Compton Scattering Calculator

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)

A worked example

Take a 10 pm X-ray photon, which carries hc/λ = 124.0 keV, and scatter it through 90°.

The shift is Δλ = 2.426 × (1 − cos 90°) = 2.426 × 1 = 2.426 pm, so the scattered photon leaves at 12.426 pm. Its energy drops to 124.0 × (10 / 12.426) = 99.78 keV, and the missing 24.2 keV goes into the recoiling electron. That is a fifth of the photon’s energy handed over in a single collision.

Now notice the part that trips people up. The shift is always 2.426 pm at 90°, whatever the incoming wavelength. It is an absolute shift, not a percentage. For a 10 pm X-ray that is 24% of the wavelength and the effect is unmissable. For 500 nm green light it is 2.426 pm out of 500,000 pm, five parts in a million, which is why nobody noticed Compton scattering until X-ray sources existed. Compton needed short wavelengths to see it at all, and that is the whole reason the discovery waited until 1923.

Compton Scattering vs. Photoelectric Effect Low photon energy (few eV): photoelectric effect dominates High photon energy (keV to MeV): Compton scattering dominates Very high energy (above ~1.02 MeV): pair production becomes possible and eventually dominates Medical CT scanners (keV) and radiotherapy (MeV) rely on Compton scattering in tissue. It is also the reason radiographers stand behind a wall: the patient becomes a source of scattered photons in every direction, and backscatter towards the tube is the strongest part of it.