When X-rays scatter off electrons, does the scattered light keep its wavelength (as a classical wave should) or does it redden — and what would a shift mean?
▶ Launch the interactive simulationFrom two conservation laws — relativistic energy and momentum for a photon (E = pc, p = h/λ) elastically striking a stationary electron — derive the wavelength shift Δλ = (h/mₑc)(1−cos θ) = λ_C(1−cos θ). Generate the scattered wavelength at eight angles for an incident Mo Kα line and least-squares fit Δλ against (1−cos θ).
the Compton wavelength λ_C = 2.426×10⁻¹² m — recovered as the SLOPE of a single straight line through the origin (intercept ≈ 0); the shift is INDEPENDENT of the incident wavelength (a softer Cu Kα line gives the identical Δλ(θ) — the classical wave theory has no parameter that could do this, and in fact predicts Δλ = 0 at every angle); and energy conservation — the photon's lost energy equals the recoil electron's kinetic energy at each angle. Compton's 1923 result, the one that made the photon a particle carrying momentum p = h/λ and the fourth pillar of early quantum theory