The correct order of dissociation energy of $N_{2}$ and $N_{2}^{+}$ is:

Bond dissociation energy is the energy required to break one mole of bonds and is directly proportional to the bond order . According to Molecular Orbital Theory, the nitrogen molecule ($N_{2}$) has 14 electrons and a bond order of 3.0 . When $N_{2}$ is ionized to form $N_{2}^{+}$, one electron is removed from the highest occupied molecular orbital, which is a bonding orbital ($\sigma 2p_{z}$) . This reduces the number of bonding electrons ($N_{b}$), resulting in a lower bond order of 2.5 for $N_{2}^{+}$ . Since $N_{2}$ has a higher bond order than $N_{2}^{+}$, it possesses a stronger bond and, consequently, a higher dissociation energy .