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+\documentclass[10pt, onekey]{exam}
+\Fullpages
+\NumberOfVersions{4}
+\def\eV{\mbox{eV}}
+
+\begin{document}
+
+\begin{frontmatter}
+\vspace*{3in}
+\begin{center}
+  \huge Modern Physics \\[6pt]
+  \Large Final Exam
+\end{center}
+\vfill
+\begin{flushright}
+  Name: \rule{3in}{.4pt} \\[10pt]
+  Student I.D.: \rule{3in}{.4pt}
+\end{flushright}
+\end{frontmatter}
+
+\begin{examtop}
+\end{examtop}
+
+\begin{shortanswer}[title={\Large Short Answer (10 pts each)},suppressprefix]
+Answer all problems in as thorough detail as possible. Be sure to include all
+your work. Partial credit will be given even if the answer is not fully correct.
+
+\begin{question}
+  Determine the charge in the rest mass of a system consisting of a proton
+  and an electron as the two particles combine to form a hydrogen atom. The
+  ionization energy of hydrogen is 13.6 eV.
+  \examvspace*{1.5in}
+  \begin{answer}
+    The rest mass of the proton is $1.672649 \times 10^{-27}$kg; that of the
+    electron is $9.109534 \times 10^{-31}$kg. When the electron and proton
+    combine to form a hydrogen atom, the ionization energy of 13.6 eV is
+    released as ultraviolet radiation. The rest mass of the hydrogen atom is
+    therefore smaller than the sum of the electron and proton rest masses by
+    the amount
+    \[
+    \Delta M = {(13.6 \eV)(1.6 \times 10^{-19} J/\eV) \over (3 \times 10^8 m/s)^2}
+             = 2.42 \times 10^{-35}kg
+    \]
+  \end{answer}
+\end{question}
+
+\begin{question}
+  The Eiffel Tower in Paris is 300m tall. What is the fractional gravitational
+  red shift due to this elevation difference?
+  \examvspace*{1in}
+  \begin{answer}
+    \[
+    {\delta\nu \over \nu} = {gH \over c^2} = {(9.8m/s^2)(300m) \over
+                            (3 \times 10^8 m/s)^2} = 3.27\times 10^{-14}
+    \]
+  \end{answer}
+\end{question}
+
+\begin{question}
+  Derive Stefan's law from Planck's law.  Using that result, obtain an
+  expression for the Stefan-Boltzmann constant $\sigma$ in terms of known
+  physical constants and determine its value.
+  \examvspace*{1.5in}
+  \begin{answer}
+    The radiance
+  \end{answer}
+\end{question}
+
+\begin{question}
+  Calculate the density of an object of one solar mass whose radius is the
+  critical Schwarzschild radius.  Compare this density with the nuclear
+  density of approximately $2.3 \times 10^{17} kg/m^3$.
+  \examvspace*{1.5in}
+  \begin{answer}
+    The mass of the sun is $2 \times 10^{30} kg$. The universal gravitational
+    constant is $6.67 \times 10^{-11} N\cdot m^2/kg^2$.
+
+    The Schwarzschild radius of one solar mass is
+    \begin{eqnarray*}
+    R_c & = & {2(2 \times 10^{30}lg)(6.67 \times 10^{-11} N\cdot m62/kg^2)
+              \over (3 \times 10^8 m/s)^2} \\
+        & = & 2.96 \times 10^3 m \approx 3 km
+    \end{eqnarray*}
+    If the sun collapsed to a sphere of 3 km radius without loss of mass, it
+    would then be a black hole. The mass density would be
+    \[
+    \rho = {M \over V} = {2 \times 10^{30} kg \over ({4\pi \over 3})
+                         (2.96 \times 10^3 m)^3} = 1.84 \times 10^{19} kg/m^3
+    \]
+  \end{answer}
+\end{question}
+\end{shortanswer}
+
+\begin{endmatter}
+  \vspace*{1.5in}
+  \centerline{\Large A Partial List of Fundamental Constants}
+  \bigskip
+  \begin{center}
+  \begin{tabular}{lcl}
+    Constant & Symbol & Approximate Value \\ \hline
+    Speed of light in vacuum & $c$ & $3.00 \times 10^8$m/s \\
+    Permeability of vacuum & $\mu_0$ & $12.6 \times 10^{-7}$H/m \\
+    Permittivity of vacuum & $\epsilon_0$ & $8.85 \times 10^{-12}$F/m \\
+    Magnetic flux quantum & $\phi_0 = {h \over 2e}$ & $2.07 \times 10^{-15}$Wb \\
+    Electron mass & $m_e$ & $9.11 \times 10^{-31}$kg \\
+    Proton mass & $m_p$ & $1.673 \times 10^{-27}$kg \\
+    Neutron mass & $m_n$ & $1.675 \times 10^{-27}$kg \\
+    Proton-electron mass ratio & $m_p \over m_e$ & 1836
+  \end{tabular}
+  \end{center}
+\end{endmatter}
+
+\end{document}