The reaction:
[tex]^{14} _7 N + ^1 _0n \to ^1 _1 H+ ^A _Z X[/tex]
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:
[tex]14+1=1+A \\
14+1-1=A \\ A=14[/tex]
The atomic numbers:
[tex]7+0=1+Z \\
7+0-1=Z \\ Z=6[/tex]
The formed nucleus has the atomic number 6, so it's a nucleus of carbon.
[tex]^{14} _7 N + ^1 _0 n \to ^1 _1 H + \boxed{^{14} _6 C}[/tex]
A nucleus of carbon-14 is formed.
