Frequently, the daughter nucleus of a radioactive parent

Chapter , Problem 73

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Frequently, the daughter nucleus of a radioactive parent nucleus is itself radioactive. Suppose the parent nucleus, designated by has a decay constant while the daughter nucleus, designated by D, has a decay constant The number of daughter nuclei are then given by the solution to the differential equation where is the number of parent nuclei. (a) Justify this differential equation. (b) Show that the solution for the equation is where is the number of parent nuclei present at when there are no daughter nuclei. (c) Show that the expression for in Part (b) gives whether or (d) Make a plot of and as a function of time when where and are the mean lifetimes of the daughter and parent nuclei, respectively.