Question

An example of one electron bond is found in the hydrogen molecule ion, $H_2^{+}$. It has a bond energy of 61 kcal/mol. The ion is less stable than $H_2$ molecule as the bond length is longer than two electrons bond in $H_2$. The excited state of alkali metal molecules involves odd electron bonds. Thus, $L{i}_2^{+}$, $K_2^{+}$,$N{a}_2^{+}$ are all bound by one electron.

Answer 1

Dear Student,

Bond length of molecule is inversely proportional to its bond order.
Bond order can be calculated as :
$\mathrm{Bond}\mathrm{order}=\frac{\mathrm{Bonding}\mathrm{electrons}-\mathrm{Antibonding}\mathrm{electrons}}{2}$
$$\begin{gathered} \mathrm{MO}\mathrm{configuration}\mathrm{of}{\mathrm{H}}_2=\mathrm{\sigma }1{\mathrm{s}}^2 \\ \mathrm{Therefore},\mathrm{Bond}\mathrm{order}=\frac{2-0}{2}=1 \\ \mathrm{MO}\mathrm{configuration}\mathrm{of}{{\mathrm{H}}_2}^{+}=\mathrm{\sigma }1{\mathrm{s}}^1 \\ \mathrm{Bond}\mathrm{order}=\frac{1-0}{2}=0.5 \\ \mathrm{Since}{\mathrm{H}}_2\mathrm{has}\mathrm{higher}\mathrm{bond}\mathrm{order}\mathrm{than}{{\mathrm{H}}_2}^{+},\mathrm{it}\mathrm{will}\mathrm{have}\mathrm{less}\mathrm{bond}\mathrm{length}\mathrm{than}{{\mathrm{H}}_2}^{+}. \end{gathered}$$