Question

According to molecular orbital theory, the species among the following that do not exist are:

• A. ${{\mathrm{He}}_2}^{-}$
• B. ${{\mathrm{He}}_2}^{+}$
• C. ${\mathrm{O}}_2^{2-}$
• D. ${\mathrm{Be}}_2$

Answer 1

The correct option is D

${\mathrm{Be}}_2$

Answer:(D)

Explanation for correct option:

$$\begin{gathered} \left(\mathrm{D}\right)\mathrm{Electronic}\mathrm{configuration}\mathrm{of}{\mathrm{Be}}_2=\left(\mathrm{\sigma }1{\mathrm{s}}^2\right),\left({\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\right),\left(\mathrm{\sigma }2{\mathrm{s}}^2\right),\left({\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\right) \\ \mathrm{Bond}\mathrm{order}\mathrm{of}{\mathrm{Be}}_2=\frac{{\mathrm{N}}_{\mathrm{b}}-{\mathrm{N}}_{\mathrm{a}}}{2}=\frac{4-4}{2}=0 \\ \mathrm{According}\mathrm{to}\mathrm{M}.\mathrm{O}.\mathrm{T},\mathrm{If}\mathrm{bond}\mathrm{order}\mathrm{of}\mathrm{chemical}\mathrm{species}\mathrm{is}\mathrm{zero}\mathrm{then}\mathrm{that}\mathrm{chemical}\mathrm{species}\mathrm{does}\mathrm{not}\mathrm{exist}. \end{gathered}$$

Explanation for incorrect option:

$$\begin{gathered} \left(\mathrm{A}\right)\mathrm{Electronic}\mathrm{configuration}\mathrm{of}{{\mathrm{He}}_2}^{-}=\left(\mathrm{\sigma }1{\mathrm{s}}^2\right),\left({\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\right) \\ \mathrm{Bond}\mathrm{order}=\frac{{\mathrm{N}}_{\mathrm{b}}-{\mathrm{N}}_{\mathrm{a}}}{2}=\frac{2-1}{2}=0.5 \\ \left(\mathrm{B}\right)\mathrm{Electronic}\mathrm{configuration}\mathrm{of}{{\mathrm{He}}_2}^{+}=\left(\mathrm{\sigma }1{\mathrm{s}}^2\right),\left({\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\right) \\ \mathrm{Bond}\mathrm{order}\mathrm{of}=\frac{{\mathrm{N}}_{\mathrm{b}}-{\mathrm{N}}_{\mathrm{a}}}{2}=\frac{2-1}{2}=0.5 \\ \left(\mathrm{D}\right)\mathrm{Electronic}\mathrm{configuration}\mathrm{of}{0}_2^{2-}=\left(\mathrm{\sigma }1{\mathrm{s}}^2\right),\left({\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\right),\left(\mathrm{\sigma }2{\mathrm{s}}^2\right),\left({\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\right),\left(\mathrm{\sigma }2{{\mathrm{p}}^2}_{\mathrm{z}}\right) \\ \left(\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{y}}}^2\right),\left(\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{x}}}^2\right)=\left({\mathrm{\pi }}^{*}2{{\mathrm{p}}_{\mathrm{y}}}^2\right) \\ \mathrm{Bond}\mathrm{order}=\frac{{\mathrm{N}}_{\mathrm{b}}-{\mathrm{N}}_{\mathrm{a}}}{2}=\frac{10-8}{2}=1 \end{gathered}$$

Hence option (D) is correct.