The increasing order of the bond order of $O_{2}, O_{2}^{+}, O_{2}^{-}$ and $O_{2}^{2 -}$ is:

O_{2}^{+}, O_{2}, O_{2}^{-}, O_{2}^{2 -}

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O_{2}^{2 -}, O_{2}^{-}, O_{2}^{+}, O_{2}

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O_{2}, O_{2}^{+}, O_{2}^{-}, O_{2}^{2 -}

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O_{2}^{2 -}, O_{2}^{-}, O_{2}, O_{2}^{+}

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Solution

The correct option is C $O_{2}^{2 -}, O_{2}^{-}, O_{2}, O_{2}^{+}$
According to MOT bond order is given by the formula:

$B . O . = \frac{N_{B} - N_{A}}{2}$ where $N_{A}, N_{B}$ are the number of electrons in antibonding and bonding molecular orbital respectively,

Bond order for $O_{2} = \frac{10 - 6}{2} = 2$

Bond order for $O_{2}^{+} = \frac{10 - 5}{2} = 2.5$

Bond order for $O_{2}^{-} = \frac{10 - 7}{2} = 1.5$

Bond order for $O_{2}^{2 -} = \frac{10 - 8}{2} = 1$

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