Calculator Inputs
Use energy or wavelength inputs, switch units, and solve for angle-dependent scattering values.
Formula Used
E′ = E₀ / [1 + (E₀ / mec²)(1 − cos θ)]
Ke = E₀ − E′
Δλ = λC(1 − cos θ)
cos θ = 1 − mec²(1/E′ − 1/E₀)
This page uses mec² = 510.99895 keV, λC = 2.42631023867 pm, and hc = 1239.841984 keV·pm.
When you enter wavelength, the calculator first converts it into photon energy, then applies the same Compton relations.
How to Use This Calculator
- Select a calculation mode based on the values you already know.
- Enter the initial photon energy or initial wavelength.
- Add the scattering angle, or provide scattered photon energy when solving for angle.
- Choose output energy units, decimal precision, and graph density.
- Press Calculate to show the result above the form and in the detailed report section.
- Review the graph to see how scattered energy and recoil energy vary with angle.
- Use the CSV or PDF buttons to save the result set.
Example Data Table
| Initial Energy (keV) | Angle (deg) | Scattered Energy (keV) | Electron KE (keV) | Wavelength Shift (pm) |
|---|---|---|---|---|
| 100.000 | 30 | 97.445 | 2.555 | 0.325 |
| 200.000 | 45 | 179.431 | 20.569 | 0.711 |
| 500.000 | 90 | 252.720 | 247.280 | 2.426 |
| 662.000 | 120 | 224.922 | 437.078 | 3.639 |
FAQs
1) What does this calculator solve?
It solves Compton scattering relationships between initial photon energy, scattered photon energy, recoil electron kinetic energy, angle, wavelength, and wavelength shift using standard photon-electron interaction equations.
2) Which unit system does the calculator use internally?
The calculator converts all energies to keV, all wavelengths to picometers, and angles to degrees internally. It then converts outputs into your selected display units.
3) Can I calculate angle from energies only?
Yes. Choose the mode using initial energy and scattered photon energy. The tool computes the physically valid scattering angle by rearranging the Compton energy equation.
4) Why must the scattered energy be lower than the initial energy?
In Compton scattering, the photon transfers part of its energy to the recoil electron. That makes the scattered photon energy equal to or lower than the initial value.
5) What happens at zero scattering angle?
At zero degrees, there is no wavelength shift. The scattered photon energy equals the initial energy, and the recoil electron kinetic energy approaches zero.
6) What does the graph show?
The graph plots scattered photon energy and recoil electron kinetic energy across the full angular range. It helps you visualize how energy transfer increases as scattering angle grows.
7) Is this suitable for X-ray and gamma-ray problems?
Yes. Compton scattering is especially important for higher-energy photons such as X-rays and gamma rays interacting with electrons in matter.
8) Why do wavelength and energy modes produce the same physics?
Photon wavelength and photon energy are directly linked through hc. Once wavelength is converted to energy, the same Compton scattering equations apply without changing the underlying physics.