Compton wavelength

The Compton wavelength λc\lambda_{c} is a conventional wavelength assigned to a particle of mass mm:

λC=hmc\lambda_{C}=\frac{h}{mc}

where hh is the Planck constant. It is the wavelength of a Photon whose energy is the rest energy of the particle, as per the mass-energy equivalence E=mc2E=mc^{2}. This definition originates from the Compton scattering phenomenon, where it appears naturally.

This relation is important because it gives a quantitative measure the "size" of a particle, as in the degree to which it is localized. The larger the rest mass, the shorter the Compton wavelength and hence the more strongly localized the particle is. As per 2022 CODATA values, the electron and proton Compton wavelengths are

λelectron≃2.426×10−12 m,λproton≃1.321×10−15 m\lambda_{\text{electron}}\simeq 2.426\times 10^{-12}\text{ m},\qquad\lambda_{\text{proton}}\simeq1.321\times10^{-15}\text{ m}