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Question
The naturally occurring radioactive isotope ${}^{232}\textrm{Th}$ does not make good fission fuel, because it has an even number of neutrons; however, it can be bred into a suitable fuel (much as ${}^{238}\textrm{U}$ is bred into ${}^{239}\textrm{Pu}$).
1. What are $Z$ and $N$ for ${}^{232}\textrm{T}$
2. Write the reaction equation for neutron capture by ${}^{232}\textrm{Th}$ and identify the nuclide ${}^\textrm{A}\textrm{X}$ produced in $n + {}^{232}\textrm{Th} \rightarrow {}^\textrm{A}\textrm{X} + \gamma$.
3. The product nucleus $\beta^-$ decays, as does its daughter. Write the decay equations for each, and identify the final nucleus.
4. Confirm that the final nucleus has an odd number of neutrons, making it a better fission fuel.
5. Look up the half-life of the final nucleus to see if it lives long enough to be a useful fuel.
1. $Z = 90$, $N = 142$
2. ${}^{233}\textrm{Th}$
3. Please see the solution video
4. Yes, the final nucleus has an odd number of neutrons: 141
5. $t_\textrm{1/2} = 1.6\times 10^{5}\textrm{ y}$
Solution Video

# OpenStax College Physics for AP® Courses Solution, Chapter 32, Problem 48 (Problems & Exercises) (3:04) 