L ( 99 \% ) = (t_{max} + 0.08 Z + 9.6)[X_0] \quad .
\end{equation}
\begin{itemize}
\item[a)] Verify the position of $t_{max}$ for 3 - 4 choices of energies in simulation
\item[b)] Verify $L (99\%)$ in simulation for a 50 GeV shower
\item[c)] How many X$_0$ are need to capture $95\%$ of the initial energy? (Careful: the simulation also includes processes such as ionisation / excitation / Compton Scattering / Rayleigh Scattering)
\item[a)] Verify qualitatively the position of $t_{max}$ for 3 - 4 choices of energies in simulation.
\item[b)] Verify qualitatively $L (99\%)$ in simulation for a 50 GeV shower. If you use PbW04 for you calorimeter, simply use the Z of tungsten here as approximation.
\item[c)] How many X$_0$ are need to capture $95\%$ of the initial energy? (Note: the simulation also includes processes such as ionisation / excitation / Compton Scattering / Rayleigh Scattering)
\end{itemize}
\item The Moliere radius describes the transversal expansion of an electromagnetic shower, mostly by low-energy electrons. What is the Moliere radius of Pb or PbWO$_4$? What does that mean for our calorimeter?
\item (optional): simulate showers in a calorimeter highly granular in $x-y$ and verify the Moliere radius qualitatively.
