An x-ray photon is scattered from a free electron (mass m) at rest. The wavelength of the scattered photon is λ′, and the final speed of the struck electron is v.

a. What was the initial wavelength λ of the photon? Express your answer in terms of λ′, v, m, and the appropriate constants. For the wavelength of the scattered photon λ′ use the notation λf. (Hint: Use the relativistic expression for the electron kinetic energy.)
b. Through what angle ϕ is the photon scattered? Express your answer in terms of λ′, λ, m, and the appropriate constants. For the wavelength of the scattered photon λ′ use the notation λf.
c. Evaluate your result in part A for a wavelength of 5.50×10−3nm for the scattered photon and a final electron speed of 1.80×10^8m/s.
d. Evaluate your result in part B for a wavelength of 5.50×10−3nm for the scattered photon and a final electron speed of v. Give ϕ in degrees.