Consider a two-stage decay chain a b NNN abc , where Na(0) = N0, Nb(0) = N0/2, and a b = = . (a) Find Nb(t) and the time, tm, at which Nb is maximum. (b) Prove that the cross over between the two decay curves occurs at t = tm. (c) Plot on one paper the normalized activities as a function of time (in units of =1/ ) of both nuclides: Aa(t)/N0 and Ab(t)/N0. Accurate plots are required, not sketches; use a computer plotting routine such as the one in MATLAB.