To determine which reaction takes place in a nuclear fission reactor, we need to understand the process of nuclear fission. Nuclear fission involves the splitting of a heavy nucleus into lighter nuclei, typically accompanied by the release of energy and additional neutrons.
Let's review each of the reactions provided:
1. [tex]\( {}_6^{13} C + {}_1^1 H \rightarrow {}_7^{14} N \)[/tex]:
- This reaction involves Carbon-13 fusing with a proton (Hydrogen-1) to form Nitrogen-14. This is a fusion reaction, not fission.
2. [tex]\( {}_{94}^{239} Pu + {}_2^4 He \rightarrow {}_{96}^{242} Cm \)[/tex]:
- In this reaction, Plutonium-239 reacts with an alpha particle (Helium-4) to form Curium-242. This is also not a fission reaction but rather a neutron capture leading to transmutation.
3. [tex]\( {}_{27}^{59} Co + {}_2^4 He \rightarrow {}_{27}^{60} Co + {}_0^1 n \)[/tex]:
- Here, Cobalt-59 reacts with an alpha particle to form Cobalt-60 and a neutron. This is an example of an (alpha, n) reaction but again, not a fission reaction.
4. [tex]\( {}_{92}^{235} U + {}_0^1 n \rightarrow {}_{36}^{94} Kr + {}_{56}^{139} Ba + 3 {}_0^1 n \)[/tex]:
- In this reaction, Uranium-235 absorbs a neutron and splits (fissions) into Krypton-94, Barium-139, and three additional neutrons. This is a classic example of a nuclear fission reaction.
Given these explanations, we can conclude that the reaction that takes place in a nuclear fission reactor is the fourth one:
[tex]\[ {}_{92}^{235} U + {}_0^1 n \rightarrow {}_{36}^{94} Kr + {}_{56}^{139} Ba + 3 {}_0^1 n \][/tex]
Thus, the correct choice is the 4th reaction.
