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I am being asked the following question for a homework: "Uranium 238 is not fissible, but it is fertile. If you have 10,000 kg of Uranium, how enriched would it need to be in order to theoretically convert all of the uranium 238 into plutonium?"

I have no idea where to begin, and I would like guidance on what book/article/lecture notes should I read to try and tackle this problem. Maybe some hint at the solution. Does the answer need to be estimated with the plutonium breeding ratio? Do I need to use the mean free path for the neutron absorption?

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  • $\begingroup$ You might find some useful info on this Wikipedia page : Breeder Reactor. There is a diagram lower down the page showing how the transformation of heavy elements in linked in these systems. $\endgroup$
    – StephenG - Help Ukraine
    Commented Mar 21, 2021 at 15:14
  • $\begingroup$ Do you have a value of "eta" for U235 available? You need one neutron per fission to keep the reactor critical, and any additional atoms can be used to transform the U238 into plutonium. Of course, this assumes that there are no fast fissions and the plutonium never absorbs a neutron. $\endgroup$
    – NuclearFission
    Commented Mar 21, 2021 at 23:21
  • $\begingroup$ I don't but found that a conversion ratio of 1 will in theory will make all the uranium-238 available into plutonium 238 $\endgroup$
    – Mark A. Ruiz
    Commented Mar 22, 2021 at 2:22

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The lack of details in the question suggests that only the most crude approximation is expected. To start with I will assume that the U238 is enriched with U235.

When it naturally fissions an atom of U235 produces a number of prompt neutrons. The exact number for each decay depends on the decay chain, but an average is around $2.5$. I think you must assume that all of these prompt neutrons are absorbed by either another U235 atom or by an atom of U238.

I think you also have to assume that whenever a neutron is absorbed by an atom of U238 then the product of that collision is eventually an atom of Pu239 (there are a couple of intermediate steps). You may also have to take into account the collision of a neutron with another U235 atom, which may produce more neutrons.

This analysis necessarily leaves out many significant factors (speed of the neutrons, geometry and size of the material, its surrounding environment, effect of fission products etc.). In my opinion the question is overly simplistic, even though it emphasises “theoretically”.

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  • $\begingroup$ @PM2Ring Yes, it should. Fixed. $\endgroup$
    – gandalf61
    Commented Mar 21, 2021 at 14:08

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