Compton wavelength

The Compton wavelength is defined as the wavelength of a photon whose energy is the same as the rest energy of that particle. The wavelength sets the minimum space required for a free relativistic particle, and it is used as a dividing line between the combinations of mass and size that require quantum mechanics and those that can be described with classical theories.

It was introduced by Arthur Compton in 1923 in his explanation of the scattering of photons by electrons (a process known as Compton scattering). The wavelength of the outgoing photon, ${\displaystyle \lambda '}$, is shifted from the incident photon wavelength,${\displaystyle \lambda _{0}}$, by an amount given by $${\displaystyle \lambda '-\lambda _{0}=\lambda _{c}(1-\cos \theta )}$$ with ${\displaystyle \lambda _{c}={h}/{mc}}$, where h is the Planck constant and c is the speed of light.