`S_(2)` molecule in vapour state is paramagnetic due to the presence of unpaired electrons is 

Options

A. Bonding boiling `sigma` orbitals
B. Anti bonding `sigma^(**)` orbtials
C. Anti bonding `pi^(**)` orbitals
D. Bonding `pi` orbitals

Answer

To determine why the \( S_2 \) molecule in vapor state is paramagnetic due to the presence of unpaired electrons, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Electron Configuration of Sulfur:**
- The atomic number of sulfur (S) is 16. Its electron configuration is \( [Ne] 3s^2 3p^4 \). This means that in its outermost shell, sulfur has 2 electrons in the 3s orbital and 4 electrons in the 3p orbital.

2. **Molecular Orbital Theory (MOT) Application:**
- When two sulfur atoms combine to form the \( S_2 \) molecule, we need to consider the molecular orbitals formed from the atomic orbitals of both sulfur atoms.
- The molecular orbitals for \( S_2 \) will include bonding and antibonding orbitals derived from the combination of the 3s and 3p orbitals.

3. **Construct the Molecular Orbital Diagram:**
- The molecular orbital diagram for \( S_2 \) will have the following order for the energy levels:
- \( \sigma(3s) \) < \( \sigma^*(3s) \) < \( \sigma(3p_z) \) < \( \pi(3p_x) = \pi(3p_y) \) < \( \pi^*(3p_x) = \pi^*(3p_y) \) < \( \sigma^*(3p_z) \).
- Fill the molecular orbitals with the total number of electrons from both sulfur atoms. Since each sulfur contributes 8 electrons (2 from 3s and 4 from 3p), \( S_2 \) has a total of 16 electrons.

4. **Filling the Molecular Orbitals:**
- Fill the molecular orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule:
- \( \sigma(3s) \): 2 electrons (filled)
- \( \sigma^*(3s) \): 0 electrons (empty)
- \( \sigma(3p_z) \): 2 electrons (filled)
- \( \pi(3p_x) \): 2 electrons (filled)
- \( \pi(3p_y) \): 2 electrons (filled)
- \( \pi^*(3p_x) \): 1 electron (unpaired)
- \( \pi^*(3p_y) \): 1 electron (unpaired)

5. **Identify Unpaired Electrons:**
- In the \( S_2 \) molecule, we find that there are 2 unpaired electrons, one in each of the \( \pi^* \) orbitals. This configuration leads to the paramagnetic nature of the molecule.

6. **Conclusion:**
- The presence of unpaired electrons in the antibonding \( \pi^* \) orbitals is what makes \( S_2 \) paramagnetic in the vapor state.