Compton Scattering Calculator
The Compton shift — how much a photon’s wavelength grows when it scatters off an electron at a given angle — with the photon energies before and after and the energy handed to the electron.
A photon carries momentum, so when it bounces off a free electron it gives some up and its wavelength lengthens by λ_C (1 − cos θ), where λ_C = h ÷ (m_e c) = 2.
How the compton scattering calculator works
A photon carries momentum, so when it bounces off a free electron it gives some up and its wavelength lengthens by λ_C (1 − cos θ), where λ_C = h ÷ (m_e c) = 2.426 pm is the Compton wavelength of the electron. The shift depends only on the angle, not on the incoming wavelength — the result that established light’s particle nature in 1923.
Formula: Δλ = (h ÷ m_e c)(1 − cos θ) = 2.426 pm × (1 − cos θ); E = hc ÷ λ
Worked examples
| Inputs | Wavelength shift (pm) | Note |
|---|---|---|
| Compton’s experiment: 71.07 pm at 90° | 2.4263 | 2.4263 pm shift |
| Back-scattering at 180° | 4.8526 | 4.8526 pm |
| 1 pm gamma ray at 60° | 1.2132 | 1.2132 pm — the photon loses over half its energy |
FAQFrequently asked questions
Why does the shift not depend on the incoming wavelength?
Because it comes from momentum conservation between a photon and an electron at rest: the geometry fixes the change in wavelength, and the Compton wavelength sets its scale. The fractional change is therefore large for X-rays and gamma rays and negligible for visible light.
What is the maximum shift?
At 180° — back-scattering — the shift is 2 λ_C, about 4.85 pm. At 90° it is exactly one Compton wavelength, 2.43 pm.
Why did Compton use molybdenum X-rays?
Their 71 pm wavelength is comparable to the Compton wavelength, so a shift of a few picometers was measurable with a crystal spectrometer. With visible light (500,000 pm) the same shift would be invisible.
What about bound electrons?
Tightly bound electrons recoil with the whole atom, giving essentially no shift — the unshifted line seen alongside the Compton peak. Loosely bound outer electrons behave as free ones.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.