Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 4 / 12C / b / Solution

At step $n$, the parent and daughter rest masses areThe decay is allowed when $M\ge m$, which holds because $M=\lambda m$ with $\lambda >1$. Hence all $N$ stages occur:The initial rest mass is $NM+m_0$ and the final rest mass is $Nm+m_0$. Thusof rest mass is converted into kinetic energy, corresponding to energy $Nm(\lambda -1)c^2$.