Compton Scattering Calculator
Energy and wavelength of a photon after bouncing off an electron, the energy the electron takes, and the Compton edge and backscatter peak of a gamma line.
Results
The dashed line marks the value you entered.
What this tool does
Arthur Compton's 1923 experiment showed X-rays bouncing off electrons as if they were particles: the scattered photon comes out with less energy, and the loss depends only on the angle. The wavelength shift can never exceed twice the Compton wavelength, about 4.85 pm, so it is invisible for light but large for gamma rays. That is where the Compton edge and the backscatter peak in a gamma spectrum come from — for the 662 keV line of caesium-137 they sit near 478 keV and 184 keV. The formula assumes a free electron at rest.
Formula
Δλ = (h ÷ mₑc)(1 − cos θ) · E′ = E ÷ (1 + (E ÷ mₑc²)(1 − cos θ)), mₑc² = 510.999 keV
Variables
| Symbol | Meaning | Unit |
|---|---|---|
en | Photon energy | keV |
th | Scattering angle | ° |
EP | Energy of the scattered photon | keV |
KE | Energy given to the electron | keV |
DL | Wavelength shift | pm |
W0 | Wavelength of the incoming photon | pm |
CE | Compton edge (most the electron can get) | keV |
BS | Backscatter peak (photon at 180°) | keV |
Worked example
- Photon energy662 keV
- Scattering angle90 °
- Energy of the scattered photon288.39 keV
- Energy given to the electron373.61 keV
- Wavelength shift2.4263 pm
- Wavelength of the incoming photon1.8729 pm
- Compton edge (most the electron can get)477.65 keV
- Backscatter peak (photon at 180°)184.35 keV
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.