To determine which type of reaction occurs in the core of a nuclear reactor in a nuclear power plant, let's analyze the given reactions:
1. [tex]\( HCl + NaOH \rightarrow H_2O + NaCl \)[/tex]
- This is a typical acid-base neutralization reaction, where hydrochloric acid (HCl) reacts with sodium hydroxide (NaOH) to produce water (H₂O) and sodium chloride (NaCl), which is common table salt.
- This reaction is chemical, not nuclear.
2. [tex]\( {}_{82}^{255}U + {}_0^1n \rightarrow {}_{38}^{\infty 0}Sr + {}_{54}^{143}Xe + 3_0^1n \)[/tex]
- This reaction involves uranium-255 ([tex]\( {}_{82}^{255}U \)[/tex]) and a neutron ([tex]\( {}_0^1n \)[/tex]), resulting in the production of strontium ([tex]\( {}_{38}^{\infty 0}Sr \)[/tex]), xenon ([tex]\( {}_{54}^{143}Xe \)[/tex]), and three additional neutrons ([tex]\( 3_0^1n \)[/tex]).
- This is indicative of a nuclear fission reaction, where a heavy uranium nucleus splits into smaller nuclei, releasing a significant amount of energy along with additional neutrons.
3. [tex]\( {}_{50}^{20}Sr + {}_{54}^{148}Ye + 3_0^1n \rightarrow {}_{02}^{225}U + {}_0^1n \)[/tex]
- This reaction appears to involve strontium ([tex]\( {}_{50}^{20}Sr \)[/tex]), a neutron ([tex]\( {}_0^1n \)[/tex]), and some other components, resulting in uranium ([tex]\( {}_{02}^{225}U \)[/tex]) and a single neutron.
- The notation and the elements involved do not correspond to any recognized nuclear reaction, and the isotopes do not match established nuclear chemistry principles. It seems to be incorrect.
4. [tex]\( C_{10}H_3 + 12 O_2 \rightarrow 10 CO_2 + 4 H_2O \)[/tex]
- This reaction is a combustion reaction, where a hydrocarbon ([tex]\( C_{10}H_3 \)[/tex]) reacts with oxygen ([tex]\( O_2 \)[/tex]) to produce carbon dioxide ([tex]\( CO_2 \)[/tex]) and water ([tex]\( H_2O \)[/tex]).
- This is a typical combustion process, not related to nuclear reactions.
Considering the descriptions of each reaction, it is evident that the reaction in option 2 is the one that corresponds to a nuclear fission reaction. The nuclear fission reaction is the type of reaction that occurs in the core of a nuclear reactor in a nuclear power plant.
Therefore, the correct answer is:
[tex]\[ {}_{82}^{255}U + {}_0^1n \rightarrow {}_{38}^{\infty 0}Sr + {}_{54}^{143}Xe + 3_0^1n \][/tex]
The corresponding answer to the question is:
[tex]\[ \boxed{2} \][/tex]
