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.
Which of the following orbitals can not undergo hybridisation amongst themselves.
(I) `3d,4s " " (II) 3d,4d`
(III) `3d,4s & 4p " " (IV) 3s,3p & 4s`

Options

A. only II
B. II and III
C. I, II and IV
D. II and IV

Answer

To solve the problem of which orbitals cannot undergo hybridization amongst themselves, we will analyze each option based on the principles of hybridization and the energy levels of the orbitals involved.

### Step-by-step Solution:

1. **Understanding Hybridization**:
Hybridization is the process where atomic orbitals mix to form new hybrid orbitals. This process typically occurs between orbitals that have similar energy levels.

2. **Energy Levels of Orbitals**:
The order of increasing energy for the orbitals is as follows:
- 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d, etc.
This order indicates that orbitals in the same energy level or close in energy can hybridize.

3. **Analyzing Each Option**:
- **(I) 3d, 4s**:
- The 3d and 4s orbitals are relatively close in energy. Therefore, they can undergo hybridization.
- **(II) 3d, 4d**:
- The 3d orbital is smaller and has a lower energy compared to the larger and higher energy 4d orbital. Due to this significant difference in size and energy, they cannot hybridize.
- **(III) 3d, 4s & 4p**:
- The 3d, 4s, and 4p orbitals have comparable energies, allowing them to hybridize with each other.
- **(IV) 3s, 3p & 4s**:
- The 3s and 3p orbitals are in the same energy level, but the 4s orbital is at a higher energy level. The significant energy difference between the 3s/3p and 4s means they cannot hybridize.

4. **Conclusion**:
Based on the analysis, the orbitals that cannot undergo hybridization amongst themselves are:
- **Option II (3d, 4d)** and **Option IV (3s, 3p & 4s)**.

### Final Answer:
The orbitals that cannot undergo hybridization amongst themselves are **(II) 3d, 4d** and **(IV) 3s, 3p & 4s**.