\begin{problem*}{9.31}
An electron has a kinetic energy five times greater than its rest
energy.  Find \Part{a} its total energy and \Part{b} its speed.
\end{problem*} % problem 9.31

\begin{solution}
The total energy is
\Part{a}
\begin{equation}
  E = K + m_0 c^2 = (5+1)m_0 c^2
    = 6\cdot 511\U{keV}
    = \ans{3.07\U{MeV}}
\end{equation}

\Part{b}
\begin{align}
  E &= m c^2 = \gamma m_0 c^2 = 6 m_0 c^2 \\
  \gamma &= \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} = 6 \\
  \frac{1}{6^2} &= 1-\frac{v^2}{c^2} \\
  \frac{v}{c} &= \sqrt{1-\frac{1}{6^2}}
    = 0.986 \\
  v &= \ans{0.986c}
\end{align}
\end{solution}
