The Compton wavelength is a quantum mechanical property associated with a particle, defined as the wavelength of a photon whose energy is equivalent to the rest mass energy of that particle. It was introduced by the American physicist Arthur H. Compton in the context of his studies on the scattering of X-rays off electrons.
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The Compton wavelength of a subatomic particle of rest mass is , where is the Planck constant and the speed of light. It is the wavelength of a photon whose energy equals that subatomic particle's rest energy . It is a characteristic scale, rather than a measured geometric radius of the subatomic particle.
The reduced Compton wavelength is , with . Keep that factor of : the Compton scattering wavelength shift below uses , not . Here we choose the rounded electron value , where ; the maximum single-collision wavelength increase is .
Why this scale? A photon of wavelength has momentum magnitude . At that momentum is comparable with , so transfer of an appreciable fraction of it can make the recoiling subatomic particle relativistic. Even for longer wavelengths, Compton scattering can resolve the small energy transferred into electron kinetic energy.