Compton scattering calculator
Enter the wavelength of the incoming photon in picometres, or its energy in keV, and the angle through which it is scattered. The calculator gives the Compton shift, the new wavelength and energy of the photon and how much energy the recoiling electron carries away.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Give the incoming photon as a wavelength in pm or an energy in keV.
- Enter the scattering angle: 0° means no deflection, 180° straight back.
- Read the shift, the scattered wavelength and energy and the electron’s energy.
- Compton shift: Δλ = λc (1 − cos θ), λc = 2.42631023867 pm
- Scattered wavelength: λ′ = λ + Δλ
- Photon energy: E (keV) = 1239.84198 ÷ λ (pm)
- Electron recoil energy: K = E − E′
- Equivalent energy form: E′ = E ÷ (1 + (E ÷ 510.999 keV)(1 − cos θ))
Worked example
X-rays of 71 pm scattered through 90°: cos 90° = 0, so Δλ = 2.42631 pm and λ′ = 73.42631 pm. The photon energy drops from 17.463 keV to 16.886 keV; the electron takes 0.577 keV, 3.3 % of the energy.
A 662 keV gamma photon scattered by 60°: λ = 1239.84198 ÷ 662 = 1.87287 pm, Δλ = 2.42631 × 0.5 = 1.21316 pm, λ′ = 3.08603 pm, E′ = 401.76 keV; the electron gets 260.24 keV (39.31 %).
Tips
- The largest shift is at 180°, twice λc. That backscatter edge shows up in gamma-ray spectra.
- High-energy photons lose a larger share. The fixed shift matters more when λ is already tiny.
- Electrons are treated as free and at rest, which works well when the photon energy is far above the binding energy.
Frequently asked questions
What is the Compton formula?
Δλ = λ′ − λ = λc × (1 − cos θ), where λc = h ÷ (mₑ c) = 2.42631 pm is the Compton wavelength of the electron and θ the scattering angle of the photon.
Does the shift depend on the incoming wavelength?
No. At 90° every photon gains 2.42631 pm and at 180° 4.85262 pm. That is a large change for hard X-rays and gamma rays but invisible for light, whose wavelength is hundreds of thousands of picometres.
How much energy does the electron get?
The difference between the photon energies before and after, E − E′, where E (keV) = 1239.84 ÷ λ (pm). A 662 keV gamma ray scattered by 60° keeps 401.76 keV and the electron gets 260.24 keV.
Why was Compton scattering important?
The shift cannot be explained by waves alone. It follows from treating light as photons with momentum h ÷ λ that collide with electrons, and it helped establish the photon picture.