`d_(x^2-y^2)` and `d_(z^2)` orbitals is involved in which of the foollowing hybridisation?

Options

A. `sp^3d^2`
B. `d^2sp^3`
C. `sp^3d^3`
D. `d^3sp^3`

Answer

To determine which hybridization involves the \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals, we will analyze each of the given hybridization options step by step.

### Step 1: Understand the hybridization types
We need to identify the hybridization types provided in the question:
1. \(sp^3d^2\)
2. \(d^2sp^3\)
3. \(3sp^3d^3\)
4. \(d^3sp^3\)

### Step 2: Analyze \(sp^3d^2\) hybridization
In \(sp^3d^2\) hybridization:
- One \(s\) orbital is used.
- Three \(p\) orbitals are used.
- Two \(d\) orbitals are used.

The \(d\) orbitals involved can be \(d_{z^2}\) and \(d_{x^2-y^2}\). Therefore, this hybridization **does involve** both \(d_{x^2-y^2}\) and \(d_{z^2}\).

### Step 3: Analyze \(d^2sp^3\) hybridization
In \(d^2sp^3\) hybridization:
- Two \(d\) orbitals are used.
- One \(s\) orbital is used.
- Three \(p\) orbitals are used.

Similar to the previous case, the \(d\) orbitals can be \(d_{z^2}\) and \(d_{x^2-y^2}\). Thus, this hybridization **also involves** both \(d_{x^2-y^2}\) and \(d_{z^2}\).

### Step 4: Analyze \(3sp^3d^3\) hybridization
In \(3sp^3d^3\) hybridization:
- One \(s\) orbital is used.
- Three \(p\) orbitals are used.
- Three \(d\) orbitals are used.

The \(d\) orbitals typically involved in this hybridization are \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\). Therefore, this hybridization **does not involve** \(d_{x^2-y^2}\) or \(d_{z^2}\).

### Step 5: Analyze \(d^3sp^3\) hybridization
In \(d^3sp^3\) hybridization:
- Three \(d\) orbitals are used.
- One \(s\) orbital is used.
- Three \(p\) orbitals are used.

Similar to the previous case, the \(d\) orbitals involved are typically \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\). Thus, this hybridization **does not involve** \(d_{x^2-y^2}\) or \(d_{z^2}\).

### Conclusion
From the analysis, we find that the hybridizations that involve \(d_{x^2-y^2}\) and \(d_{z^2}\) are:
- \(sp^3d^2\)
- \(d^2sp^3\)

### Final Answer
The correct hybridization types that involve \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals are **\(sp^3d^2\) and \(d^2sp^3\)**.

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