Explanation:

\(\mathrm{O}_{2}^{2-}\) (Number of electrons \(=18\) does not contain unpaired electrons)
\({\rm{O}}_2^{2 - }\)
\( = \sigma 1\;{{\rm{s}}^2},\mathop \sigma \limits^* 1\;{{\rm{s}}^2},\sigma 2\;{{\rm{s}}^2},\mathop \sigma \limits^* 2\;{{\rm{s}}^2},\sigma 2{\rm{p}}{{\rm{z}}^2},\pi 2{\rm{p}}_z^2\)
\( \approx {\rm{\pi 2p}}_{\rm{y}}^{\rm{2}}{\rm{,}}\mathop {\rm{\pi }}\limits^{\rm{*}} {\rm{2p}}_{\rm{x}}^{\rm{2}} \approx \mathop {\rm{\pi }}\limits^{\rm{*}} {\rm{2p}}_{\rm{y}}^{\rm{2}}\)

Explanation:

Explanation:

According to molecular orbital theory, Number of unpaired electrons in \({{\rm{O}}_{\rm{2}}}\) molecule is two, whereas in \({\rm{O}}_{\rm{2}}^{\rm{ + }}\) molecule is one, so paramagnetic character decreases in the conversion of \({{\rm{O}}_{\rm{2}}}\,\,{\rm{to}}\,\,{\rm{O}}_{\rm{2}}^{\rm{ + }}\).
\({\rm{Bond}}\,\,{\rm{order = }}\left( {\frac{{{{\rm{N}}_{\rm{b}}}{\rm{ - }}{{\rm{N}}_{\rm{a}}}}}{{\rm{2}}}} \right)\)
\(\therefore \,\,{\rm{Bond}}\,\,{\rm{order}}\,\,{\rm{in}}\) \({{\rm{O}}_{\rm{2}}}{\rm{ = }}\left( {\frac{{{\rm{8 - 4}}}}{{\rm{2}}}} \right){\rm{ = 2}}\)
Bond order in \({\rm{O}}_{\rm{2}}^{\rm{ + }}{\rm{ = }}\left( {\frac{{{\rm{8 - 3}}}}{{\rm{2}}}} \right){\rm{ = 2}}{\rm{.5}}\)
\(\therefore \) Bond order increases in the conversion of \({{\rm{O}}_{\rm{2}}}\,\,{\rm{to}}\,\,{\rm{O}}_{\rm{2}}^{\rm{ + }}\).

Explanation:

The bond order of \({{\rm{B}}_{\rm{2}}}\) molecule is 1. The ground state electron configuration of B is \({\rm{1}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{p}}^{\rm{1}}}\). So, \({{\rm{B}}_{\rm{2}}}\) molecule has a total of ten electrons, which are arranged in MOs.
\({\left( {{\rm{\sigma 1s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{1s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{2s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{2s}}} \right)^{\rm{2}}}\left( {{{\rm{\pi }}_{{\rm{2p}}_{\rm{y}}^{\rm{1}}}}{\rm{ = }}{{\rm{\pi }}_{{\rm{2p}}_{\rm{y}}^{\rm{1}}}}} \right)\)
Bond order \({\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}\) (Number of bonding electrons - number of anti-bonding electrons)
\({\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}\left( {{\rm{6 - 4}}} \right){\rm{ = 1}}\)

Explanation:

\(\mathrm{O}_{2}^{2-}\) (Number of electrons \(=18\) does not contain unpaired electrons)
\({\rm{O}}_2^{2 - }\)
\( = \sigma 1\;{{\rm{s}}^2},\mathop \sigma \limits^* 1\;{{\rm{s}}^2},\sigma 2\;{{\rm{s}}^2},\mathop \sigma \limits^* 2\;{{\rm{s}}^2},\sigma 2{\rm{p}}{{\rm{z}}^2},\pi 2{\rm{p}}_z^2\)
\( \approx {\rm{\pi 2p}}_{\rm{y}}^{\rm{2}}{\rm{,}}\mathop {\rm{\pi }}\limits^{\rm{*}} {\rm{2p}}_{\rm{x}}^{\rm{2}} \approx \mathop {\rm{\pi }}\limits^{\rm{*}} {\rm{2p}}_{\rm{y}}^{\rm{2}}\)

Explanation:

Explanation:

