= Compton wavelength
{c}
{title2=$\lambda_C=h/(mc)$}
{wiki}
The <Compton wavelength> of a <subatomic particle> of <rest mass> $m>0$ is $\lambda_C=h/(mc)$, where $h$ is the <Planck constant> and $c$ the <speed of light>. It is the <wavelength> of a <photon> whose <energy> $hc/\lambda_C$ equals that <subatomic particle>'s <rest energy> $mc^2$. It is a characteristic scale, rather than a measured geometric radius of the <subatomic particle>.
The reduced <Compton wavelength> is $\bar\lambda_C=\hbar/(mc)=\lambda_C/(2\pi)$, with $\hbar=h/(2\pi)$. Keep that factor of $2\pi$: the <Compton scattering> <wavelength> shift below uses $h/(m_ec)$, not $\hbar/(m_ec)$. Here we choose the rounded <electron> value $\lambda_C=2.426\,\mathrm{pm}$, where $1\,\mathrm{pm}=10^{-12}\,\mathrm m$; the maximum single-collision <wavelength> increase is $2\lambda_C=4.852\,\mathrm{pm}$.
Why this scale? A <photon> of <wavelength> $\lambda$ has <momentum> magnitude $h/\lambda$. At $\lambda\sim\lambda_C$ that <momentum> is comparable with $mc$, 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>.
Back to article page
