In a simple case of chain radioactive decay, a parent radioactive nucleus, A, decays with a decay constant λ1 into a daughter radioactive Nucleus, B, which then decays with a decay constant λ2 to a stable nucleus, C.
(a) Write the equations describing the number of nuclei of each of the three types as a function of time, and derive expressions for the number of daughter nuclei, N2, as a function of time and for the activity of the daughter nuclei, A2, as a function of time.
(b) Discuss the results in the case when λ2 > λ, (λ2 = 10 λ1) and when λ2 >> λ1 (λ1 = 100 λ1).