- Define nuclear fission as the splitting of a heavy nucleus into smaller ones upon neutron absorption, releasing energy and more neutrons.
- Review each option to identify a heavy nucleus (U-235) and neutron reactants resulting in smaller fragments and extra neutrons.
- Identify that \({ }_{92}^{235} \mathrm{U} + { }_0^1 \mathrm{n} \rightarrow { }_{36}^{94} \mathrm{Kr} + { }_{56}^{139} \mathrm{Ba} + 3{ }_0^1 \mathrm{n}\) is the reaction characteristic of nuclear reactor fission.
- The correct reaction is \(\boxed{{ }_{92}^{235} \mathrm{U} + { }_0^1 \mathrm{n} \rightarrow { }_{36}^{94} \mathrm{Kr} + { }_{56}^{139} \mathrm{Ba} + 3{ }_0^1 \mathrm{n}}\).
Explanation
- Analysis of Nuclear Fission
Nuclear fission is a process in which the nucleus of a heavy atom, such as Uranium-235 or Plutonium-239, splits into two or more smaller, lighter nuclei, often referred to as fission fragments. This reaction is typically triggered when the heavy nucleus absorbs a neutron, becoming unstable. The splitting process also releases additional neutrons and a significant amount of energy, which sustains the chain reaction necessary for a nuclear reactor to operate. To identify the correct reaction for a nuclear fission reactor, we must look for an equation where a heavy nucleus interacts with a neutron to produce two smaller, distinct nuclei and extra neutrons.
- Evaluation of the Reactions
We examine each provided reaction:
- \({ }_8^{13} \mathrm{C} + { }_1^1 \mathrm{H} \rightarrow { }_7^{14} \mathrm{N}\): This is a nuclear fusion-like transmutation where a proton is captured by a carbon nucleus.
- \({ }_{94}^{239} \mathrm{Pu} + { }_2^4 \mathrm{He} \rightarrow { }_{96}^{243} \mathrm{Cm}\): This is a nuclear transmutation involving an alpha particle capture.
- \({ }_{27}^{59} \mathrm{Co} + { }_2^4 \mathrm{He} \rightarrow { }_{27}^{62} \mathrm{Co} + { }_0^1 \mathrm{n}\): This represents an (alpha, n) reaction, a type of transmutation.
- \({ }_{92}^{235} \mathrm{U} + { }_0^1 \mathrm{n} \rightarrow { }_{36}^{94} \mathrm{Kr} + { }_{56}^{139} \mathrm{Ba} + 3{ }_0^1 \mathrm{n}\): This reaction involves a heavy Uranium-235 nucleus capturing a neutron (\({ }_0^1 \mathrm{n}\)), splitting into Krypton-94 and Barium-139, and releasing three more neutrons. This perfectly matches the criteria for fission in a nuclear reactor.
- Conclusion
The reaction \({ }_{92}^{235} \mathrm{U} + { }_0^1 \mathrm{n} \rightarrow { }_{36}^{94} \mathrm{Kr} + { }_{56}^{139} \mathrm{Ba} + 3{ }_0^1 \mathrm{n}\) is the classic representation of fission in a nuclear reactor. It features a heavy fissile nucleus (U-235) being split by a neutron into smaller fission products (Kr-94 and Ba-139) with the release of more neutrons, enabling the chain reaction process. Therefore, this is the correct choice. The final answer is \(\boxed{{ }_{92}^{235} \mathrm{U} + { }_0^1 \mathrm{n} \rightarrow { }_{36}^{94} \mathrm{Kr} + { }_{56}^{139} \mathrm{Ba} + 3{ }_0^1 \mathrm{n}}\).
Examples
Nuclear fission is the foundational process of nuclear power plants. By harnessing the energy released when heavy atoms like Uranium-235 are split by neutrons, we produce heat, which turns water into steam to drive turbines that generate electricity for our homes and businesses. Understanding this reaction is critical for engineers and scientists managing the safety and efficiency of nuclear energy, as it allows for the precise control of power output and the responsible management of radioactive materials.