Compton Scattering Calculator
Calculate Compton wavelength shift, scattered photon energy, and recoil electron kinetic energy.
Apply the Compton effect formula for X-ray and gamma-ray scattering from electrons.
The Compton Effect Arthur Holly Compton (USA, 1923) discovered that X-rays scattered from electrons shift to longer wavelengths. This proved that photons carry momentum, confirming the particle nature of light. Nobel Prize in Physics awarded to Compton in 1927.
Compton Wavelength Shift Formula Δλ = λ_c × (1 − cos θ) Where: Δλ = wavelength shift (m) λ_c = Compton wavelength of electron = h/(m_e × c) = 2.426 × 10⁻¹² m (2.426 pm) θ = scattering angle of the photon (degrees) h = Planck constant = 6.626 × 10⁻³⁴ J·s m_e = electron rest mass = 9.109 × 10⁻³¹ kg c = speed of light = 2.998 × 10⁸ m/s
Special Angles θ = 0°: no shift (forward scatter, Δλ = 0) θ = 90°: Δλ = λ_c = 2.426 pm (maximum partial shift) θ = 180°: Δλ = 2λ_c = 4.852 pm (backscatter, maximum shift)
Photon Energies E = hc/λ (in Joules) = 1240 eV·nm / λ_nm Incident photon: E₀ = hc/λ₀ Scattered photon: E’ = hc/(λ₀ + Δλ) Recoil electron kinetic energy: K = E₀ − E’ (energy conservation)
Compton Scattering vs. Photoelectric Effect Low photon energy (few eV): photoelectric effect dominates High photon energy (keV–MeV): Compton scattering dominates Very high energy (MeV+): pair production dominates Medical CT scanners (keV) and radiotherapy (MeV) rely on Compton scattering in tissue.