Homework Solution

TQ 14-1

A spontaneous chain reaction requires that at least one neutron from each generation of fissions go on to produce a fission in the next generation.

In uranium only ²³⁵U has a substantial fission cross section (and that only at thermal neutron energies), the fraction of uranium that is ²³⁵U would have to be at least comparable to that found in a light water reactor, 3-5%. A source of moderating water would also need to be present to thermalize the neutrons. If no thermalization of the neutrons occurred, more than 90% of the uranium would have to be ²³⁵U .

In nature at the present, ²³⁵U accounts for approximately 0.72% of natural uranium, insufficient for a sustaining a chain reaction.

However, since ²³⁵U is radioactive with a shorter half-life than ²³⁸U , which makes up most of natural uranium, at sometime in the past, the portion of natural uranium that was ²³⁵U was higher. The Oklo natural reactor is proof that a sustainable chain reaction in uranium did occur.