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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} $

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    $\begingroup$ Search term: "secular equilibrium." Also, $10^{20}\rm\,s^{-1}$ is a lot of neutrons. $\endgroup$ – rob May 28 '19 at 0:49
  • $\begingroup$ For the differential eq. I found $N(t) = N(0)e^{-\lambda t} + 10^{20}/\lambda $ Thank you for the tip, I keep thinking about it. $\endgroup$ – quielywhis May 28 '19 at 1:05
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    $\begingroup$ @rob that isn’t just a lot of neutrons. That’s 10x or more of the neutron dose for structural materials across the lifetime of a modern nuclear reactor... $\endgroup$ – Jon Custer May 28 '19 at 2:15
  • $\begingroup$ The exercise was posed in class, maybe I didn't write it down correctly.:) $\endgroup$ – quielywhis May 28 '19 at 2:17
  • $\begingroup$ Speaking of lots of neutrons, check out physics.stackexchange.com/questions/437245/… $\endgroup$ – PM 2Ring May 28 '19 at 5:01

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