Which reaction takes place in a nuclear fission reactor?


A${ }_6^{13} C +{ }_1^1 H \rightarrow{ }_7^{14} N$
B${ }_{94}^{239} Pu +{ }_2^4 He \rightarrow{ }_{96}^{242} Cm$
C${ }_{27}^{59} Co +{ }_2^4 He \rightarrow{ }_{27}^{60} Co +$
D${ }_{92}^{235} U +{ }_0^1 n \rightarrow{ }_{36}^{94} Kr +{ }_{56}^{139} Ba +3{ }_0^1 n$

Verified Answer :

  • Nuclear fission is a process where a heavy nucleus splits into lighter ones after neutron capture, obeying conservation of mass and atomic number.
  • Analyzing the provided options, the reaction \({ }_{92}^{235} \text{U} + { }_{0}^{1} \text{n} \rightarrow { }_{36}^{94} \text{Kr} + { }_{56}^{139} \text{Ba} + 3{ }_{0}^{1} \text{n}\) perfectly satisfies these conservation laws and matches the definition of fission.
  • All other reactions represent different nuclear processes like fusion or transmutation.
  • The final answer is \(\boxed{{ }_{92}^{235} \text{U} + { }_{0}^{1} \text{n} \rightarrow { }_{36}^{94} \text{Kr} + { }_{56}^{139} \text{Ba} + 3{ }_{0}^{1} \text{n}}\).

Explanation

  1. Defining Nuclear Fission and Conservation Laws

Nuclear fission is a process in which a heavy, unstable atomic nucleus splits into two or more smaller, more stable nuclei (fission products). This process is typically triggered by the absorption of a neutron and results in the release of additional neutrons and a significant amount of energy. A nuclear fission reactor relies on this chain reaction to produce power. In any nuclear reaction, two fundamental conservation laws must be observed:

  1. The conservation of the mass number (total number of protons and neutrons, denoted as \(A\)): \(\sum A_{left} = \sum A_{right}\).
  2. The conservation of the atomic number (total number of protons, denoted as \(Z\)): \(\sum Z_{left} = \sum Z_{right}\).
  1. Evaluating the Options

We analyze each option to determine if it describes a nuclear fission process and if it satisfies the conservation laws.

  • Option 1: \({ }_{6}^{13} \text{C} + { }_{1}^{1} \text{H} \rightarrow { }_{7}^{14} \text{N}\)

This is a fusion-type reaction where two lighter nuclei combine to form a heavier nucleus. It does not fit the definition of nuclear fission.

  • Option 2: \({ }_{94}^{239} \text{Pu} + { }_{2}^{4} \text{He} \rightarrow { }_{96}^{242} \text{Cm} + \dots\)

This is an alpha-capture reaction. Comparing the mass numbers: \(239+4=243\) on the left, while \(242\) is on the right. This indicates an incomplete reaction that does not represent fission.

  • Option 3: \({ }_{27}^{59} \text{Co} + { }_{2}^{4} \text{He} \rightarrow { }_{27}^{60} \text{Co} + \dots\)

Similarly, this reaction does not satisfy the conservation of mass and atomic numbers correctly and is not a fission process.

  • Option 4: \({ }_{92}^{235} \text{U} + { }_{0}^{1} \text{n} \rightarrow { }_{36}^{94} \text{Kr} + { }_{56}^{139} \text{Ba} + 3{ }_{0}^{1} \text{n}\)

Let's check the conservation laws:

  • Mass number (\(A\)): Left side: \(235 + 1 = 236\). Right side: \(94 + 139 + (3 \times 1) = 233 + 3 = 236\). Conservation holds.
  • Atomic number (\(Z\)): Left side: \(92 + 0 = 92\). Right side: \(36 + 56 + 0 = 92\). Conservation holds.

This reaction involves a heavy nucleus (U-235) splitting into lighter nuclei (Kr-94 and Ba-139) upon neutron absorption, releasing more neutrons. This is the definition of nuclear fission.

  1. Conclusion

Based on the analysis, the reaction \({ }_{92}^{235} \text{U} + { }_{0}^{1} \text{n} \rightarrow { }_{36}^{94} \text{Kr} + { }_{56}^{139} \text{Ba} + 3{ }_{0}^{1} \text{n}\) is the only one that represents a typical nuclear fission process used in reactors. The final answer is the fourth option.

Examples

Nuclear fission is the process that powers commercial nuclear power plants. By controlling the fission reaction of uranium fuel rods, reactors generate immense heat, which is used to boil water into steam. This steam then turns massive turbines connected to generators to produce the electricity that powers our homes and businesses. Understanding these equations helps scientists manage the chain reactions safely, ensuring a steady supply of energy while maintaining reactor stability.