Compton Scattering Calculator – Wavelength Shift & Energy

Compton scattering is a fundamental quantum mechanical phenomenon in which a photon — typically an X-ray or gamma ray — collides with a free or loosely bound electron and transfers part of its energy to the electron. As a result, the scattered photon emerges with a longer wavelength (lower energy) than the incident photon, while the electron recoils with the transferred kinetic energy. The discovery of this effect by American physicist Arthur H. Compton in 1923 provided crucial experimental evidence for the particle-like nature of light and earned him the Nobel Prize in Physics in 1927. The wavelength shift produced by Compton scattering is given by the Compton formula: Δλ = λ_c(1 − cosθ), where Δλ is the change in wavelength, λ_c = h/(m_e c) = 2.42631 pm is the Compton wavelength of the electron, and θ is the scattering angle between the incident and scattered photon directions. The scattered photon energy is: E′ = E₀ / [1 + (E₀/m_e c²)(1 − cosθ)], where E₀ is the incident photon energy and m_e c² = 511 keV is the electron rest energy. The kinetic energy transferred to the electron equals E₀ − E′. The scattering angle governs how much energy is transferred. At θ = 0° (forward scattering), no energy transfer occurs and the photon passes through unaffected. At θ = 90°, partial energy transfer occurs and the wavelength shift equals exactly one Compton wavelength (2.426 pm). At θ = 180° (backscattering), the maximum possible energy transfer occurs and the wavelength shift equals 2λ_c = 4.853 pm. Compton scattering has extensive applications across science and medicine. In diagnostic radiology and computed tomography (CT), Compton scattering is the dominant interaction mechanism for X-ray photons in the diagnostic energy range (30–150 keV), contributing to image noise and scatter artefacts. In nuclear medicine and positron emission tomography (PET), understanding Compton interactions is essential for accurate image reconstruction. Compton cameras exploit the scattering geometry to determine the direction of incoming gamma rays without physical collimators, enabling new approaches to gamma-ray imaging. In radiation physics and shielding design, Compton scattering dominates over photoelectric absorption and pair production in the intermediate energy range (around 100 keV to 10 MeV for common materials). Astrophysicists study Compton scattering in cosmic X-ray sources, and inverse Compton scattering — where energetic electrons boost photon energies — is responsible for some of the highest-energy radiation observed in the universe.