COMPTON SCATTERING FORMULA

As we all know, light is made up of particles called photons, and it has momentum which can be seen when a photon with high energy collides with a stationary electron. Some of the energy and momentum are transferred to the electron (known as the Compton effect), but both momentum and energy are conserved in this elastic collision. After the collision, the photon has energy hf^/ and the electron has acquired a kinetic energy K. 

Conservation of energy: hf = hf/ + K

Combining this with the momentum conservation equations, it can be shown that the wavelength of the outgoing photon is related to the wavelength of the incident photon by the equation:

Δλ = λ/ - λ = (h/mec) (1 - cosθ)

h = Planck's Constant = 6.62x10-34m2kg/s

me = Mass of electron = 9.11x10-31kg

c = Speed of light = 3x108m/s

The collision causes the photon wavelength to increase by somewhere between 0 (for a scattering angle of 0°) and twice the Compton wavelength (for a scattering angle of 180°).

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