Question

Considering MOT comment on the stability:

• A. ${\mathrm{Li}}_2^{+}$ stable ${\mathrm{Li}}_2^{-}$unstable
• B. ${\mathrm{Li}}_2^{+}$unstable ${\mathrm{Li}}_2^{-}$unstable
• C. ${\mathrm{Li}}_2^{+}$unstable ${\mathrm{Li}}_2^{-}$ unstable
• D. ${\mathrm{Li}}_2^{+}$stable ${\mathrm{Li}}_2^{-}$ stable

Answer 1

The correct option is C

${\mathrm{Li}}_2^{+}$unstable ${\mathrm{Li}}_2^{-}$ unstable

Explanation for the correct option:

(C) ${\mathrm{Li}}_2^{+}\to 5{\mathrm{e}}^{-}$

Electronic configuration: $\mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{s}}^1$

Bond order $=$ (Number of Bonding electrons $-$ Number of Non-bonding electrons)$/2$

$$\begin{gathered} =({\mathrm{N}}_{\mathrm{b}}-{\mathrm{N}}_{\mathrm{a}})/2 \\ =(3-2)/2 \\ =1/2 \end{gathered}$$

${\mathrm{Li}}_2^{-}\to 7{\mathrm{e}}^{-}$

Electronic configuration: $\mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{s}}^2{\mathrm{\sigma }}^{{}^{*}}2{\mathrm{s}}^1$

Bond order $=$ (Number of Bonding electrons $-$ Number of Non-bonding electrons)$/2$

$$\begin{gathered} =({\mathrm{N}}_{\mathrm{b}}-{\mathrm{N}}_{\mathrm{a}})/2 \\ =(4-3)/2 \\ =1/2 \end{gathered}$$

As you can see from above explanation ${\mathrm{Li}}_2^{+}$ and ${\mathrm{Li}}_2^{-}$ have same bond order having value $0.5$. The bond order doesn't exist and shows the unstable nature of given molecule.

Therefore, both ${\mathrm{Li}}_2^{+}$ and ${\mathrm{Li}}_2^{-}$ are unstable.

Explanation for the incorrect option:

(A) The above detailed calculation shows that both ${\mathrm{Li}}_2^{+}$ and ${\mathrm{Li}}_2^{-}$are unstable. Hence option A is incorrect.

(B) The above detailed calculation shows that both ${\mathrm{Li}}_2^{+}$ and ${\mathrm{Li}}_2^{-}$are unstable. Hence option B is incorrect.

(D) The above detailed calculation shows that both ${\mathrm{Li}}_2^{+}$ and ${\mathrm{Li}}_2^{-}$are unstable. Hence option D is incorrect.

Hence, option C is correct.