If `Delta_(0) lt P`, the correct electronic configuration for `d^(4)` system will be -

Options

A. `t_(2)^(4) e_(g)^(0)`
B. `t_(2g)^(3) e_(g)^(1)`
C. `t_(2g)^(0)e_(g)^(4)`
D. `t_(2g)^(2)e_(g)^(2)`

Answer

To determine the correct electronic configuration for a d⁴ system when Δ₀ < P (where Δ₀ is the crystal field splitting energy and P is the pairing energy), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding d-Orbital Splitting**:
- In a d⁴ system, the five d-orbitals (dxy, dyz, dzx, dx²-y², dz²) split into two energy levels when ligands approach: the lower energy level (t₂g) and the higher energy level (eₕ).
- The t₂g level can hold a maximum of 6 electrons, while the eₕ level can hold a maximum of 4 electrons.

2. **Analyzing the Condition Δ₀ < P**:
- When Δ₀ < P, the energy required to pair electrons in the lower t₂g level is greater than the energy gained from occupying the higher eₕ level.
- This condition favors the high-spin configuration, where electrons prefer to occupy higher energy orbitals rather than pairing up in the lower energy orbitals.

3. **Filling the Electrons**:
- For a d⁴ configuration, we have 4 electrons to place in the split d-orbitals.
- According to the high-spin configuration:
- The first three electrons will occupy the three t₂g orbitals singly (t₂g³).
- The fourth electron will occupy one of the eₕ orbitals (eₕ¹).
- Thus, the electronic configuration will be t₂g³ eₕ¹.

4. **Final Configuration**:
- Therefore, the correct electronic configuration for the d⁴ system under the condition Δ₀ < P is:
- **t₂g³ eₕ¹**.

### Conclusion:
The correct answer is **option B: t₂g³ eₕ¹**.