Question 7.3: Suppose that a fuel rod in a thermal water reactor consists ......
Suppose that a fuel rod in a thermal water reactor consists of 3% enriched UO_2. What is the eta of the fuel in this case?
We know from our earlier discussion that we can ignore the presence of the oxygen atoms in the fuel in our calculation of the value for η and that this fuel is not likely to contain any significant amounts of U-234. So to perform our calculation, we can assume that the fuel consists of a mixture of 3% U-235 and 97% U-238. Ignoring for the moment the slight difference in the weight of U-235 and U-238, the eta in this case is
\eta= \frac{v ^{U235}e^{U235}\sigma ^{U235}_{f} }{(e^{U235}\sigma ^{U235}_{a} + e^{U238}\sigma ^{U238}_{a}) } = \frac{2.088 \times 0.03\times 582.2}{\left(0.03 \times 680.8 + 0.97 \times 2.7\right) } = 1.58
Notice that we have ignored the contribution of U-238 in the numerator because this nuclide does not have a significant probability to fission with low-energy neutrons. A fuel rod containing fuel that is enriched to 4% would of course have a higher value of η.