Compton Scattering Calculator

How Compton Scattering Works?

The Compton Scattering Calculator models the interaction between an incoming photon and a stationary electron. When the photon scatters through an angle $\theta$, it transfers part of its energy and momentum to the electron. The photon therefore leaves with a longer wavelength and lower energy.

The wavelength increase is determined by the Compton wavelength of the electron and the scattering geometry:

Here, $h$ is Planck's constant, $m_e$ is the electron rest mass, $c$ is the speed of light, and $\theta$ is the angle between the incident and scattered photon directions. The scattered wavelength is the incident wavelength plus this shift:

The photon energy and frequency follow from its wavelength. The calculator uses the photon energy relation $E=hf=\frac{h}{c}\lambda$ and the frequency relation:

Consequently, the incident and scattered photon energies are calculated as:

Energy conservation gives the electron's recoil kinetic energy as the energy lost by the photon. The percentage transferred is:

Photon momentum is $p=\frac{h}{\lambda }$. Applying momentum conservation to the incident and scattered photon vectors gives the electron recoil momentum:

Finally, the recoil direction relative to the original photon direction is obtained from the vector components:

Practical Use Cases

Physics students can enter an incident wavelength and scattering angle to verify textbook Compton-effect calculations, compare photon energies before and after scattering, and observe how the electron's recoil energy changes with geometry.

Radiation and medical-imaging researchers can estimate the energy retained by a scattered photon and the energy transferred to an electron, which helps when studying scatter contributions in photon-based imaging and detection systems.

Astrophysics students and researchers can use the calculator to examine wavelength and frequency changes in high-energy photon interactions, including how different scattering angles affect the observed photon energy.

Particle and nuclear physics learners can calculate the recoil momentum and direction of the electron while applying energy and momentum conservation to photon-electron collisions.

Laboratory instructors can use selected wavelengths and angles to prepare demonstrations, compare measured scattering results with the ideal free-electron prediction, and illustrate the relationship between photon wavelength, energy, and frequency.

Accuracy and Limitations

The calculator uses the ideal Compton-scattering model for a photon interacting with a stationary, free electron, with the wavelength shift determined by $h/\left(m_{e}c\right)$ and photon energies calculated from $E=hc/\lambda$. Results are mathematically precise within the selected input range, but real materials can introduce electron binding effects, multiple scattering, detector resolution, and Doppler broadening from electron motion. The model does not account for material composition, electron momentum distribution, absorption, or polarization-dependent cross sections, so it is most suitable for single-scattering theoretical estimates.

Quick Examples