The nuclear equation for the beta decay of nitrogen-13 is:

$$ ^{13} _7 N \rightarrow ^{13} _6 C + ^{0} _-1 e + \bar{\nu} _e $$

In this equation, nitrogen-13 (N-13) undergoes beta decay to transform into carbon-13 (C-13), releasing a beta particle (e-) and an antineutrino (ν¯e).