# Compton Scattering Calculator Δλ = (h/m_e·c)(1 − cos θ) for X-ray photons: Compton wavelength, shifted wavelength/energy, recoil electron energy and angle, 0°/180° edge cases. > Canonical page: https://elysiatools.com/en/tools/compton-scattering-calculator - **Category:** Science & Education - **Keywords:** compton scattering, compton wavelength, x-ray, photon electron collision, recoil electron, quantum mechanics, modern physics ## Overview The Compton Scattering Calculator computes the quantum wavelength shift, scattered photon energy, and recoil electron kinematics when high-energy photons collide with stationary electrons. By evaluating the fundamental equation Δλ = (h/m_e·c)(1 − cos θ), it provides instant conversions across picometers, Ångströms, and nanometers alongside full relativistic energy transfers. ## Inputs - **Incident wavelength λ** (number): e.g. 71 - **λ unit** (select) - **Scattering angle θ (degrees)** (number): e.g. 90 ## When to use - Analyzing X-ray or gamma-ray scattering off electrons in modern physics coursework and laboratory experiments. - Determining photon energy loss and recoil electron trajectories at specific detector angles between 0° and 180°. - Evaluating backscattering limits and edge cases for radiation shielding or detector calibration. ## How it works - Enter the incident photon wavelength and select the measurement unit (pm, Å, or nm). - Specify the photon scattering angle θ in degrees (ranging from 0° forward transmission to 180° backscattering). - Calculate the shifted wavelength, scattered photon energy in keV/eV, electron recoil kinetic energy, and recoil angle. ## Use cases - Verifying quantum scattering equations in modern physics and quantum mechanics problem sets. - Predicting detector photon energy peaks in X-ray spectroscopy and Compton camera setups. - Modeling secondary radiation spectra and electron recoil angles for medical physics dosimetry. ## Frequently asked questions ### What is the electron Compton wavelength? The electron Compton wavelength λ_C = h/(m_e·c) is approximately 2.42631 pm (0.02426 Å). ### What happens at a scattering angle of 0°? At θ = 0°, cos θ = 1, resulting in zero wavelength shift and no kinetic energy transferred to the electron. ### What produces the maximum Compton shift? Maximum shift occurs at θ = 180° (backscattering), where Δλ = 2λ_C ≈ 4.85262 pm. ### Does the wavelength shift depend on incident photon energy? No, the wavelength shift Δλ depends only on the scattering angle θ and fundamental physical constants. ### How is the recoil electron kinetic energy determined? 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