In vapour state, sulphur `(S_2)` shows paramagnetic behaviour due to

Options

A. Presence of one unpaired electron in the antibonding `sigma^**` orbitals
B. Presence of two unpaired electrons in the bonding pi orbitals
C. Presence of one unpaired electrons in the bonding pi^** orbitals
D. Presence of two unpaired electrons in the antibonding pi^** orbitals

Answer

To understand why sulfur in its vapor state (S₂) exhibits paramagnetic behavior, we need to analyze the electronic configuration of the S₂ molecule and the presence of unpaired electrons.

### Step-by-Step Solution:

1. **Identify the Molecular Formula**:
- The molecule in question is diatomic sulfur, represented as S₂.

2. **Determine the Electron Configuration**:
- Each sulfur atom has an atomic number of 16, which means it has 16 electrons.
- The electron configuration for a single sulfur atom is:
\[ 1s^2 2s^2 2p^6 3s^2 3p^4 \]
- For two sulfur atoms in S₂, the total number of electrons is \( 16 \times 2 = 32 \).

3. **Construct the Molecular Orbital Diagram**:
- In the molecular orbital theory, the 32 electrons of S₂ will fill the molecular orbitals formed from the atomic orbitals of the two sulfur atoms.
- The relevant molecular orbitals for S₂ are:
- σ(1s), σ*(1s), σ(2s), σ*(2s), σ(2p_z), π(2p_x), π(2p_y), π*(2p_x), π*(2p_y).
- The 3p orbitals will contribute to the formation of π and π* molecular orbitals.

4. **Filling the Molecular Orbitals**:
- The filling of the molecular orbitals for S₂ will lead to the following configuration:
\[ (σ(1s))^2 (σ*(1s))^2 (σ(2s))^2 (σ*(2s))^2 (σ(2p_z))^2 (π(2p_x))^2 (π(2p_y))^2 (π*(2p_x))^1 (π*(2p_y))^1 \]
- This shows that there are two unpaired electrons in the π* orbitals.

5. **Conclusion on Paramagnetism**:
- The presence of unpaired electrons in the π* orbitals leads to the paramagnetic behavior of the S₂ molecule. Paramagnetism occurs due to the presence of unpaired electrons that can align with an external magnetic field.

### Final Answer:
Sulfur (S₂) in the vapor state shows paramagnetic behavior due to the presence of two unpaired electrons in the anti-bonding π* orbitals.

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