`d_(x)2-_(y)2` orbital is involved in which of the following hybridisation ?

Options

A. `a.sp^(3)d^(3)`
B. `b.dsp^(2)`
C. `c.sp^(3)d^(2)`
D. `d.sp^(3)d`

Explanation

To determine which hybridization involves the \( d_{x^2-y^2} \) orbital, we can analyze each hybridization type and see where this particular orbital is utilized.

### Step-by-Step Solution:

1. **Identify the Hybridizations**: We need to look at the different types of hybridizations mentioned in the question: \( sp^3d^3 \), \( dsp^2 \), \( sp^3d^2 \), and \( sp^3d \).

2. **Analyze \( sp^3d^3 \)**:
- In \( sp^3d^3 \) hybridization, we have:
- 1 s orbital
- 3 p orbitals (px, py, pz)
- 3 d orbitals (including \( d_{xy} \), \( d_{z^2} \), and \( d_{x^2-y^2} \))
- **Conclusion**: The \( d_{x^2-y^2} \) orbital is involved in \( sp^3d^3 \).

3. **Analyze \( dsp^2 \)**:
- In \( dsp^2 \) hybridization, we have:
- 1 d orbital (which can be \( d_{x^2-y^2} \))
- 1 s orbital
- 2 p orbitals (px, py)
- **Conclusion**: The \( d_{x^2-y^2} \) orbital is involved in \( dsp^2 \).

4. **Analyze \( sp^3d^2 \)**:
- In \( sp^3d^2 \) hybridization, we have:
- 1 s orbital
- 3 p orbitals (px, py, pz)
- 2 d orbitals (including \( d_{x^2-y^2} \) and possibly \( d_{z^2} \))
- **Conclusion**: The \( d_{x^2-y^2} \) orbital is involved in \( sp^3d^2 \).

5. **Analyze \( sp^3d \)**:
- In \( sp^3d \) hybridization, we have:
- 1 s orbital
- 3 p orbitals (px, py, pz)
- 1 d orbital (which can be \( d_{x^2-y^2} \))
- **Conclusion**: The \( d_{x^2-y^2} \) orbital is involved in \( sp^3d \).

6. **Summarize Findings**:
- All four hybridizations (\( sp^3d^3 \), \( dsp^2 \), \( sp^3d^2 \), and \( sp^3d \)) involve the \( d_{x^2-y^2} \) orbital.

### Final Answer:
The \( d_{x^2-y^2} \) orbital is involved in all of the following hybridizations: \( sp^3d^3 \), \( dsp^2 \), \( sp^3d^2 \), and \( sp^3d \).