AIEEE 2006 Solved Paper

(A) Molecular orbital configuration of $\mathrm{O}_2^{2-}$ (18 electrons) is $\sigma_{1s^{2}} \sigma_{1s^{2}}^{*} \sigma_{2s^{2}} \sigma_{2s^{2}}^{*} \sigma_{2p_z^{2}} \pi_{2p_x^{2}}=\pi_{2p_y^{2}} \pi_{2p_x^{2}}^{*}=\pi_{2p_y^{2}}^{*}$ So $\mathrm{O}_2^{2-}$ has no unpaired electrons. (B) Molecular orbital configuration of $\mathrm{B}_2$ ( 10 electrons) is $\sigma_{1s^{2}} \sigma_{1s^{2}}^{*} \sigma_{2s^{2}} \sigma_{2s^{2}}^{*} \pi_{2p_x^{1}}=\pi_{2p_y^{1}}$ Here in $\mathrm{B}_2, 2$ unpaired electrons present. (C) Molecular orbital configuration of $\mathrm{N}_2^{+}$(13 electrons) $= \sigma_{1s^{2}} \sigma_{1s^{2}}^{*} \sigma_{2s^{2}} \sigma_{2s^{2}}^{*} \pi_{2p_x^{2}}=\pi_{2p_y^{2}} \sigma_{2p_z^{1}}$Here in $\mathrm{N}_2^{+}, 1$ unpaired electron present. (D) Molecular orbital configuration of $\mathrm{O}_2$ ( 16 electrons) isSo $\mathrm{O}_2$ has 2 unpaired electrons. $\sigma_{1s^{2}} \sigma_{1s^{2}}^{*} \sigma_{2s^{2}} \sigma_{2s^{2}}^{*} \sigma_{2p_z^{2}} \pi_{2p_x^{2}}=\pi_{2p_y^{2}} \pi_{2p_x^{1}}^{*}=\pi_{2p_y^{1}}^{*}$ So $\mathrm{O}_2$ has 2 unpaired electrons.