In the valence bond theory, hybridisation of orbitals is an integral part of bond formation.Hybridisation consists of mixing or linear combination of the "pure" atomic orbitals in such a way as to form new hybrid orbitals such as `sp, sp^2, sp^3, sp^3d , sp^3d^2` etc.
Now answer the following questions :
Which one of the following molecular geometrices (i.e. shapes) is not possible for the `sp^3d^3` hybridisation ?

Options

A. Capped octahedral
B. Octahedral
C. Square planar
D. Square pyramidral

Explanation

To determine which molecular geometries are not possible for the `sp^3d^3` hybridization, we can follow these steps:

### Step 1: Understand Hybridization
Hybridization involves the mixing of atomic orbitals to form new hybrid orbitals. For `sp^3d^3` hybridization, we are mixing:
- 1 s orbital
- 3 p orbitals
- 3 d orbitals

This results in the formation of **seven hybrid orbitals**.

### Step 2: Determine the Steric Number
The steric number is calculated as the sum of the number of bond pairs and lone pairs around the central atom. For `sp^3d^3` hybridization, the steric number is **7**.

### Step 3: Identify Possible Geometries
The molecular geometry corresponding to a steric number of 7 is:
- **Pentagonal bipyramidal**: This geometry has five atoms in a plane and two atoms above and below this plane.

### Step 4: Evaluate Other Geometries
For `sp^3d^3` hybridization, we need to check which geometries are not possible:
1. **Octahedral**: This geometry corresponds to a steric number of 6, which is not applicable here.
2. **Square planar**: This geometry also corresponds to a steric number of 4, which is not applicable here.
3. **Square pyramidal**: This geometry corresponds to a steric number of 5, which is not applicable here.

### Conclusion
The geometries that are **not possible** for `sp^3d^3` hybridization are:
- **Octahedral**
- **Square planar**
- **Square pyramidal**

### Final Answer
The molecular geometries that are not possible for `sp^3d^3` hybridization are **octahedral, square planar, and square pyramidal**.

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