To identify the fissile nucleus in the given nuclear fission reaction, we need to ensure that both the atomic numbers (protons) and mass numbers (total nucleons: protons + neutrons) are conserved in the equation.
The given fission reaction is:
[tex]\[\square +{ }_0^1 n \rightarrow{ }_{53}^{131} I +{ }_{39}^{101} Y +2{ }_0^1 n\][/tex]
Let's analyze the components of the reaction step by step:
1. Identify the sum of atomic numbers (protons):
- Iodine (I) has an atomic number of 53.
- Yttrium (Y) has an atomic number of 39.
- There are two free neutrons, but their contribution to the atomic number is 0.
Therefore, the sum of the atomic numbers is:
[tex]\[
53 (I) + 39 (Y) = 92
\][/tex]
2. Identify the sum of mass numbers (total nucleons):
- Iodine (I) has a mass number of 131.
- Yttrium (Y) has a mass number of 101.
- There are two free neutrons, each with a mass number of 1.
Therefore, the sum of the mass numbers is:
[tex]\[
131 (I) + 101 (Y) + 2 \times 1 (neutrons) = 234
\][/tex]
3. Determine the characteristics of the fissile nucleus:
Since the atomic number (Z) of the fissile nucleus that absorbed the neutron is 92 and the resulting mass number (A) considering the neutron is 235. These numbers correspond to Uranium with an atomic number of 92. (Also, Two free neutrons are created, confirming the fissile nucleus must indeed be uranium).
Given the mass number of the fissile nucleus must sum to 235 including an extra neutron, thus the fissile nucleus should indeed be Uranium-235 with 92 protons (atomic number 92) and 235 nucleons in total.
Based on this analysis, the fissile nucleus is:
(B) [tex]\({ }_{92}^{235} U\)[/tex]
