The ionic radius decreases as the charge on the ion increases for ions with the same electron configuration. The correct order is:
- \( Al^{3+} \) has the smallest ionic radius due to its 3+ charge, followed by \( Mg^{2+} \) (2+ charge), and then \( N^{3-} \) (3- charge), which has the largest radius due to its negative charge.
Therefore, the correct order is \( Al^{3+} < Mg^{2+} < N^{3-} \).