Compton scattering describes what happens when a high-energy photon — typically an X-ray or gamma ray — collides with an electron and bounces off with less energy and a longer wavelength. This calculator computes the wavelength shift, the resulting scattered wavelength, and the photon's energy loss from the scattering angle, using the same physics Arthur Compton used to win the 1927 Nobel Prize in Physics.
How the Compton Scattering Calculator works
The calculator applies the Compton scattering formula, Δλ = (h/mₑc)(1 − cosθ), derived by treating the photon-electron collision as an elastic particle collision that conserves both energy and momentum — even though the photon has no rest mass. The constant h/(mₑc) works out to 2.426×10⁻¹² m (2.426 pm), the Compton wavelength of the electron. Because this constant does not depend on the photon's incoming wavelength, the wavelength shift Δλ is the same for any X-ray or gamma-ray photon scattered at a given angle — only the fractional change in wavelength (and therefore the visibility of the effect) depends on the starting wavelength.
Once Δλ is known, the scattered wavelength follows directly: λ′ = λ + Δλ. Converting both wavelengths to photon energy via E = hc/λ gives the energy the photon lost to the electron, which appears as the electron's recoil kinetic energy.
Inputs and what they mean
The scattering angle (θ, in degrees) is the only input required for the wavelength shift — it can range from 0° (photon undeflected, no shift) to 180° (photon scattered straight back, maximum shift). The initial wavelength (in nanometers) is needed only to compute the actual scattered wavelength and energy change; it has no effect on Δλ itself. Compton scattering is most significant for short-wavelength, high-energy photons — X-rays (roughly 0.01–10 nm) and gamma rays — because the fixed 2.426 pm shift is a large fraction of their wavelength. For visible light (hundreds of nanometers), the same absolute shift is utterly negligible.
Limits and edge cases
This calculator assumes the target electron is free and initially at rest, which is an excellent approximation for outer-shell (loosely bound) electrons struck by X-ray or gamma-ray photons whose energy far exceeds the electron's binding energy. For photons scattering off tightly bound inner-shell electrons, or for very low photon energies, the electron's binding energy modifies the result and a full quantum treatment is needed. The formula also does not account for multiple scattering events, Doppler broadening from the electron's initial momentum distribution, or relativistic effects on the electron beyond simple energy-momentum conservation. For angles outside 0°–180°, the calculator flags the input as out of range, since scattering angle is defined only within that interval.