The correct order of bond dissociation energy among N$$_2$$, O$$_2$$, O$$_2^-$$ is shown in which of the following arrangements?

To determine the correct order of bond dissociation energy among N2, O2, and O2-, we need to understand that bond dissociation energy is directly related to bond order. A higher bond order indicates a stronger bond and thus higher bond dissociation energy. We will calculate the bond orders using molecular orbital theory.

First, recall the molecular orbital configurations:

For N2 (total electrons = 14, ignoring core 1s orbitals):

• Valence molecular orbitals: σ2s2, σ*2s2, π2px2, π2py2, σ2pz2
• Bonding electrons: σ2s2 (2 electrons), π2px2 and π2py2 (4 electrons), σ2pz2 (2 electrons) → total bonding electrons = 2 + 4 + 2 = 8
• Antibonding electrons: σ*2s2 (2 electrons)
• Bond order = (number of bonding electrons - number of antibonding electrons) / 2 = (8 - 2) / 2 = 6 / 2 = 3

For O2 (total electrons = 16, ignoring core 1s orbitals):

• Valence molecular orbitals: σ2s2, σ*2s2, σ2pz2, π2px2, π2py2, π*2px1, π*2py1
• Bonding electrons: σ2s2 (2 electrons), σ2pz2 (2 electrons), π2px2 and π2py2 (4 electrons) → total bonding electrons = 2 + 2 + 4 = 8
• Antibonding electrons: σ*2s2 (2 electrons), π*2px1 and π*2py1 (2 electrons) → total antibonding electrons = 2 + 2 = 4
• Bond order = (8 - 4) / 2 = 4 / 2 = 2

For O2- (superoxide ion, total electrons = 16 + 1 = 17, ignoring core 1s orbitals):

• Valence molecular orbitals: σ2s2, σ*2s2, σ2pz2, π2px2, π2py2, π*2px2, π*2py1 (or equivalent due to degeneracy)
• Bonding electrons: same as O2 → σ2s2 (2), σ2pz2 (2), π2px2 and π2py2 (4) → total bonding electrons = 8
• Antibonding electrons: σ*2s2 (2 electrons), π* orbitals have 3 electrons (since O2 has 2 in π* and O2- adds one more) → total antibonding electrons = 2 + 3 = 5
• Bond order = (8 - 5) / 2 = 3 / 2 = 1.5

Summary of bond orders:

• N2: bond order = 3
• O2: bond order = 2
• O2-: bond order = 1.5

Since bond dissociation energy increases with bond order, the order should be N2 > O2 > O2-.

Now, comparing with the options:

• A: N2 > O2- > O2 → incorrect because O2 should be greater than O2-
• B: O2- > O2 > N2 → incorrect because N2 has the highest bond order
• C: N2 > O2 > O2- → matches our order
• D: O2 > O2- > N2 → incorrect because N2 should be the highest

Hence, the correct answer is Option C.