Isotope A decays to isotope B, which subsequently decays to stable isotope C. The half-life of A is 20min, and the half-life of B is 5.0min. At t=0 the sample consists of N0=1.2×1020 atoms of A and no atoms of B or C.
(1) Part 1: (a) Derive an algebraic expression for the time tpeak at which the activity of isotope B attains its maximum value. Express your result solely in terms of the decay constants of A and B.
(2) Part 2: (b) Calculate the numerical value of tpeak using the given half-lives.
(3) Part 3: (c) Determine the activity of isotope B at tpeak and express it as a fraction of the initial activity of isotope A at t=0.