Solution to 2008 Problem 97

Let \hat{\mathbf{x}} be the direction of the incoming photon, and let \hat{\mathbf{y}} be the direction of the outgoing photon. Let E' be the energy of the photon after it is scattered and let (p_x,p_y) be the momentum of the electron after the the photon scatters off of it. Conservation of energy and momentum gives
\begin{align*}E + mc^2 &= E' + \sqrt{p_x^2 c^2 +p_y^2 c^2 + m^2 c^4} \\\frac{E}{c} &= p_x \\0 &= \frac{E'}{c} + p...
Plugging the second and third equations into the first equation gives
\begin{align*}&& E + mc^2 &= E' + \sqrt{E^2 + E^2 + m^2 c^4} \\&\Longrightarrow& E - E' + mc^2 &= \sq...
Therefore, answer (E) is correct.

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