# Enrichment needs of a uranium sample to convert all of the Uranium 238 into plutonium

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?

• 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. – StephenG Mar 21 at 15:14
• 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. – NuclearFission Mar 21 at 23:21
• I don't but found that a conversion ratio of 1 will in theory will make all the uranium-238 available into plutonium 238 – Mark A. Ruiz Mar 22 at 2:22

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.