Frequently, the “daughter” of a radioactive “parent” is itself radioactive. Suppose the parent, designated by A has a decay constant λ_A, while the daughter, designated B has a decay constant λ_B. The number of nuclei of B are then given by the solution to the differential equation

dN_B/dt = λ_AN_A - λ_BN_B

(a) Justify this differential equation.

(b) Show that the solution for this equation is

Where N_A0 is the number of A nuclei present at t = 0 when there are no B nuclei.

(c) Show that N_B(t) > 0 whether λ_A > λ_B or λ_B > λ_A.

(d) Make a plot of N_A(t) and N_B(t) as a function of time when τ_B = 3τ_A.

Transcribed Image Text:

-(e¯h^t - e A!) NA0A NB(1) = 2в — 2л