Compton Scattering Calculator

Compton scattering is an inelastic interaction between a high-energy photon (typically X-ray or gamma-ray) and a loosely bound or free charged particle, usually an electron. During the collision, the photon transfers some of its energy to the electron, causing the photon's wavelength to increase and its direction to change. This effect confirmed the particle-like nature of light (photons).

The Compton wavelength shift is given by Δλ = (h / mₑc)(1 − cos θ), where h is Planck's constant (6.626 × 10⁻³⁴ J·s), mₑ is the electron rest mass (9.109 × 10⁻³¹ kg), c is the speed of light (3 × 10⁸ m/s), and θ is the scattering angle. The factor h/(mₑc) ≈ 2.426 pm is known as the Compton wavelength of the electron.

The Compton wavelength of the electron is λ_C = h/(mₑc) ≈ 2.42631 pm (picometers). This constant sets the maximum possible wavelength shift, which occurs at θ = 180° (backscattering), giving Δλ_max = 2 × λ_C ≈ 4.853 pm.

At θ = 0°, cos(0°) = 1, so Δλ = 0 — there is no wavelength shift and the photon continues in its original direction unchanged. At θ = 180° (backscattering), cos(180°) = −1, so Δλ = 2h/(mₑc) ≈ 4.853 pm, which is the maximum possible wavelength shift for Compton scattering off a free electron.

Yes. The Compton scattering formula applies to any free charged particle. For a proton or heavier particle, the Compton wavelength is much smaller (since λ_C = h/mc and m is larger), meaning the wavelength shift is negligible. Compton scattering is most significant for electrons because of their small mass.

Thomson scattering is an elastic process (no energy transfer) applicable to low-energy photons — the photon wavelength does not change. Rayleigh scattering involves photons scattering off whole atoms or molecules with negligible energy transfer. Compton scattering is inelastic and occurs at higher photon energies (X-ray and gamma-ray), resulting in a measurable wavelength increase and electron recoil.

Energy is conserved in the collision. The photon transfers part of its kinetic energy to the recoiling electron. Since photon energy E = hc/λ, a lower energy corresponds to a longer wavelength. The scattered photon therefore always has a longer wavelength (lower energy) than the incident photon, and the energy difference appears as kinetic energy of the recoiling electron.

This calculator accepts the incident wavelength in picometers (pm), nanometers (nm), or meters (m). X-ray photons commonly used in Compton scattering experiments have wavelengths on the order of 0.01–0.1 nm (10–100 pm). You can select your preferred unit from the dropdown, and the calculator converts automatically before computing.