Project 1

Part I for both PHYS460 and PHYS660

Consider a radiactive decay problem involving two types of nuclei, A and B, with populations $N_{A}(t)$ and $N_{B}(t)$. Suppose that type A nuclei decay to form type B nuclei, which then also decay, according to differential equations:

${\frac {dN_{A}}{dt}}=-{\frac {N_{A}}{\tau _{A}}}$,

${\frac {dN_{B}}{dt}}={\frac {N_{A}}{\tau _{A}}}-{\frac {N_{B}}{\tau _{B}}}$,

where $\tau _{A}$ and $\tau _{B}$ are the decay time constants for each type of nucleus. Use the Euler method to solve these coupled equations numerically for $N_{A}(t)$ and $N_{B}(t)$ as a function of time.