Question

In Compton scattering, the wavelength of the scattered photon is a function of the wavelength of the incident photon and the angle of the scattered photon. Write an expression which relates these two variables. Draw a picture and identify all the variables that you use in your answer.

Answer 1

Compton scattering involves a photon scattering off an electron, resulting in a photon of longer wavelength. The change in the photon's wavelength (Compton shift Δλ) is described by Δλ = (h/m_ec)(1 - cosθ).

Step-by-step explanation:

In Compton scattering, the wavelength of a scattered photon (λ') is related to the wavelength of the incident photon (λ) and the angle of scattering (θ). The expression that relates these variables is given by the Compton wavelength shift formula: Δλ = λ' - λ = (h/m_ec)(1 - cosθ), where Δλ is the Compton shift, h is Planck's constant, m_e is the electron rest mass, c is the speed of light, and cosθ is the cosine of the scattering angle. This formula assumes that an incident photon collides with an electron, transferring some energy and momentum to it, resulting in a scattered photon of longer wavelength.

The scenario can be visualized with a diagram where an incident photon of wavelength λ approaches an electron at rest, scatters at an angle θ, and exits with a longer wavelength λ'. These components can be labeled accordingly on a representative drawing. The largest Compton shift occurs when the scattering angle is 180°, which results in the maximum value of Δλ.