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$\text{HINT: B.O. } = \frac{\text{N}_\text{b} - \text{N}_\text{a}}{2}\n\n\text{Explanation:}\n\text{1. Electronic configuration of } \text{O}_2 \text{ (16 electrons)} = \sigma_{1s}^2, \sigma_{1s}^{\ast 2}, \sigma_{2s}^2, \sigma_{2s}^{\ast 2}, \sigma_{2p_z}^2, \pi_{2p_x}^2 \approx \pi_{2p_y}^2, \pi_{2p_x}^{\ast 1} \approx \pi_{2p_y}^{\ast 1}\n\text{Bond order} = \frac{1}{2}(\text{N}_\text{b} - \text{N}_\text{a}) = \frac{1}{2}(10 - 6) = 2\n\n\text{2. Electronic configuration of } \text{O}_2^{+} \text{ (15 electrons)} = \sigma_{1s}^2, \sigma_{1s}^{\ast 2}, \sigma_{2s}^2, \sigma_{2s}^{\ast 2}, \sigma_{2p_z}^2, \pi_{2p_x}^2 \approx \pi_{2p_y}^2, \pi_{2p_x}^{\ast 1} \approx \pi_{2p_y}^{\ast 0}\n\text{Bond order} = \frac{1}{2}(\text{N}_\text{b} - \text{N}_\text{a}) = \frac{1}{2}(10 - 5) = 2.5\n\n\text{3. Electronic configuration of } \text{O}_2^{-} \text{ (17 electrons)} = \sigma_{1s}^2, \sigma_{1s}^{\ast 2}, \sigma_{2s}^2, \sigma_{2s}^{\ast 2}, \sigma_{2p_z}^2, \pi_{2p_x}^2 \approx \pi_{2p_y}^2, \pi_{2p_x}^{\ast 2} \approx \pi_{2p_y}^{\ast 1}\n\text{Bond order} = \frac{1}{2}(\text{N}_\text{b} - \text{N}_\text{a}) = \frac{1}{2}(10 - 7) = 1.5\n\n\text{4. Electronic configuration of } \text{O}_2^{2-} \text{ (18 electrons)} = \sigma_{1s}^2, \sigma_{1s}^{\ast 2}, \sigma_{2s}^2, \sigma_{2s}^{\ast 2}, \sigma_{2p_z}^2, \pi_{2p_x}^2 \approx \pi_{2p_y}^2, \pi_{2p_x}^{\ast 2} \approx \pi_{2p_y}^{\ast 2}\n\text{Bond order} = \frac{1}{2}(\text{N}_\text{b} - \text{N}_\text{a}) = \frac{1}{2}(10 - 8) = 1\n\n\text{Thus, } \text{O}_2^{-} \text{ shows the bond order 1.5}$

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