The observed bond length of `N_(2)^(+)` is larger than `N_(2)` while the bond length in `NO^(+)` is less than in NO. Why ?

Explanation

(a) (i) By molecular orbital theory, the bond order of both `N_(2)^(+)` is 2.5 whereas `N_(2)` is 3.
(ii) `N_(2) has 5e^(-)` in the antibonding molecular orbital whereas `N_(2)^(+) has 4e^(-)` in the antibonding molecular orbital. So `N_(2)^(+)` will make a stronger and shorter bond lenght.
9iii) More the bond order and bond strength, and lesser will be the bond length
So we can easily conclude `N-(2)` has more bond length than `N_(2)`
Bond order in `N_(2) = (N_(b)-N_(a))/(2)=(10 -4)/(2)=(6)/(2)=3`
Bond order in `N_(2)^(+)=(N_(b)-N_(a))/(2)=(9-4)/(2)=(5)/(2)=2.5`
So, `N_(2)` is more stable than `N_(2)^(+)`. But bond length `N_(2)^(+)` is greater than `N_(2)`.
(b) `NO^(+)` & NO
Bond order of NO = 2.5
Bond order of `NO^(+) = 3`
Due to lesser bond order in NO, the bond length is greater than `NO^(+)`
So, `NO^(+)` bond lenght is shorter than NO bond lenght.