Question

Which of the following are predicted by the molecular orbital model to be stable diatomic species?

$$\begin{gathered} \mathbf{a}\mathbf{.}{\mathbf{H}}_{\mathbf{2}}^{\mathbf{+}}\mathbf{,}\mathbf{}{\mathbf{H}}_{\mathbf{2}\mathbf{,}\mathbf{}}{\mathbf{H}}_{\mathbf{2}}^{\mathbf{-}}\mathbf{,}\mathbf{}{\mathbf{H}}_{\mathbf{2}}^{\mathbf{2}\mathbf{-}} \\ \mathbf{b}\mathbf{.}{\mathbf{N}}_{\mathbf{2}}^{\mathbf{2}\mathbf{-}}\mathbf{,}\mathbf{}{\mathbf{O}}_{\mathbf{2}}^{\mathbf{2}\mathbf{-}}\mathbf{,}\mathbf{}{\mathbf{F}}_{\mathbf{2}}^{\mathbf{2}\mathbf{-}} \\ \mathbf{c}\mathbf{.}\mathbf{}{\mathbf{Be}}_{\mathbf{2}\mathbf{,}}\mathbf{}{\mathbf{B}}_{\mathbf{2}}\mathbf{,}\mathbf{}\mathbf{}{\mathbf{Ne}}_{\mathbf{2}} \end{gathered}$$

Short answer

The stable diatomic species are:

(a) ${\mathrm{H}}_2$

(b) ${\mathrm{N}}_2^{-}$

(c) ${\mathrm{B}}_2$

Step-by-step solution

Part-(a)

Electronic configuration of H atom: $1S^1$

role="math" localid="1664121351322" ${\mathrm{H}}_2^{+}:{\left(\mathrm{\sigma }1\mathrm{s}\right)}^1$

B.O.role="math" localid="1664121702711" $=\frac{1-0}{2}=\frac{1}{2}$, stable

role="math" localid="1664121447221" ${\mathrm{H}}_2^{}:{\left(\mathrm{\sigma }1\mathrm{s}\right)}^2$

B.O.$=\frac{2-0}{2}=1$, stable

$H_2^{+}$:${\left(\sigma 1s\right)}^2{\left(\sigma 1s*\right)}^1$

B.O.$=\frac{2-1}{2}=\frac{1}{2}$, stable

${\mathrm{H}}_2^{2-}:{\left(\mathrm{\sigma }1\mathrm{s}\right)}^2{\left(\mathrm{\sigma }1\mathrm{s}*\right)}^2$

B.O.$=\left(\frac{2-2}{2}\right)=0$ , not stable

Part-(b)

${\mathrm{N}}_2^{2-}:{\left(\mathrm{\sigma }2\mathrm{s}\right)}^2{\left(\mathrm{\sigma }2\mathrm{s}*\right)}^2{\left(\mathrm{\pi }2\mathrm{p}\right)}^4{\left(\mathrm{\sigma }2\mathrm{p}\right)}^2{\left(\mathrm{\sigma }2\mathrm{p}*\right)}^2$

B.O.$=\frac{8-4}{2}=2$, stable

role="math" localid="1664122879471" $O_2^{2-}:{\left(\mathrm{\sigma }2\mathrm{s}\right)}^2{(\mathrm{\sigma }2\mathrm{s}*)}^2{\left(\mathrm{\sigma }2\mathrm{p}\right)}^2{\left(\mathrm{\pi }2\mathrm{p}\right)}^4{(\mathrm{\pi }2\mathrm{p}*)}^4$

B.O.$=\frac{8-6}{2}=1$, stable

role="math" localid="1664122984470" ${\mathrm{F}}_2^{2-}:{\left(\mathrm{\sigma }2\mathrm{s}\right)}^2{(\mathrm{\sigma }2\mathrm{s}*)}^2{\left(\mathrm{\sigma }2\mathrm{p}\right)}^2{\left(\mathrm{\pi }2\mathrm{p}\right)}^4{(\mathrm{\pi }2\mathrm{p}*)}^4{(\mathrm{\sigma }2\mathrm{p}*)}^2$

B.O.data-custom-editor="chemistry" $=\frac{8-8}{2}=0$ , not stable

Part-(3)

${\mathrm{Be}}_2:{\left(\mathrm{\sigma }2\mathrm{s}\right)}^2{\left(\mathrm{\sigma }2\mathrm{s}*\right)}^2$

B.O.$=\frac{2-2}{2}=0$, not stable

$B_2:{\left(\mathrm{\sigma }2\mathrm{s}\right)}^2{(\mathrm{\sigma }2\mathrm{s}*)}^2{\left(\mathrm{\pi }2\mathrm{p}\right)}^2$

B.O.$=\frac{4-2}{2}=1$, stable

$N{e}_2:{\left(\mathrm{\sigma }2\mathrm{s}\right)}^2{(\mathrm{\sigma }2\mathrm{s}*)}^2{\left(\mathrm{\pi }2\mathrm{p}\right)}^4{(\mathrm{\pi }2\mathrm{p}*)}^4{(\mathrm{\sigma }2p*)}^2$

B.O.$=\frac{8-8}{2}=0$ , not stable