de Broglie wavelength vs kinetic energy

What you are seeing: the de Broglie wavelength $\lambda = h/p$ plotted on a log-log axis against kinetic energy for five particle species: massless photon, electron, proton, neutron, and a $^{12}$C atom. The relativistic momentum $pc = \sqrt{(T + mc^2)^2 - (mc^2)^2}$ is used so the curves are valid in both the non-relativistic ($T \ll mc^2$) and relativistic regimes.

Look for the slope-1/2 line at low energies (non-relativistic $\lambda \propto T^{-1/2}$) breaking to a slope-1 line at high energies (ultra-relativistic $\lambda \propto T^{-1}$). The transition happens at $T \sim mc^2$, which is why electrons go relativistic around 1 MeV but protons only around 1 GeV. The photon line is the universal relativistic asymptote, $\lambda = hc/E$, a clean slope-1 line. Reference horizontal lines mark a typical atomic spacing (0.1 nm) and a nuclear scale (1 fm = 10$^{-6}$ nm).