# In a previous lecture, we talked about radioactive decay chains, and the Bateman equations are a…

In a preceding disquisition, we talked environing radioactive waning chains, and the Bateman equations are a public analytical breach to the isotopic eagernesss in these waning fastenings. Suppose that there are three isotopes in a waning fastening that we achieve overcome isotopes A, B, and C. Part 1: Write down an self-evident equation for their age-dependent eagernesss bombastic that their half-lives are 1 day, 3 days, and 2 days, respectively, and that the moderate eagerness of A at t = 0 is Ao. Assume that the eagernesss of the other two isotopes (B and C) in the waning fastening are 0 at t = 0. Part 2: Do any of these three isotopes feel a “bump” in their eagerness curves as a function of age? If so, which ones feel these bumps, and when do these bumps occur? Part 3: By what content do we dilate the half-lives of each of these elements to get their mean career? Part 4: What are the waning constants (in inverse days) for each of the isotopes that we feel used in this issue?