22.3 Compton Scattering and Photon Momentum Evidence

Compton scattering treats light-electron interaction as a two-body collision: an incident photon strikes a near-free electron, the photon leaves at a new angle with reduced energy, and the electron recoils with kinetic energy. Because the scattered photon has lower energy, its wavelength is longer. This effect is strongest for X-ray and gamma-ray wavelengths where photon energies are high enough for measurable shifts.

The key point is not only that energy changes, but that momentum-conservation equations with photon momentum p = h/lambda correctly predict angle-dependent wavelength shift. That is stronger than the photoelectric argument because it uses two-dimensional collision geometry rather than only threshold energetics.

Forward scattering (theta near 0 degrees) gives almost no shift because the photon continues nearly in its original direction and transfers little momentum. Backscatter (theta near 180 degrees) gives maximum shift because momentum reversal demand is largest. This angle control is exactly what experiments verify.

After finding shifted wavelength, recover scattered photon energy from E' = hc/lambda'. Electron kinetic energy is then K_e = E - E'. Keeping units consistent matters because keV, pm, and SI joules are frequently mixed in one question. If the shift is tiny relative to original wavelength, only a small energy fraction goes into electron recoil.