Step 1:
First, we write down the Compton scattering equation:
\[
\lambda' - \lambda = \frac{h}{m_e c}(1 - \cos\theta)
\]
where $\lambda'$ is the wavelength after scattering, $\lambda$ is the initial wavelength, $h$ is Planck's constant, $m_e$ is the electron mass,
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