The question asks about the relationship between the dissociation energies of nitrogen molecule (\(N_2\)) and its ion (\(N_2^+\)). To address this, we need to delve into molecular bonding and the effect of ionization on molecular stability.
- The N_2 molecule is known for its strong triple bond, making it a stable and robust diatomic molecule with high bond dissociation energy.
- When \(N_2\) is ionized to form \(N_2^+\), one electron is removed, leading to a change in bond order and molecular stability.
- Removing an electron from \(N_2\) results in a decrease in electron density between the nitrogen atoms. This reduction weakens the bond strength relative to the neutral molecule.
- As a consequence of the weaker bond in \(N_2^+\), the dissociation energy required to break this bond is lower than for \(N_2\).
- Thus, we conclude that the dissociation energy of \(N_2\) is greater than the dissociation energy of \(N_2^+\).
Based on this understanding, the correct answer is: dissociation energy of N_2 > dissociation energy of N_2^+.
Reasons why other options are incorrect:
- dissociation energy of N_2^+ > dissociation energy of N_2: This is incorrect because ionization reduces the bond strength in \(N_2^+\), not increases it.
- dissociation energy of N_2 = dissociation energy of N_2^+: This is incorrect as ionization changes the bond characteristics, making their energy requirements unequal.
- dissociation energy of N_2 can either be lower or higher than the dissociation energy of N_2^+: This is a vague statement without theoretical backing in this context.
Hence, the dissociation energy of \(N_2\) is indeed greater than that of \(N_2^+\), due to the innate stability and bond strength of the \(N_2\) molecule.