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Molecular orbital theory is based on the principle of linear combination of atomic orbitals. According to this approach when atomic orbitals of the atoms come closer, they undergo constructive interference as well as destructive interference giving molecular orbitals, i.e., two atomic orbitals overlap to form two molecular orbitals, one of which lies at a lower energy level (bonding molecular orbital) than the other at higher energy level (antibonding molecular orbital). Each molecular orbital can hold one or two electrons in accordance with Pauli exclusion
principle and Hund's rule of maximum multiplicity. For molecules upto \( \mathrm{N}_{2} \), the order of filling of orbitals is:
\[
\begin{aligned}
\sigma(1 s), \sigma(1 s), \sigma(2 s), \sigma^{*}(2 s), \pi\left(2 p_{x}\right)=\pi\left(2 p_{y}\right), \sigma\left(2 p_{z}\right), \pi\left(2 p_{x}\right) \\
&=\stackrel{*}{\pi}\left(2 p_{y}\right),{ }^{*} \sigma\left(2 p_{z}\right)
\end{aligned}
\]
and for molecules after \( \mathrm{N}_{2} \), the order of filling is:
\[
\begin{aligned}
\sigma(1 s), \sigma(1 s), \sigma(2 s), \sigma(2 s), \sigma\left(2 p_{2}\right), \pi\left(2 p_{x}\right) &=\pi\left(2 p_{y}\right), \pi^{*}\left(2 p_{x}\right) \\
&=\pi\left(2 p_{y}\right), \sigma^{*}\left(2 p_{z}\right)
\end{aligned}
\]
Bond order \( =\frac{1}{2} \) [bonding electrons \( - \) antibonding electrons]
Bond order gives the following information:
(i) If bond order is greater than zero, the molecule/ion exists otherwise not.
(ii) Higher the bond order, higher is the bond dissociation energy.
(iii) Higher the bond order, greater is the bond stability.
(iv) Higher the bond order, shorter is the bond length.
\( \mathrm{O}_{2}^{2-} \) will have:
(A) bond order lower than \( \mathrm{O}_{2} \)
(B) bond order higher than \( \mathrm{O}_{2} \)
(C) bond order equal to \( \mathrm{O}_{2} \)
(D) bond order equal to \( \mathrm{H}_{2} \)
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