Compton Scattering
Calculate Compton scattering wavelength shift Δλ = h/(mc)(1−cosθ) for any particle mass and angle. Free online quantum mechanics calculator with photon energy loss, scattered wavelength, and interactive charts.
About This Calculator
What is Compton Scattering?
Compton scattering is a fundamental quantum phenomenon where a photon (X-ray or gamma ray) scatters inelastically off a charged particle — typically a free or weakly bound electron. The photon transfers part of its energy to the electron, resulting in a scattered photon with a longer wavelength (lower energy). The Compton scattering calculator computes this wavelength shift using the formula Δλ = h/(mc)(1 − cosθ), where h is Planck's constant, m is the particle mass, c is the speed of light, and θ is the scattering angle. This effect, discovered by Arthur Holly Compton in 1923, earned him the Nobel Prize in Physics in 1927 and provided some of the first direct evidence for the particle (photon) nature of electromagnetic radiation.
Methodology and Formula
The calculator uses the standard Compton scattering equation: Δλ = λ′ − λ = h/(mₑc) × (1 − cosθ). The term h/(mₑc) is known as the Compton wavelength of the target particle — approximately 2.426 × 10⁻¹² m (2.426 pm) for an electron. The wavelength shift is zero at θ = 0°, reaches one Compton wavelength at θ = 90°, and peaks at two Compton wavelengths at θ = 180° (backscattering). When an initial wavelength is provided, the calculator also determines the scattered wavelength λ′ = λ + Δλ and computes photon energies using E = hc/λ, with results in keV for the incident photon, scattered photon, and the energy loss.
Applications
Compton scattering has numerous practical applications. In medical physics, it is the dominant interaction mechanism for X-ray imaging and radiation therapy dosimetry. In material science, Compton profilometry uses the energy broadening to study electron momentum distributions in solids. In astrophysics, the Sunyaev-Zel'dovich effect — where cosmic microwave background photons scatter off hot electrons in galaxy clusters — is a cosmological application of inverse Compton scattering. Radiation shielding calculations also account for Compton scattering when designing protection around nuclear reactors and medical linear accelerators.
Frequently Asked Questions
What is Compton scattering?
Compton scattering is the inelastic scattering of a photon by a charged particle, usually an electron. When a high-energy photon (like X-ray or gamma ray) collides with a free or weakly bound electron, it transfers some of its energy to the electron, resulting in a longer wavelength (lower energy) scattered photon. This phenomenon, discovered by Arthur Compton in 1923, provided crucial evidence for the particle nature of light.
What is the Compton scattering formula?
The Compton scattering formula is Δλ = h/(mₑc) × (1 − cosθ), where Δλ is the wavelength shift, h is Planck's constant (6.626×10⁻³⁴ J·s), mₑ is the electron rest mass (9.109×10⁻³¹ kg), c is the speed of light (3×10⁸ m/s), and θ is the scattering angle. The quantity h/(mₑc) is the Compton wavelength of the electron, approximately 2.426 pm.
Why is Compton scattering important?
Compton scattering is important because it confirmed the particle nature of light (photon concept), providing direct evidence for quantum theory. It is widely used in medical imaging (X-ray and gamma-ray diagnostics), material science (Compton profilometry to study electron momentum distributions), radiation shielding calculations, and astrophysics (studying high-energy phenomena in space).
At what angle is the maximum wavelength shift in Compton scattering?
The maximum wavelength shift occurs at a scattering angle of 180° (backscattering), where cos(180°) = −1, giving Δλ_max = 2h/(mₑc), which equals twice the Compton wavelength of the electron (about 4.852 pm). At θ = 0°, there is no shift (the photon passes undeflected), and at θ = 90°, the shift equals exactly one Compton wavelength.
Can Compton scattering happen with particles other than electrons?
Yes, Compton scattering can occur with any charged particle, including protons, muons, and even whole atoms. However, the Compton wavelength is inversely proportional to the particle mass, so for heavier particles (like protons, which are about 1836 times heavier than electrons), the wavelength shift is negligible. That is why Compton scattering is most significant for electrons.
How do I use the Compton scattering calculator?
Enter the particle mass in kilograms (default is the electron mass 9.109×10⁻³¹ kg) and the scattering angle in degrees (0° to 180°). Optionally, enter an initial wavelength in picometers to compute the scattered wavelength and photon energy loss. Click Calculate to see the Compton wavelength, wavelength shift Δλ, and if initial wavelength is provided, the scattered wavelength, incident and scattered photon energies in keV, and energy loss.
What is the unit of the Compton wavelength?
The Compton wavelength is expressed in picometers (pm) for subatomic particles. For an electron, the Compton wavelength is approximately 2.426 pm (2.426 × 10⁻¹² m). For heavier particles like protons, it is about 1.321 fm (femtometers, 10⁻¹⁵ m), which is roughly 1836 times smaller than the electron's Compton wavelength.
Does Compton scattering affect visible light?
Compton scattering has a negligible effect on visible light because the wavelength shift (a few picometers) is extremely small compared to visible light wavelengths (400-700 nm, or 4×10⁵ to 7×10⁵ pm). The fractional change is about 0.0003% for visible light. However, for X-rays (10-100 pm) and gamma rays, the shift represents a significant fraction of the initial wavelength, making Compton scattering readily observable.