I need help on a homework problem. It asks: Consider a reactor in which the production rate of U-239 via the 238U(n, gamma) 239U reaction is 10^5 atoms/s. Calculate the activity of 239 Pu after an irradiation of a) 1 day b) 1 month c) 1 year

Can you interrupt each of my questions with a response, so that all my questions are answered?

I don't want the actual answer, but I am not sure what they mean by 238 U (n, gamma) 239 U. I have a vague understanding that U 238 is used to produce plutonium. But what do they mean by 238 U (n, gamma)? I tried to search for this on the internet, but I did find this: 238U(n, gamma) --> 239U --(beta)--> 239Np --(beta)--> 239Pu.

Is the n in 238U(n, gamma) indicating neutron capture? What does the gamma mean? Does that mean a gamma ray is emitted? Then the (n, gamma) symbol is very ambiguous. How is the n and gamma ray participating in the reaction. Which one is a product and reactant!? I don't know the notation.

What do they mean by "after an irradiation of [x time]..?" Does that mean how long the production of U 239 was done?

When I calculate activity, does that mean I want the activity at t = 0 after the irradiation?

Does this mean I have to take into account the decay rates of 239 Np? I would have to set up a differenital equation for the production of 239, decay of U-239 and production of Np-239, decay of Np-239 and production of Pu-239, and then the decay of Pu-239? That seems hard!! But perhaps I can ignore the Np-239 for irradiation of 1 year, because its half life is so small?

Perhaps I should use Bateman equations? Guess I answered all my own questions...