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_(s^(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, let's break down the steps:

### Step-by-Step Solution:

1. **Understand Hybridization**:
- Hybridization is the mixing of atomic orbitals to form new hybrid orbitals that are suitable for the pairing of electrons to form chemical bonds in molecular geometry.

2. **Identify the Hybridization Type**:
- The given hybridization is sp³d². This indicates that one s orbital, three p orbitals, and two d orbitals are involved in the hybridization process.

3. **Determine the Geometry**:
- The geometry associated with sp³d² hybridization is octahedral. This is important because it helps us understand the arrangement of orbitals in space.

4. **Identify the Involved Orbitals**:
- For sp³d² hybridization:
- The s orbital involved is the 4s orbital.
- The three p orbitals involved are the 3p orbitals (px, py, pz).
- The d orbitals involved are specifically the d orbitals that can accommodate the octahedral geometry.

5. **Select the d Orbitals**:
- In an octahedral arrangement, the d orbitals that are typically involved are:
- \(d_{x^2-y^2}\) (which lies in the xy-plane)
- \(d_{z^2}\) (which has a different orientation and is oriented along the z-axis)
- The other d orbitals, \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\), do not participate in this hybridization for octahedral complexes.

6. **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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