 Solution

ID: past-exam-of-the-short-options-paper-of-the-physics-prelims-of-the-university-of-oxford/2019/s3/2/b/solution

Take a stationary initial electron of mass

m_{e}

, a photon incident along

x

, and a nonrelativistic recoil velocity of magnitude

v

. Choose

θ

above

x

for the scattered photon and

ϕ

below

x

\frac{h ν}{c} = \frac{h ν ^{'}}{c} cos θ + m_{e} v cos ϕ, 0 = \frac{h ν ^{'}}{c} sin θ - m_{e} v sin ϕ .

The electron's unchanged rest energy cancels in conservation of energy, leaving

h ν = h ν^{'} + \frac{1}{2} m_{e} v^{2} .

Equivalently use

h ν / c = h / λ

and

h ν = h c / λ

v / c ≪ 1

, and treating the electron as free requires its binding energy to be negligible on the scale of the collision.

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