NEET 2020 Chemistry Question 91 Solution

According to Molecular Orbital Theory (MOT), a homonuclear diatomic molecule exists as a stable chemical entity only if the number of bonding electrons exceeds antibonding electrons ($$N_b > N_a$$), yielding a positive non-zero bond order ($$\text{BO} > 0$$).

Helium ($$Z = 2$$) has configuration $$1s^2$$. For hypothetical $$He_2$$ ($$4\text{ electrons}$$): $$\text{MO Configuration} = (\sigma 1s)^2 (\sigma^* 1s)^2$$ $$\text{Bond Order} = \frac{N_b - N_a}{2} = \frac{2 - 2}{2} = 0$$ Because the antibonding electrons completely cancel the stabilization of the bonding electrons, $$He_2$$ is energetically unstable and does not exist.

- $$Li_2$$ (6 electrons): $$(\sigma 1s)^2 (\sigma^* 1s)^2 (\sigma 2s)^2 \implies \text{BO} = \frac{4 - 2}{2} = 1$$ (exists in vapor phase). - $$C_2$$ (12 electrons): $$(\sigma 1s)^2 (\sigma^* 1s)^2 (\sigma 2s)^2 (\sigma^* 2s)^2 (\pi 2p_x^2 = \pi 2p_y^2) \implies \text{BO} = \frac{8 - 4}{2} = 2$$ (double bond consisting entirely of two pi bonds). - $$O_2$$ (16 electrons): $$\text{BO} = \frac{10 - 6}{2} = 2$$ (paramagnetic with 2 unpaired electrons in $$\pi^* 2p$$).

Only $$He_2$$ has a bond order of zero, confirming that it does not exist.