According to molecular orbital theory, Number of unpaired electrons in \({{\rm{O}}_{\rm{2}}}\) molecule is two, whereas in \({\rm{O}}_{\rm{2}}^{\rm{ + }}\) molecule is one, so paramagnetic character decreases in the conversion of \({{\rm{O}}_{\rm{2}}}\,\,{\rm{to}}\,\,{\rm{O}}_{\rm{2}}^{\rm{ + }}\).
\({\rm{Bond}}\,\,{\rm{order = }}\left( {\frac{{{{\rm{N}}_{\rm{b}}}{\rm{ - }}{{\rm{N}}_{\rm{a}}}}}{{\rm{2}}}} \right)\)
\(\therefore \,\,{\rm{Bond}}\,\,{\rm{order}}\,\,{\rm{in}}\) \({{\rm{O}}_{\rm{2}}}{\rm{ = }}\left( {\frac{{{\rm{8 - 4}}}}{{\rm{2}}}} \right){\rm{ = 2}}\)
Bond order in \({\rm{O}}_{\rm{2}}^{\rm{ + }}{\rm{ = }}\left( {\frac{{{\rm{8 - 3}}}}{{\rm{2}}}} \right){\rm{ = 2}}{\rm{.5}}\)
\(\therefore \) Bond order increases in the conversion of \({{\rm{O}}_{\rm{2}}}\,\,{\rm{to}}\,\,{\rm{O}}_{\rm{2}}^{\rm{ + }}\).

Explanation:

The bond order of \({{\rm{B}}_{\rm{2}}}\) molecule is 1. The ground state electron configuration of B is \({\rm{1}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{p}}^{\rm{1}}}\). So, \({{\rm{B}}_{\rm{2}}}\) molecule has a total of ten electrons, which are arranged in MOs.
\({\left( {{\rm{\sigma 1s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{1s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{2s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{2s}}} \right)^{\rm{2}}}\left( {{{\rm{\pi }}_{{\rm{2p}}_{\rm{y}}^{\rm{1}}}}{\rm{ = }}{{\rm{\pi }}_{{\rm{2p}}_{\rm{y}}^{\rm{1}}}}} \right)\)
Bond order \({\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}\) (Number of bonding electrons - number of anti-bonding electrons)
\({\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}\left( {{\rm{6 - 4}}} \right){\rm{ = 1}}\)

Explanation:

\(\mathrm{O}_{2}^{2-}\) (Number of electrons \(=18\) does not contain unpaired electrons)
\({\rm{O}}_2^{2 - }\)
\( = \sigma 1\;{{\rm{s}}^2},\mathop \sigma \limits^* 1\;{{\rm{s}}^2},\sigma 2\;{{\rm{s}}^2},\mathop \sigma \limits^* 2\;{{\rm{s}}^2},\sigma 2{\rm{p}}{{\rm{z}}^2},\pi 2{\rm{p}}_z^2\)
\( \approx {\rm{\pi 2p}}_{\rm{y}}^{\rm{2}}{\rm{,}}\mathop {\rm{\pi }}\limits^{\rm{*}} {\rm{2p}}_{\rm{x}}^{\rm{2}} \approx \mathop {\rm{\pi }}\limits^{\rm{*}} {\rm{2p}}_{\rm{y}}^{\rm{2}}\)

Explanation:

Explanation:

According to molecular orbital theory, Number of unpaired electrons in \({{\rm{O}}_{\rm{2}}}\) molecule is two, whereas in \({\rm{O}}_{\rm{2}}^{\rm{ + }}\) molecule is one, so paramagnetic character decreases in the conversion of \({{\rm{O}}_{\rm{2}}}\,\,{\rm{to}}\,\,{\rm{O}}_{\rm{2}}^{\rm{ + }}\).
\({\rm{Bond}}\,\,{\rm{order = }}\left( {\frac{{{{\rm{N}}_{\rm{b}}}{\rm{ - }}{{\rm{N}}_{\rm{a}}}}}{{\rm{2}}}} \right)\)
\(\therefore \,\,{\rm{Bond}}\,\,{\rm{order}}\,\,{\rm{in}}\) \({{\rm{O}}_{\rm{2}}}{\rm{ = }}\left( {\frac{{{\rm{8 - 4}}}}{{\rm{2}}}} \right){\rm{ = 2}}\)
Bond order in \({\rm{O}}_{\rm{2}}^{\rm{ + }}{\rm{ = }}\left( {\frac{{{\rm{8 - 3}}}}{{\rm{2}}}} \right){\rm{ = 2}}{\rm{.5}}\)
\(\therefore \) Bond order increases in the conversion of \({{\rm{O}}_{\rm{2}}}\,\,{\rm{to}}\,\,{\rm{O}}_{\rm{2}}^{\rm{ + }}\).

