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.
In `sp^(3)d^(2)` hybridisation, which sets of d-orbitals is involved ?

Options

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

Answer

To determine which sets of d-orbitals are involved in sp³d² hybridization, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Hybridization**: Hybridization is the process of combining atomic orbitals to form new hybrid orbitals that can accommodate bonding. In the case of sp³d² hybridization, we are combining one s orbital, three p orbitals, and two d orbitals.

2. **Identify the Geometry**: The sp³d² hybridization typically leads to an octahedral geometry. In an octahedral arrangement, the central atom is surrounded by six other atoms.

3. **Identify the d-Orbitals**: There are five d-orbitals:
- \(d_{xy}\)
- \(d_{yz}\)
- \(d_{zx}\)
- \(d_{x^2-y^2}\)
- \(d_{z^2}\)

4. **Determine the Sets of d-Orbitals**: In the context of octahedral hybridization:
- The orbitals \(d_{x^2-y^2}\) and \(d_{z^2}\) are oriented along the axes (x, y, z) and are involved in the hybridization.
- The orbitals \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\) are oriented between the axes and are not used in sp³d² hybridization.

5. **Conclusion**: Therefore, the d-orbitals involved in sp³d² hybridization are \(d_{x^2-y^2}\) and \(d_{z^2}\).

### Final Answer:
The sets of d-orbitals involved in sp³d² hybridization are \(d_{x^2-y^2}\) and \(d_{z^2}\).

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