Last updated: 2026-06-16

Compton Scattering

Compton scattering is the increase in a photon’s wavelength when it collides with an electron. A high-energy photon — an X-ray or gamma ray — strikes a loosely bound electron, transfers some of its energy and momentum, and emerges deflected and with a longer wavelength. Arthur Compton measured the effect in 1923, providing decisive evidence that light carries momentum and behaves as a particle.

This calculator takes the scattering angle $\theta$ and the incident wavelength $\lambda$, and returns the wavelength shift $\Delta\lambda$ and the scattered wavelength $\lambda'$.

How Compton scattering works

Treating the photon as a particle with energy $E = hc/\lambda$ and momentum $p = h/\lambda$, the collision conserves both energy and momentum just like two billiard balls. The electron recoils, carrying away energy, so the photon must lose energy. Since lower energy means a longer wavelength, the scattered photon is always redshifted relative to the incident one.

Formula

The shift depends only on the angle and the electron’s Compton wavelength, never on the incident wavelength.

Worked example

An X-ray of wavelength $\lambda = 10\ \text{pm}$ scatters at $\theta = 90^\circ$.

Step 1 — wavelength shift:

Step 2 — scattered wavelength:

The deflected photon is longer by one Compton wavelength, having handed the difference in energy to the recoiling electron.

Shift at different angles

Forward scattering produces no shift, while direct backscatter at 180° gives the maximum, twice the Compton wavelength.

Real-world relevance

Compton scattering is central to radiation physics. It is the dominant way X-rays and gamma rays interact with tissue in the energy range used for medical imaging and radiotherapy, and it governs shielding design for nuclear facilities. Gamma-ray telescopes and Compton cameras use the angle–wavelength relationship to reconstruct the direction of incoming high-energy photons.

Limitation

This calculator assumes scattering from a free or loosely bound electron initially at rest. Binding energy, electron motion and scattering from nuclei introduce small corrections, and at very high energies pair production competes with Compton scattering. For typical X-ray and gamma-ray problems the simple formula is accurate.