When hybridisation involving d-orbitals are considered then all the five d-orbitals are not degenerate, rather `d_(x^(2)-y^(2)),d_(s^(2)) and d_(xy),d_(zx)` form two different sets of orbitals and orbitals of appropriate set is involved in the hybridisation.
Molecule having trigonal bipyramidal geometry and `sp^(3)`d hybridisation, d-orbitals involved is :

Options

A. `d_(xy)`
B. `d_(yz)`
C. `d_(x^(2)-y^(2))`
D. `d_(z^(2))`

Answer

To determine which d-orbital is involved in the hybridization of a molecule with trigonal bipyramidal geometry and sp³d hybridization, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Hybridization**:
- Hybridization involves the mixing of atomic orbitals to form new hybrid orbitals. In this case, we are considering sp³d hybridization, which involves one s orbital, three p orbitals, and one d orbital.

2. **Geometry of the Molecule**:
- The trigonal bipyramidal geometry consists of five regions of electron density around the central atom. There are three equatorial positions and two axial positions.

3. **Identifying the Orbitals**:
- In sp³d hybridization, we need to identify which d-orbital is involved. The five d-orbitals are: dₓᵧ, dₓ²−y², dᵧ², dᵨz, and dₓz.

4. **Character of Axial and Equatorial Bonds**:
- In a trigonal bipyramidal structure, the axial bonds are aligned along the z-axis, while the equatorial bonds lie in the xy-plane. The axial positions have 0% x-character, meaning they do not contribute to the x-axis.

5. **Splitting the Hybridization**:
- We can split the sp³d hybridization into two parts: sp² (for the equatorial plane) and pd (for the axial positions). The sp² hybridization involves one s orbital and two p orbitals (px and py), which lie in the xy-plane.

6. **Identifying the d-Orbital**:
- For the axial positions, we need an orbital that lies along the z-axis. The only d-orbital that lies along the z-axis is the dᵨz orbital.

7. **Conclusion**:
- Therefore, the d-orbital involved in the sp³d hybridization for a molecule with trigonal bipyramidal geometry is the **dᵨz orbital**.

### Final Answer:
The d-orbital involved in the sp³d hybridization for a molecule with trigonal bipyramidal geometry is **dᵨz**.

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