2.42631
pm
73.12631
pm
17.536662
keV
16.9548
keV
0.581861
keV
0.034318
2.42631
pm
73.12631
pm
17.536662
keV
16.9548
keV
0.581861
keV
0.034318
The Compton Scattering Calculator computes the wavelength shift and energy change of an X-ray or gamma-ray photon scattered by a free electron. Arthur Compton discovered this effect in 1923 and received the 1927 Nobel Prize in Physics for demonstrating it, providing definitive proof that light behaves as a particle (photon) carrying both energy and momentum.
When a high-energy photon collides with an electron, it transfers some of its energy and momentum to the electron, emerging with a longer wavelength (lower energy) at a different angle. Classical wave theory predicted no wavelength change, only a change in intensity. The observed wavelength shift depended only on the scattering angle, not on the photon's initial wavelength — a result explicable only by treating the photon as a particle with momentum p = h/lambda.
The Compton wavelength shift is given by delta_lambda = (h / m_e * c) * (1 - cos(theta)), where h/(m_e*c) = 2.426 pm is the Compton wavelength of the electron. At 90 degrees the shift is exactly one Compton wavelength (2.426 pm). At 180 degrees (backscatter) the maximum shift is 4.852 pm.
Compton scattering is the dominant X-ray interaction mechanism in human tissue for photon energies between about 100 keV and 10 MeV, which is the range used in radiation therapy, CT scanning, and nuclear medicine. Understanding it is essential for radiation dosimetry, medical imaging physics, and shielding design.
The Compton effect also plays roles in astrophysics: inverse Compton scattering (energetic electrons transferring energy to low-energy photons) boosts microwave background photons to X-ray energies in galaxy clusters (Sunyaev-Zeldovich effect) and powers high-energy emission from active galactic nuclei.
The Compton formula is delta_lambda = lambda_C * (1 - cos(theta)), where lambda_C = h/(m_e*c) = 2.426 pm is the electron Compton wavelength and theta is the photon scattering angle. The scattered wavelength is lambda_f = lambda_i + delta_lambda. Photon energies are computed as E = hc/lambda, using hc = 1239.8 keV·pm.
The wavelength shift ranges from 0 (forward scatter, theta=0) to 4.852 pm (backscatter, theta=180 degrees). For low-energy X-rays (long wavelength) the fractional shift is small and energy loss is small. For hard X-rays and gamma rays (short wavelength) the relative energy loss to the electron is significant. The recoil electron carries the energy difference.
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Results
A 17.5 keV X-ray scattered at 90 degrees shifts wavelength by 2.426 pm (one Compton wavelength) and loses about 0.6 keV to the recoil electron.
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Results
A 124 keV gamma ray backscattered at 180 degrees loses about 40 keV to the electron. This is the maximum possible Compton energy transfer.
The Compton wavelength of the electron is lambda_C = h/(m_e*c) = 2.426 pm. It sets the scale of the wavelength shift in Compton scattering and appears in quantum field theory as the length scale below which quantum effects dominate over relativistic effects.
The photon transfers energy and momentum to the electron. Since photon energy E = hc/lambda, a lower-energy scattered photon has a longer wavelength.
The maximum shift occurs at theta = 180 degrees (backscatter): delta_lambda_max = 2 * lambda_C = 4.852 pm.
In the photoelectric effect the photon is completely absorbed and an electron ejected. In Compton scattering the photon is only partially absorbed — it scatters with reduced energy while the electron recoils.
In tissue/water, Compton scattering dominates from about 100 keV to 10 MeV. Below this range photoelectric effect dominates; above it pair production takes over.
When a relativistic electron collides with a low-energy photon, the electron gives energy to the photon (inverse process). This can boost microwave photons to X-ray energies and is important in astrophysics.
Yes, but the fractional wavelength shift is negligible because visible light wavelengths (~500 nm) are much larger than lambda_C (0.0024 nm). The effect is only detectable for X-rays and gamma rays.
It proved the photon is a real particle with momentum p = h/lambda, not just a wave. Classical electromagnetism could not explain the observed wavelength shift, but treating photons as particles and applying conservation of energy and momentum did.
The kinetic energy of the recoil electron equals the energy lost by the photon: KE_e = E_initial - E_final = hc/lambda_i - hc/lambda_f.
Yes. CT uses X-rays at 80-140 kVp where Compton scattering in tissue is a major interaction. Scattered photons degrade image contrast and contribute to patient dose outside the primary beam.
Roboculator Team
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