When X-rays strike a thin metal foil, the scattered X-rays are observed to have a longer wavelength than the incident beam. Compton applied energy and momentum conservation to show that the wavelength shift depends on the scattering angle. The result confirmed that light quanta (photons) carry momentum even though they are massless, giving major support to the rapidly emerging quantum mechanics. Knowledge of the Compton effect is now used, for example, in designing medical X-ray devices and in eliminating unwanted scattering in materials analysis.

Compton treated the electron as a loosely bound (essentially free) particle and modeled the interaction as an elastic two-body collision in special relativity. The resulting Compton formula, Δλ = (h/m_e c)(1 − cosθ), predicts a wavelength shift proportional to the scattering angle θ, where h is Planck’s constant, m_e the electron mass, and c the speed of light. Agreement with experiment decisively favored the light-quantum hypothesis over classical wave explanations and deepened our grasp of wave–particle duality. At higher energies, inverse Compton scattering is a key mechanism behind cosmic γ-ray sources, illustrating the effect’s reach into astrophysics.

In quantum electrodynamics, Compton scattering is a fundamental tree-level process whose differential cross-section, dσ/dΩ = (r_e^2/2)(λ′/λ)^2(λ/λ′ + λ′/λ − sin^2θ), is expressed with the classical electron radius r_e. Measured spectra have evolved into Compton profile analysis, a direct probe of electron momentum distributions in solids. For high-Z targets, binding-energy corrections and multiple-scattering terms become significant, making the effect a benchmark for validating photon algorithms in Monte Carlo radiation-transport codes.