Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2021 / Module NE1 / 1 / c / Solution

Over $N$ half-lives, the duration is $T=N{t}_{1/2}=N\ln 2/\lambda$. The time-averaged thermal power isSince $\lambda T=N\ln 2$ and $e^{-\lambda T}=2^{-N}$,This is a time average, not the arithmetic mean of the initial and final powers. It follows directly from the assumed constant nuclear decay constant and constant recovered energy per decay.