Arrange the following species in the correct order of their stability
`C _(2), Li _(2),O_(2) ^(+) He _(2) ^(+)`

Options

A. `Li _(2) lt He _(2) ^(+) lt O _(2) ^(+)`
B. `C _(2) lt O _(2) ^(+) lt Li _(2) He _(2) ^(+)`
C. `He _(2) ^(+) lt Li _(2) lt C _(2)lt O _(2) ^(+)`
D. `O _(2) ^(+) lt C_(2) lt Li _(2) lt He _(2) ^(+)`

Answer

C

Explanation

Higher the bond order, more is the stability. The bond order of the given species can be calculated as
MO configuration of `C _(2) = (6+6 = 12)`
`= sigma 1 s ^(2), sigma ^(**)1s ^(2) , sigma ^(**) 2s ^(2), pi 2p_(x) ^(2) ~~ pi 2p_(y) ^(2)`
`BO = ( N _(b) - N _(a))/( 2) = ( 8-4)/( 2 ) = (4)/(2) = 2 `
MO configuration of `Li _(2) = (3 +3 = 6) = sigma 1 s ^(2), sigma ^(**) 1s ^(2), sigma 2 s ^(2)`
`BO = ( 4-2)/(2) =1 `
MO configuration of `O _(2) ( 8 + 8-1 =15)`
`= sigma 1s ^(2) , sigma ^(**), sigma 2 s ^(2), sigma 2 p _(z) ^(2)pi 2p_(x) ^(2)`
`~~pi 2p_(y) ^(3) overset(**) (pi) 2p _(x) ^(1)`
`BO = (10 -5)/(2) = 2.5`
MO configuration of `He _(2) = (2 + 2 -1=3) = sigma 1 s ^(2), sigma ^(**) 1s ^(2)`
`BO = (2 -1)/(2 ) = (1)/(2) = 0.5`
Thus, the order of bond orders of the given species is
`H e _(2) ^(+) lt Li _(2) lt C _(2) lt O _(2) ^(+)`
Since bond order `alpha` statibity.
Thus, order of stability will also be the same.