# Coupled Diff EQ

1. Mar 3, 2010

### blaksheep423

1. The problem statement, all variables and given/known data
Consider a radiactive decay problem involving two types of nuclei, A and B, with populations Na(t) and Nb(t). Suppose that type A nuclei decay to form type B nuclei, which then also decay, according to differential equations:

2. Relevant equations

dNa/dt = - Na/Ta

dNb/dt = Na/Ta - Nb/Tb

where Ta and Tb are the decay constants. Na(0) = 100 and Nb(0) = 0.
3. The attempt at a solution

I solved the equation for Na(t) and got 100*e^(-t/Ta), but I'm not sure about Nb. Intuitively, I think it has to be something like:

100*(1 - e^(-t/Ta))*e^(-t/Tb)

but I know this is wrong

2. Mar 3, 2010

### blaksheep423

.......anyone?

3. Mar 3, 2010

### vela

Staff Emeritus
Just plug it in and solve! ;)

$$N'_b(t)+\frac{1}{T_b} N_b(t) = 100e^{-t/T_a}$$