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 of the following atomic orbitals does not participitate in trigonal bipyramidal hybridisation i.e. `sp^3d` hybridisation ?

Options

A. s
B. `d_(x^2-y^2)`
C. `p_x`
D. `p_y`

Explanation

To determine which atomic orbital does not participate in trigonal bipyramidal hybridization (sp³d hybridization), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Hybridization**:
- Hybridization involves the mixing of atomic orbitals to form new hybrid orbitals. In the case of sp³d hybridization, five atomic orbitals are involved: one s orbital, three p orbitals, and one d orbital.

2. **Identifying the Orbitals Involved**:
- For sp³d hybridization, the participating orbitals are:
- 1 s orbital (1s)
- 3 p orbitals (typically px, py, and pz)
- 1 d orbital (from the d subshell)

3. **Geometry of Trigonal Bipyramidal**:
- The trigonal bipyramidal geometry consists of three atoms forming a triangle in one plane and two additional atoms positioned above and below this plane. This arrangement minimizes electron repulsion.

4. **Choosing the d Orbital**:
- Among the d orbitals (dxy, dyz, dxz, dx²-y², dz²), the dz² orbital is typically used in sp³d hybridization because it is oriented along the z-axis and does not have lobes in the xy-plane, thus minimizing repulsion with the other orbitals.

5. **Identifying the Non-Participating Orbital**:
- The d orbital that does not participate in this hybridization is dx²-y². This is because it has lobes in the xy-plane, which would lead to increased repulsion with the p orbitals that lie in the same plane.

6. **Conclusion**:
- Therefore, the atomic orbital that does not participate in trigonal bipyramidal hybridization (sp³d hybridization) is **dx²-y²**.

### Final Answer:
The atomic orbital that does not participate in trigonal bipyramidal hybridization is **dx²-y²**.