Compton Scattering Calculator
When an X-ray photon collides with an electron, the photon loses part of its energy and its wavelength increases by Δλ = λc(1 − cos θ) — θ is the scattering angle, λc the Compton wavelength of the target particle. This calculator uses CODATA 2018 (NIST) constants and runs 100% in the browser.
Valid only when 0 ≤ Δλ ≤ 2λc = 4.8526 pm (electron).
E′ = E / (1 + (E/mec²)(1 − cos θ)), with mec² = 510,998.95 eV (CODATA 2018).
Verified examples
Frequently asked questions
What is Compton scattering?
Compton scattering is the collision of an X-ray or gamma photon with an electron (treated as free and at rest). The incoming photon loses part of its energy to the electron, so its wavelength increases by Δλ = λc(1 − cos θ). Discovered by Arthur Compton in 1923, it was direct evidence of the particle nature of light.
What is the Compton wavelength of the electron?
λc = h/(mec) = 2.42631023867×10⁻¹² m = 2.4263 pm, per CODATA 2018 (NIST). This is not a directly measurable wavelength but a characteristic scale: at a 90° scattering angle the shift is exactly λc.
When is the Compton shift maximal?
At θ = 180° (backscatter, the photon bounces back), Δλ = 2λc = 4.8526 pm for the electron. At θ = 0° (the photon continues straight) the shift is zero — no effective collision.
How do I calculate the scattering angle from a measured shift?
Invert the formula: θ = arccos(1 − Δλ/λc). The result is valid only when 0 ≤ Δλ ≤ 2λc; outside that range no physical angle fits (the second tab of this calculator rejects it).
How do I calculate the scattered photon energy?
E′ = E / (1 + (E/mec²)(1 − cos θ)), with the electron rest energy mec² = 510,998.95 eV (CODATA 2018). The difference E − E′ is the kinetic energy of the recoil electron. Example: a 1 MeV photon at 90° becomes 338.19 keV.
Why are the units picometers (pm)?
Because the electron λc = 2.4263 pm and typical X-rays have wavelengths of 10–100 pm, making the Compton shift significant and measurable. For visible light (400–700 nm), a 2.4 pm shift is a million times smaller than its wavelength — practically unobservable.
Does this formula apply to the proton?
Yes, with the proton λc = h/(mpc) = 1.32141 fm — about 1836× smaller than the electron. Because the shift is so tiny, Compton scattering off protons is practically unobservable; the fourth tab of this calculator computes λc for the electron, proton, neutron, or a custom mass.
How does it differ from the photoelectric effect?
In the photoelectric effect, the photon is fully absorbed by a bound electron (Ek = hν − φ). In Compton scattering, the photon only loses part of its energy when scattering off an electron treated as free. The photoelectric effect dominates at low photon energies; Compton dominates at medium energies.
How does it differ from Bragg diffraction?
Bragg law (nλ = 2d·sinθ) explains X-ray diffraction by crystal planes — the photon wavelength does not change. Compton scattering is a photon-electron collision — the photon wavelength increases. Both use X-rays, but the physics differs.
When does the Compton effect dominate photon-matter interaction?
For medium-energy photons (about 0.1–10 MeV in light matter such as water or tissue). At lower energies the photoelectric effect dominates; above 1.022 MeV, electron-positron pair production starts to compete.
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