Question

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.

Part A Part complete 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.) Express your answer in terms of the variables λf, v, m, the speed of light in vacuum c, and the Planck's constant h. λ = λfhh+⎛⎝⎜⎜⎜11−v2c2⎷−1⎞⎠⎟⎟⎟mcλf SubmitPrevious Answers Correct Part B Part complete 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. Express your answer in terms of the variables λf, λ, m, the speed of light in vacuum c, and the Planck's constant h. ϕ = cos−1(1−(λf−λ)mch)

Part 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 1.55×108m/s.

Part 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.

Answer 1