Question

According to MO theory, the molecule which contain only π-Bonds between the atoms is

• A. $C_2$
• B. $N_2$
• C. $O_2$
• D. $B_2$

Answer 1

The Correct Option is A

To solve the problem, we need to identify which molecule, according to Molecular Orbital (MO) theory, contains only π (pi) bonds and no σ (sigma) bonds between atoms.

1. Understanding MO Theory for C₂:
According to MO theory, the molecular orbital configuration of diatomic carbon (C₂) is:

$\sigma_{1s}^2\, \sigma_{1s}^*{}^2\, \sigma_{2s}^2\, \sigma_{2s}^*{}^2\, \pi_{2p_x}^2\, \pi_{2p_y}^2$

From the configuration above, we note:

• The bonding electrons in $\pi_{2p_x}$ and $\pi_{2p_y}$ contribute to π-bonds.
• There are no electrons in $\sigma_{2p_z}$, meaning there is no σ-bond formed by the 2p orbitals.

2. Bond Order of C₂:
Bond order = ½ (Number of bonding electrons − Number of antibonding electrons)
= ½ (8 − 2) = 3

But this bond order includes 2 π bonds and one bond due to lower energy levels, but not from 2p σ overlap. Effectively, between the two carbon atoms, only π bonds contribute from 2p orbitals.

3. Comparison with Other Molecules:

• N₂: Has both σ and π bonds.
• O₂: Has σ and π bonds, and also unpaired electrons in π* orbitals.
• B₂: Has only π bonds but fewer electrons and a lower bond order than C₂.

Only C₂ meets the condition of having exclusively π bonds (no 2p σ bond).

Final Answer:
The molecule that contains only π bonds between the atoms is $ \textbf{C}_2 $.