Compton Scattering Calculator

Compton scattering describes how high-energy photons lose energy and increase in wavelength when they bounce off charged particles. The fundamental formula governing this phenomenon is expressed as delta_wavelength = (h / (m * c)) * (1 - cos(theta)), where h is Planck's constant, m is the mass of the scattering particle, c is the speed of light in a vacuum, and theta is the scattering angle. The term (h / (m * c)) is known as the Compton wavelength of the particle. As the scattering angle approaches 180 degrees, the wavelength shift reaches its absolute maximum.

Consider an X-ray photon colliding with a stationary electron (mass m = 9.109 x 10^-31 kg) and scattering at an angle of 60 degrees. First, evaluate the Compton wavelength constant: h / (m * c) evaluates to approximately 2.43 x 10^-12 meters or 2.43 picometers. Next, calculate the angular factor: 1 - cos(60 degrees) = 1 - 0.5 = 0.5. Multiplying these together yields a wavelength shift of delta_wavelength = 2.43 x 10^-12 * 0.5 = 1.215 x 10^-12 meters, meaning the scattered photon emerges with a wavelength 1.215 picometers longer than its initial state.

Always ensure your angles are set to the correct units—degrees or radians—depending on your workspace requirements. When substituting mass values for particles other than electrons, such as protons or muons, make sure to use exact kilogram measurements to maintain precision. Keep in mind that Compton scattering is most pronounced for high-frequency electromagnetic radiation like X-rays and gamma rays, whereas visible light experiences negligible relative wavelength shifts.