A) \[{{C}_{2}}>C_{2}^{2-}\]
B) \[B_{2}^{+}>{{B}_{2}}\]
C) \[Li_{2}^{+}>L{{i}_{2}}\]
D) \[N_{2}^{+}>{{N}_{2}}\]
E) \[{{O}_{2}}>O_{2}^{-}\]
Correct Answer: E
Solution :
Greater the bond order, shorter is the bond length. \[\therefore \] \[Bond\text{ }order\propto \frac{1}{bond\text{ }length}\] (i) Electronic configurations and bond orders of\[{{C}_{2}}\]and\[C_{2}^{2-}\]ions: EC of \[{{C}_{2}}=KK\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{2},\pi 2p_{y}^{2}\] Bond order \[=\frac{1}{2}(6-2)=2\] EC of \[C_{2}^{2-}=KK\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{2},\pi 2p_{y}^{2},\sigma 2p_{z}^{2}\] Bond order\[=\frac{1}{2}(8-2)=3\] \[\therefore \]The order of bond lengths: \[B_{2}^{+}>{{B}_{2}}\] (ii) Electronic configurations and bond orders of\[B_{2}^{+}\]and\[{{B}_{2}}\] EC of \[{{B}_{2}}=KK\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{1},\pi 2p_{x}^{1},\pi 2p_{1}^{y}\] Bond order\[=\frac{1}{2}(4-2)=1\] EC of\[B_{2}^{+}=KK\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{1}\] Bond order\[=\frac{1}{2}(3-2)=\frac{1}{2}\] \[\therefore \]The order of bond lengths:\[B_{2}^{+}>{{B}_{2}}\] (iii) Electronic configurations and bond orders of\[L{{i}_{2}}\]and \[Li_{2}^{+}\] EC of \[L{{i}_{2}}=KK\,\sigma 2{{s}^{2}}\] Bond order \[=\frac{1}{2}(2-0)=1\] EC of \[Li_{2}^{+}=\,KK\,\sigma 2{{s}^{1}}\] Bond order \[=\frac{1}{2}(1-0)=\frac{1}{2}\] \[\therefore \]The order of bond lengths: \[Li_{2}^{+}>L{{i}_{2}}\] (iv) Electronic configurations and bond orders of\[{{N}_{2}}\]and\[N_{2}^{+}\] EC of \[{{N}_{2}}=KK\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{2},\pi 2p_{y}^{2},\sigma 2p_{z}^{2}\] Bond order \[=\frac{1}{2}(8-2)\,=3\] EC of \[N_{2}^{+}=KK\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\pi 2p_{x}^{2},\pi 2p_{y}^{2},\sigma 2p_{z}^{1}\] Bond order\[=\frac{1}{2}(7-2)=2.5\] \[\therefore \]The order of bond lengths\[=N_{2}^{+}>{{N}_{2}}\] (v) Electronic configurations and bond orders of\[{{O}_{2}}\]and\[O_{2}^{-}\]: EC of \[{{O}_{2}}=KK\,\,\sigma 2{{s}^{2}},{{\sigma }^{*}}2{{s}^{2}},\sigma 2p_{z}^{2},\pi 2p_{x}^{2}\] \[\pi 2p_{y}^{2},\overset{*}{\mathop{\pi }}\,2p_{x}^{1},\overset{*}{\mathop{\pi }}\,2p_{y}^{1}\] Bond order\[=\frac{1}{2}\,(8-4)=2\] EC of \[O_{2}^{-}=KK\sigma 2{{s}^{2}},\overset{*}{\mathop{\sigma }}\,2{{s}^{2}},\pi 2p_{z}^{2},\pi 2p_{x}^{2},\pi 2p_{y}^{2},\] \[\overset{*}{\mathop{\pi }}\,2p_{x}^{2},\overset{*}{\mathop{\pi }}\,2p_{y}^{1}\] Bond order \[=\frac{1}{2}(8-5)=1.5\] \[\therefore \]The correct order of bond lengths \[=O_{2}^{-}>{{O}_{2}}\]
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