Binary branching model of an electromagnetic shower ($n_{\mathrm{stop}}=\lceil {\log }_2(E_0/E_c)\rceil$)

If every particle branches into two equal-energy daughters after one radiation length, the multiplicity is $2^n$ and each energy is $E_0/2^n$. Multiplication stops at the critical energy of an electromagnetic shower. This predicts a branching depth, not a realistic containment quantile: stochastic interaction distances, unequal radiation spectra and the residual stopping range produce a longitudinal tail.