Step 1: Nuclear Reaction Analysis.
The nuclear reaction provided involves the reaction of a nitrogen-7 nucleus with a neutron. The reaction will produce a carbon-14 nucleus and an unknown particle \( X \).
Step 2: Balancing the Reaction.
In the given reaction, the atomic number and mass number should be conserved. The nitrogen-7 nucleus has an atomic number of 7 and a mass number of 14, and the neutron has an atomic number of 0 and mass number 1. The resulting carbon-14 nucleus has an atomic number of 6 and mass number 14.
The missing particle \( X \) must account for the difference in atomic number and mass number between the reactants and products. The only particle that satisfies this is a proton, which has an atomic number of 1 and mass number 1.
Step 3: Conclusion.
Thus, \( X \) is a proton, making the correct answer (A).