Certainly! Let's examine each of the given nuclear reactions to identify which one occurs in a nuclear fission reactor.
1. [tex]\(\ce{^{13}_6 C + ^1_1 H \rightarrow ^{14}_7 N}\)[/tex]
- This reaction involves a carbon-13 nucleus capturing a proton and producing a nitrogen-14 nucleus.
- This is an example of a nuclear fusion or proton capture reaction, not fission.
2. [tex]\(\ce{^{239}_{94} Pu + ^4_2 He \rightarrow ^{242}_{96} Cm}\)[/tex]
- This reaction involves plutonium-239 capturing an alpha particle and producing curium-242.
- This is an example of an alpha capture reaction, not fission.
3. [tex]\(\ce{^{59}_{27} Co + ^4_2 He \rightarrow ^{60}_{27} Co + ^1_0 n}\)[/tex]
- This reaction involves cobalt-59 capturing an alpha particle and producing cobalt-60 and a neutron.
- This is an example of an alpha capture reaction, not fission.
4. [tex]\(\ce{^{235}_{92} U + ^1_0 n \rightarrow ^{94}_{36} Kr + ^{139}_{56} Ba + 3 ^1_0 n}\)[/tex]
- This reaction involves uranium-235 capturing a neutron and splitting into krypton-94 and barium-139, along with the release of three neutrons.
- This is the classic example of a nuclear fission reaction, where a heavy nucleus splits into lighter nuclei, releasing energy and more neutrons that can propagate the fission chain reaction.
From the above examination, the reaction that occurs in a nuclear fission reactor is:
[tex]\[
\boxed{ \ce{^{235}_{92} U + ^1_0 n \rightarrow ^{94}_{36} Kr + ^{139}_{56} Ba + 3 ^1_0 n} }
\][/tex]
