This is an exercise about neutron capture. I want the remaining $^{198}$Au after a time t and I know $\lambda$.
$^{197}$Au absorps a neutron and transforms to $^{198}$Au which then decays. The sample absorps 10$^{20}$ neutrons every second, but how do I include the decay for the atoms the sample gains every second?
Because for N(t) = $C*e^{-t\lambda}+10^{20}*t$ wouldn't C = 0 because of N(0) = 0?
Edit: So I guess I have to solve the differential $N'(t) + \lambda N(t) = 10^{20} $
