`PCl_5` molecule has

Options

A. Three fold axis of symmetry
B. Two fold axis of symmetry
C. Both
D. None of these

Explanation

To determine the symmetry of the PCl5 molecule, we will analyze its structure and identify the axes of symmetry present.

### Step-by-Step Solution:

1. **Determine the Structure of PCl5**:
- Phosphorus (P) is the central atom, and it has 5 valence electrons.
- It forms 5 sigma bonds with 5 chlorine (Cl) atoms, resulting in no lone pairs on the phosphorus atom.
- The hybridization of phosphorus in PCl5 is sp³d, which corresponds to a trigonal bipyramidal geometry.

2. **Visualize the Geometry**:
- In a trigonal bipyramidal structure, there are two types of positions for the chlorine atoms:
- Three Cl atoms are in the equatorial plane (forming a triangle).
- Two Cl atoms are in the axial positions (one above and one below the equatorial plane).
- This can be visualized as a pyramid with a triangular base.

3. **Identify Axes of Symmetry**:
- **Three-Fold Axis of Symmetry**:
- A three-fold axis of symmetry (C3) means that if you rotate the molecule by 120 degrees around this axis, it looks the same.
- In PCl5, this axis runs through the central phosphorus atom and the three equatorial chlorine atoms. Rotating the molecule by 120 degrees around this axis will result in the same arrangement of chlorine atoms.

- **Two-Fold Axis of Symmetry**:
- A two-fold axis of symmetry (C2) means that if you rotate the molecule by 180 degrees around this axis, it looks the same.
- In PCl5, this axis runs through the central phosphorus atom and any one of the axial chlorine atoms. Rotating the molecule by 180 degrees around this axis will also yield the same arrangement.

4. **Conclusion**:
- Since PCl5 has both a three-fold axis of symmetry and a two-fold axis of symmetry, the correct answer is option C: both.