How's It Work?
The scattering is demonstrated in the picture to the right. A high-energy photon (generally X-ray or gamma-ray) collides with a target, which has loosely-bound electrons on its outer shell. The incident photon has the following energy E and linear momentum p:
E = hc / lambdaThe photon gives part of its energy to one of the almost-free electrons, in the form of kinetic energy, as expected in a particle collision. We know that total energy and linear momentum must be conserved. Analyzing these energy and momentum relationships for the photon and electron, you end up with three equations:
p = E / c
- x-component momentum
- y-component momentum
- phi, the scattering angle of the electron
- theta, the scattering angle of the photon
- Ee, the final energy of the electron
- E', the final energy of the photon
1 / E' - 1 / E = 1/(me c2) * (1 - cos theta)The value h/(me c) is called the Compton wavelength of the electron and has a value of 0.002426 nm (or 2.426 x 10-12 m). This isn't, of course, an actual wavelength, but really a proportionality constant for the wavelength shift.
lambda' - lambda = h/(me c) * (1 - cos theta)
Why Does This Support Photons?
This analysis and derivation is based on a particle perspective and the results are easy to test. Looking at the equation, it becomes clear that the entire shift can be measured purely in terms of the angle at which the photon gets scattered. Everything else on the right side of the equation is a constant. Experiments show that this is the case, giving great support to the photon interpretation of light.