According to crystal filed theory , five d-orbitals of an octahedral complex split to give

Options

A. Two orbitals with lower energy and three orbitals with higher energy
B. Three orbitals with lower energy and two orbitals with higher energy
C. One orbitals with lower energy and four orbitals with higher energy
D. Four orbitals with lower energy and one orbital with higher energy

Answer

To solve the question regarding the splitting of d-orbitals in an octahedral complex according to crystal field theory, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the d-Orbitals**:
- In an isolated atom, there are five d-orbitals: \(d_{xy}\), \(d_{yz}\), \(d_{zx}\), \(d_{x^2-y^2}\), and \(d_{z^2}\).

2. **Approach of Ligands**:
- When ligands approach the central metal ion in an octahedral complex, they create an electric field that affects the energy levels of the d-orbitals due to electron-electron repulsion.

3. **Splitting of d-Orbitals**:
- In an octahedral field, the d-orbitals split into two sets due to the different degrees of repulsion experienced by the orbitals:
- **Higher Energy Set (E_g)**: This set consists of the orbitals that point directly towards the ligands, which are \(d_{x^2-y^2}\) and \(d_{z^2}\). These orbitals experience maximum repulsion and thus have higher energy.
- **Lower Energy Set (T_2g)**: This set consists of the orbitals that lie between the axes, which are \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\). These orbitals experience less repulsion and thus have lower energy.

4. **Energy Level Diagram**:
- The energy level diagram for an octahedral complex shows the T_2g set at a lower energy level and the E_g set at a higher energy level.

5. **Conclusion**:
- Therefore, according to crystal field theory, the five d-orbitals of an octahedral complex split to give 3 orbitals with lower energy (T_2g) and 2 orbitals with higher energy (E_g).

### Final Answer:
The correct answer is: **3 orbitals with lower energy (T_2g) and 2 orbitals with higher energy (E_g)**.

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