Explanation:

The bond order of \({{\rm{B}}_{\rm{2}}}\) molecule is 1. The ground state electron configuration of B is \({\rm{1}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{p}}^{\rm{1}}}\). So, \({{\rm{B}}_{\rm{2}}}\) molecule has a total of ten electrons, which are arranged in MOs.
\({\left( {{\rm{\sigma 1s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{1s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{2s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{2s}}} \right)^{\rm{2}}}\left( {{{\rm{\pi }}_{{\rm{2p}}_{\rm{y}}^{\rm{1}}}}{\rm{ = }}{{\rm{\pi }}_{{\rm{2p}}_{\rm{y}}^{\rm{1}}}}} \right)\)
Bond order \({\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}\) (Number of bonding electrons - number of anti-bonding electrons)
\({\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}\left( {{\rm{6 - 4}}} \right){\rm{ = 1}}\)

Explanation:

\(\mathrm{O}_{2}^{2-}\) (Number of electrons \(=18\) does not contain unpaired electrons)
\({\rm{O}}_2^{2 - }\)
\( = \sigma 1\;{{\rm{s}}^2},\mathop \sigma \limits^* 1\;{{\rm{s}}^2},\sigma 2\;{{\rm{s}}^2},\mathop \sigma \limits^* 2\;{{\rm{s}}^2},\sigma 2{\rm{p}}{{\rm{z}}^2},\pi 2{\rm{p}}_z^2\)
\( \approx {\rm{\pi 2p}}_{\rm{y}}^{\rm{2}}{\rm{,}}\mathop {\rm{\pi }}\limits^{\rm{*}} {\rm{2p}}_{\rm{x}}^{\rm{2}} \approx \mathop {\rm{\pi }}\limits^{\rm{*}} {\rm{2p}}_{\rm{y}}^{\rm{2}}\)

Explanation:

Explanation:

According to molecular orbital theory, Number of unpaired electrons in \({{\rm{O}}_{\rm{2}}}\) molecule is two, whereas in \({\rm{O}}_{\rm{2}}^{\rm{ + }}\) molecule is one, so paramagnetic character decreases in the conversion of \({{\rm{O}}_{\rm{2}}}\,\,{\rm{to}}\,\,{\rm{O}}_{\rm{2}}^{\rm{ + }}\).
\({\rm{Bond}}\,\,{\rm{order = }}\left( {\frac{{{{\rm{N}}_{\rm{b}}}{\rm{ - }}{{\rm{N}}_{\rm{a}}}}}{{\rm{2}}}} \right)\)
\(\therefore \,\,{\rm{Bond}}\,\,{\rm{order}}\,\,{\rm{in}}\) \({{\rm{O}}_{\rm{2}}}{\rm{ = }}\left( {\frac{{{\rm{8 - 4}}}}{{\rm{2}}}} \right){\rm{ = 2}}\)
Bond order in \({\rm{O}}_{\rm{2}}^{\rm{ + }}{\rm{ = }}\left( {\frac{{{\rm{8 - 3}}}}{{\rm{2}}}} \right){\rm{ = 2}}{\rm{.5}}\)
\(\therefore \) Bond order increases in the conversion of \({{\rm{O}}_{\rm{2}}}\,\,{\rm{to}}\,\,{\rm{O}}_{\rm{2}}^{\rm{ + }}\).

Explanation:

The bond order of \({{\rm{B}}_{\rm{2}}}\) molecule is 1. The ground state electron configuration of B is \({\rm{1}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{s}}^{\rm{2}}}{\rm{2}}{{\rm{p}}^{\rm{1}}}\). So, \({{\rm{B}}_{\rm{2}}}\) molecule has a total of ten electrons, which are arranged in MOs.
\({\left( {{\rm{\sigma 1s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{1s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{2s}}} \right)^{\rm{2}}}{\left( {{{\rm{\sigma }}^{\rm{*}}}{\rm{2s}}} \right)^{\rm{2}}}\left( {{{\rm{\pi }}_{{\rm{2p}}_{\rm{y}}^{\rm{1}}}}{\rm{ = }}{{\rm{\pi }}_{{\rm{2p}}_{\rm{y}}^{\rm{1}}}}} \right)\)
Bond order \({\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}\) (Number of bonding electrons - number of anti-bonding electrons)
\({\rm{ = }}\frac{{\rm{1}}}{{\rm{2}}}\left( {{\rm{6 - 4}}} \right){\rm{ = 1}}\)