Compton Scattering Calculator
Calculate the final wavelength of an X-ray or gamma-ray photon after it scatters off an electron at a given angle. Used in nuclear physics and medical imaging to quantify energy loss during photon–electron collisions.
About this calculator
Compton scattering occurs when a high-energy photon collides with a loosely bound (essentially free) electron and transfers part of its energy to the electron, emerging at a longer wavelength. The wavelength shift is given by Δλ = λ_C (1 − cos θ), where λ_C = h / (m_e c) ≈ 2.426 × 10⁻¹² m is the Compton wavelength of the electron, and θ is the scattering angle. The final wavelength is therefore λ_f = λ_i + 2.426 × 10⁻¹² × (1 − cos θ). The shift is independent of the initial photon energy — it depends only on the scattering angle. Maximum shift (Δλ = 2λ_C ≈ 4.85 pm) occurs at θ = 180° (backscattering). Compton's 1923 discovery of this shift provided direct experimental proof of the photon's particle nature.
How to use
An X-ray photon with initial wavelength λ_i = 0.071 nm = 7.1 × 10⁻¹¹ m scatters at θ = 90°. Enter initial_wavelength = 7.1 × 10⁻¹¹ m and scattering_angle = 90°. cos(90°) = 0, so the shift = 2.426 × 10⁻¹² × (1 − 0) = 2.426 × 10⁻¹² m. Final wavelength = 7.1 × 10⁻¹¹ + 2.426 × 10⁻¹² = 7.343 × 10⁻¹¹ m ≈ 0.0734 nm. The photon's wavelength increased by about 3.4%, meaning it lost that fraction of its energy to the recoiling electron.
Frequently asked questions
Why does Compton scattering only matter for high-energy photons like X-rays and not for visible light?
The Compton wavelength shift (up to ~4.85 pm) is fixed regardless of the initial photon energy. For visible light with wavelengths around 500 nm, a 5 pm shift is less than 0.001% — completely undetectable. For X-rays with wavelengths of ~0.1 nm, the same shift represents several percent, which is measurable and physically significant. This is why Compton scattering is relevant in X-ray and gamma-ray physics but irrelevant in optics. At low energies, Thomson scattering (elastic, no wavelength shift) dominates instead.
What is the Compton wavelength and what does it represent physically?
The Compton wavelength λ_C = h / (m_e c) ≈ 2.426 × 10⁻¹² m is a characteristic length scale for the electron derived from its rest mass. Physically, it represents the wavelength of a photon whose energy equals the rest-mass energy of the electron (m_e c²). When a photon's wavelength approaches or falls below λ_C, quantum relativistic effects — including Compton scattering and pair production — become important. It sets the boundary between classical electromagnetic scattering and genuinely quantum mechanical photon–electron interactions.
How does Compton scattering affect medical imaging techniques like CT and PET scans?
In CT and PET scanners, photons passing through tissue undergo Compton scattering, which degrades image quality by redirecting photons away from their original paths and creating scattered radiation at the detector. Scattered photons that still reach the detector carry false positional information, reducing contrast and spatial resolution. Anti-scatter grids and software correction algorithms are used to mitigate this effect. Understanding the angular and energy distribution of Compton-scattered photons is essential for designing detector geometries and improving the diagnostic accuracy of high-energy medical imaging systems.