Compton Scattering Calculator Formula
Understand the math behind the compton scattering calculator. Each variable explained with a worked example.
Formulas Used
Wavelength Shift
wavelength_shift = (6.626e-34 / (9.109e-31 * 2.998e8)) * (1 - cos(scattering_angle * pi / 180))Shift (pm)
shift_pm = (6.626e-34 / (9.109e-31 * 2.998e8)) * (1 - cos(scattering_angle * pi / 180)) * 1e12Variables
| Variable | Description | Default |
|---|---|---|
scattering_angle | Scattering Angle(deg) | 90 |
How It Works
Compton Scattering
When a photon scatters off a free electron, its wavelength increases. The shift depends only on the scattering angle.
Formula
delta_lambda = lambda_C * (1 - cos theta)
where lambda_C = h / (m_e c) = 2.426 pm is the Compton wavelength of the electron.
Maximum shift (2 lambda_C = 4.85 pm) occurs at 180 degrees (backscattering).
Worked Example
Photon scattered at 90 degrees.
- 01delta_lambda = lambda_C * (1 - cos 90)
- 02lambda_C = 6.626e-34 / (9.109e-31 * 2.998e8) = 2.426e-12 m
- 03cos(90) = 0
- 04delta_lambda = 2.426e-12 * (1 - 0) = 2.426 pm
Frequently Asked Questions
Does the shift depend on the initial photon energy?
No. The wavelength shift depends only on the scattering angle. However, the fractional energy change is larger for higher-energy (shorter-wavelength) photons.
Why was Compton scattering important historically?
It provided direct evidence that photons carry momentum, confirming the particle nature of light and earning Arthur Compton the 1927 Nobel Prize.
Does Compton scattering occur with protons?
Yes, but the Compton wavelength of the proton is about 1836 times smaller, so the shift is negligible unless the photon energy is very high.
Ready to run the numbers?
Open Compton Scattering Calculator