The reaction:
\(^{14} _7 N + ^1 _0n \to ^1 _1 H+ ^A _Z X\)
The sum of the mass numbers and the sum of the atomic numbers must be the same on both sides of the reaction.
The mass numbers:
\(14+1=1+A \\
14+1-1=A \\ A=14\)
The atomic numbers:
\(7+0=1+Z \\
7+0-1=Z \\ Z=6\)
The formed nucleus has the atomic number 6, so it's a nucleus of carbon.
\(^{14} _7 N + ^1 _0 n \to ^1 _1 H + \boxed{^{14} _6 C}\)
A nucleus of carbon-14 is formed.
