Compton scattering

By the early twentieth century, the photoelectric effect had already shown that light interacts with matter in discrete energy packets — photons — but some physicists still hoped a purely classical wave picture might eventually account for it. Compton scattering closed that door. When X-ray photons are directed at a target containing loosely bound or effectively free electrons, the scattered X-rays come back with a longer wavelength than the incoming beam, and the size of that wavelength shift depends on the scattering angle in a way that a classical wave picture cannot reproduce at all — classical electromagnetic theory predicts the scattered radiation should keep the same wavelength as the incident wave, just redistributed in direction.

The effect is explained cleanly by treating the interaction as a particle-like collision between a photon and an electron, each carrying momentum as well as energy. Conservation of both energy and momentum in this photon-electron "collision" — using the photon's momentum p = h/λ, familiar from the de Broglie relation and applied in reverse here — predicts exactly the observed relationship between the wavelength shift and the scattering angle: the photon loses some momentum and energy to the recoiling electron, and by the same p = h/λ relation, a photon that has lost momentum must have gained wavelength. The larger the scattering angle, the more momentum is transferred and the larger the wavelength shift, up to a maximum at backscattering.

Compton scattering was decisive evidence, alongside the photoelectric effect, that light must be treated as discrete, momentum-carrying photons in this regime, not merely a wave. It remains an important interaction mechanism today: it is one of the main ways gamma rays and X-rays lose energy when passing through matter, relevant to radiation shielding, medical imaging, and astrophysical observations of high-energy radiation.