Calculate wavelength shift, scattered photon energy, and recoil kinetic energy for Compton scattering off electrons, protons, or muons.
Compton scattering is the inelastic scattering of a photon by a charged particle, usually an electron. Discovered by Arthur Holly Compton in 1923, the effect provided direct evidence that electromagnetic radiation has particle-like properties — a cornerstone of quantum mechanics. When a high-energy photon (X-ray or gamma ray) strikes a free or loosely bound electron, it transfers part of its energy and momentum to the electron and continues in a different direction with a longer wavelength.
The wavelength shift depends only on the scattering angle and the mass of the target particle, not on the incident photon wavelength. This shift is described by the Compton formula: Δλ = (h/mc)(1 − cos θ), where h/mc is the Compton wavelength of the target. For electrons, the Compton wavelength is about 2.43 pm, making the effect most noticeable for X-ray and gamma-ray photons whose wavelengths are comparable.
This calculator computes the wavelength shift, scattered and recoil energies, and the recoil angle for photon scattering off electrons, protons, or muons. An angular scan table shows how these quantities vary from forward to back-scattering, providing a complete picture of the Compton effect for any incident photon energy.
Compton scattering calculations are essential in X-ray physics, radiation therapy, nuclear engineering, and astrophysics. This calculator instantly provides wavelength shifts, energy transfers, and angular distributions — saving significant time compared to manual computation. The angular scan table is particularly useful for designing scattering experiments or understanding detector response. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain.
Compton Scattering Formula: • Wavelength shift: Δλ = (h / mc)(1 − cos θ) • Compton wavelength: λ_C = h / (mc) ≈ 2.426 pm (electron) • Scattered wavelength: λ' = λ + Δλ • Photon energy: E = hc / λ • Recoil energy: K = E − E' = E − hc / λ' • Recoil angle: cot φ = (1 + E/mc²) tan(θ/2)
Result: Δλ = 2.426 pm, E_recoil = 0.588 keV
A 0.071 nm X-ray photon scattered at 90° gains 2.426 pm in wavelength (one Compton wavelength). The electron recoils with about 0.588 keV of kinetic energy.
Arthur Compton's 1923 experiment with molybdenum X-rays scattered off graphite was pivotal in establishing that photons carry momentum p = h/λ. Classical wave theory predicted no wavelength change upon scattering (Thomson scattering), but Compton observed a systematic, angle-dependent shift that perfectly matched his quantum calculation treating the photon as a relativistic particle colliding with an electron.
In medical imaging, Compton scatter is both a source of image noise (scatter artifacts in CT and SPECT) and a useful signal in Compton cameras that reconstruct gamma-ray source positions. In industrial radiography, understanding the energy spectrum of Compton-scattered photons helps design collimators and shielding. In astrophysics, inverse Compton scattering — where high-energy electrons boost low-energy photons to X-ray or gamma-ray energies — is responsible for much of the high-energy emission from quasars and galaxy clusters.
The full quantum electrodynamic treatment by Klein and Nishina (1929) gives the differential cross section for Compton scattering, which reduces to the classical Thomson cross section at low energies and shows strong forward-peaking at high energies. This cross section is essential for Monte Carlo radiation transport codes used in reactor physics and medical physics.
Compton scattering is the scattering of a photon by a charged particle (typically an electron) where the photon loses energy and emerges with a longer wavelength. It provided key evidence for the particle nature of light.
The Compton formula Δλ = (h/mc)(1−cos θ) is independent of the incident wavelength because it arises from relativistic energy-momentum conservation. The shift is a fixed quantity determined solely by the scattering geometry and target mass.
The Compton wavelength λ_C = h/(mc) is the characteristic wavelength at which quantum effects become significant for a particle. For an electron it is about 2.426 pm, for a proton about 1.32 fm.
In principle yes, but the wavelength shift (≈ 2.4 pm) is negligible compared to visible light wavelengths (400–700 nm). The effect is only measurable with X-rays or gamma rays.
At 0° (forward scattering) there is no wavelength shift. At 180° (back-scattering) the shift is maximum at 2λ_C, and the photon loses the most energy to the recoiling particle.
It is used in Compton cameras for medical imaging, in gamma-ray telescopes, in radiation shielding design, and as a calibration tool in X-ray spectroscopy. Use this as a practical reminder before finalizing the result.