An x-ray photon is scattered from a free electron (mass m ) at rest. The wavelen

Question

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

Part A

What was the initial wavelength of the photon? Express your answer in terms of , v, m, and the appropriate constants. For the wavelength of the scattered photon use the notation f. (Hint: Use the relativistic expression for the electron kinetic energy.)

Express your answer in terms of the variables f, v, m, the speed of light in vacuum c, and the Planck's constant h.

Part B

Through what angle is the photon scattered? Express your answer in terms of , , m, and the appropriate constants. For the wavelength of the scattered photon use the notation f.

Express your answer in terms of the variables f, , m, the speed of light in vacuum c, and the Planck's constant h.

Explanation / Answer

A) The wavelength of the scattered photon is given by the Compton shift

' = + (h/mv)(1 - cos)

So the initial wavelength of the photon =   =  f - [(h/mv)(1 - cos)]

B) = scattering Angle

   =  cos-1[1 - (mv/h)(' - )]

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