Assume an electromagnetic shower inside Pb $($Z$=82)$ material from an incident electron. Find X$\_0($radiation length$),$ E$\_$c $($critical energy$)$ and the energy per cm that a MIP deposits to Pb$.$ If the electron has energy $1$GeV find the number of particles and energy per particle for all the particles until the maximum point of the shower, find the total number of particles until that point.