\begin{problem}
You are working in the radiology department at a vetrinary hospital.  The cat you are trying to X-ray refuses to hold still so you volunteer to stand at the table and hold the cat down during the exposure.  If X-rays of wavelength $\lambda = 24\U{pm}$ enter the cat from above, what is the wavelength of the photons that enter your head after scattering through a $135\dg$ angle?
\end{problem}

\begin{solution}
Compton effect
\begin{align}
  \lambda' - \lambda_0 &= \frac{h}{m_e c}(1-\cos\theta) \\
  \lambda' &= \lambda_0 + \frac{h}{m_e c}(1-\cos\theta)
    = \lambda_0 + \frac{hc}{m_e c^2}(1-\cos\theta)
    = 24\U{pm} + \frac{1240\U{eV$\cdot$nm}}{511\U{keV}}(1-\cos 135\dg)
    = \ans{28.1\U{pm}} \;.
\end{align}
These are still quite penatrative X-rays, which is why radiologists
try to hold down cats with tape and sandbags when taking radiographs.
Determining the intensity of the scattered beam is more complicated
and would involve some sort of volume integral over the atoms in the
cat and the scattering cross section per atom.
\end{solution}
