Question

Which of the following cannot exist on the basis of MO theory?

• A. ${H_2}^{+}$
• B. ${H{e}_2}^{+}$
• C. $H{e}_2$
• D. $O_2$

Answer 1

The correct option is C

$H{e}_2$

To find out about the existence of a molecule, we have to check the bond order. If the bond order is 0 or negative, then the molecule does not exist.

So, to check the bond order,

Let's draw their MO diagrams.

Now,

For ${H_2}^{+}\to$ We have 1 less electron in energy level diagram

For ${H{e}_2}^{+}\to$ We have 1 less electron in energy level diagram (Because of the + sign, i.e., it means one less electron)

Now,

Bond Order = $\frac{1}{2}$ [Bonding electrons - Anti Bonding electrons]

(BE) - (ABE)

For ${H_2}^{+}$

Bond order = $\frac{1}{2}$ [1 - 0] = 1/2 [Possible]

For ${H{e}_2}^{+}$

Bond order = $\frac{1}{2}$ [2 - 1] = 1/2 [Possible]

For $H{e}_2$

Bond order = $\frac{1}{2}$ [2 - 2] = 0 [Not possible]

For $O_2$

Bond order =$\frac{1}{2}$ [10 - 6] = 2 [Possible]

So, only $H{e}_2$ has bond order 0, therefore not possible.