Which of the following is the correct electronic configuration in octahedral complex with `d^4` configuration?

Options

A. `t_(2g)^4, e_g^0`, `triangle_0 lt P`
B. `t_(2g)^3, e_g^1`, `triangle_0 gt P`
C. `t_(2g)^2, e_g^2`, `triangle_0 lt P`
D. `t_(2g)^3, e_g^1`, `triangle_0 lt P`

Answer

To determine the correct electronic configuration for an octahedral complex with a `d^4` configuration, we need to consider the influence of crystal field splitting and pairing energy on the arrangement of electrons in the d-orbitals.

### Step-by-Step Solution:

1. **Understand the d-orbital splitting in octahedral complexes**: In an octahedral field, the five d-orbitals split into two sets: the lower energy set (t2g) which consists of three orbitals, and the higher energy set (eg) which consists of two orbitals.

2. **Identify the number of electrons**: For a d^4 configuration, we have four electrons to place in the d-orbitals.

3. **Consider the splitting energy vs pairing energy**: The arrangement of electrons depends on the relative values of the splitting energy (Δ) and the pairing energy (P).
- If Δ < P (splitting energy is less than pairing energy), electrons will occupy the t2g orbitals before pairing occurs.
- If Δ > P (splitting energy is greater than pairing energy), electrons will pair up in the t2g orbitals before occupying the eg orbitals.

4. **Evaluate the options**:
- **Option 1**: t2g4 eg0 (implies all four electrons are in t2g, which is possible only if Δ < P).
- **Option 2**: t2g3 eg1 (implies three electrons in t2g and one in eg, which is possible if Δ > P).
- **Option 3**: t2g2 eg2 (implies two electrons in t2g and two in eg, which is not possible for d^4).
- **Option 4**: t2g3 eg1 (implies three electrons in t2g and one in eg, which is possible if Δ > P).

5. **Determine the correct configuration**:
- If we assume Δ < P, the configuration would be t2g4 eg0. However, this is not a stable configuration as it would lead to high electron repulsion.
- If we assume Δ > P, the configuration would be t2g3 eg1, which is a stable arrangement as it minimizes electron repulsion and adheres to the rules of crystal field theory.

6. **Conclusion**: The correct electronic configuration for a d^4 octahedral complex is **t2g3 eg1** when the splitting energy is greater than the pairing energy.

### Final Answer:
The correct electronic configuration in an octahedral complex with d^4 configuration is **t2g3 eg1**.