Compton wavelength of the electron

Arthur Compton's 1923 X-ray scattering experiment ended the debate about whether light was a wave: scattered X-rays came back with longer wavelengths that depended on angle, exactly as billiard-ball collisions between photons and electrons would predict, and Δλ = λ_C(1 − cos θ). At 90° the shift is one Compton wavelength, 2.43 pm — invisible for visible light, which is why the effect only shows up with X-rays and gammas.

Beyond the scattering formula, λ_C marks where a particle stops being a particle. Confine an electron to a box smaller than its Compton wavelength and the momentum uncertainty exceeds m_e c, so the energy is enough to create electron-positron pairs and single-particle quantum mechanics gives way to quantum field theory. Note that the electron's Compton wavelength is 137 times smaller than the Bohr radius and 137 times larger than the classical electron radius — α is the rung spacing of that ladder.