservation of energy gives

Squaring both sides of the last equation gives(7)

(7)-(6) and simplifying the result gives

Dividing byand rearranging gives

Butandso