Greater the bond order, shorter is the bond length.
`therefore` Bond order `prop (1)/("bond length")`
(i) Electronic configurations and bond orders of `C_(2) and C_(2)^(2-)` ions :
EC of `C_(2) = KK sigma 2s^(2), overset("*")(sigma) 2s^(2), pi 2p_(x)^(2), pi 2p_(y)^(2)`
Bond order `= (1)/(2) (6-2) = 2`
EC of `C_(2)^(2-) = KK sigma 2s^(2), overset("*")(sigma) 2s^(2), pi 2p_(x)^(2), pi 2p_(y)^(2), sigma 2p_(z)^(2)`
Bond order `= (1)/(2) (8 - 2) = 3`
`therefore` The order of bond lengths `: C_(2) gt C_(2)^(2-)`
(ii) Electronic configurations and bond orders of `B_(2)^(+) and B_(2)`
EC of `B_(2) = KK sigma 2s^(2), overset("*")(sigma) 2s^(2), pi 2p_(x)^(1), pi 2p_(y)^(1)`
Bond order `= (1)/(2) (4-2) = 1`
EC of `B_(2)^(+) = KK sigma 2s^(2), overset("*")(sigma) 2s^(2),pi 2p_(x)^(1)`
Bond order `= (1)/(2) (3-2) = (1)/(2)`
`therefore` The order of bond lengths `: B_(2)^(+) gt B_(2)`
(iii) Electronic configurations and bond orders of `Li_(2) and Li_(2)^(+)`
EC of `Li_(2) = KK sigma 2s^(2)`
Bond order `= (1)/(2) (2-0) = 1`
EC of `Li_(2)^(+) = KK sigma 2s^(1)`
Bond order `= (1)/(2) (1-0) = (1)/(2)`
`therefore` The order of bond lengths `: Li_(2)^(+) gt Li_(2)`
(iv) Electronic configuration and bond orders of `N_(2) and N_(2)^(+)`
EC of `N_(2) = KK sigma 2s^(2), overset("*")(sigma)2s^(2), pi 2p_(x)^(2), pi 2p_(y)^(2), sigma 2p_(z)^(2)`
Bond order `= (1)/(2) (8-2) = 3`
EC of `N_(2)^(+) = KK sigma 2s^(2), overset("*")(sigma)2s^(2), pi 2p_(x)^(2), pi 2p_(y)^(2), sigma 2p_(z)^(1)`
Bond order `= (1)/(2) (7-2) = 2.5`
`therefore` The order of bond lengths `= N_(2)^(+) gt N_(2)`
(v) Electronic configurations and bond orders of `O_(2) and O_(2)^(-)` :
EC of `O_(2) = KK sigma 2s^(2), overset("*")(sigma) 2s^(2), sigma 2p_(z)^(2), pi 2p_(x)^(2) pi 2p_(y)^(2), overset("*")(pi)2p_(x)^(1), overset("*")(pi) 2p_(y)^(1)`
Bond order `= (1)/(2) (8-4) = 2`
EC of `O_(2)^(-) = KK sigma 2s^(2), overset("*")(sigma)2s^(2), sigma 2p_(z)^(2), pi 2p_(x)^(2), pi 2p_(y)^(2), overset("*")(pi)2p_(x)^(2), overset("*")(pi) 2p_(y)^(1)`
Bond order `= (1)/(2) (8-5) = 1.5`
`therefore` The correct order of bond lengths `= O_(2)^(-) gt O_(2)`
