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

Options

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

Explanation

To solve the question regarding the electronic configuration of a d⁴ system when the splitting energy (Δ₀) is less than the pairing energy (P), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the d-Orbital Splitting**:
In an octahedral field, the five d-orbitals split into two sets due to the presence of ligands. The lower energy set is called t₂g (comprising three orbitals), and the higher energy set is called eₕ (comprising two orbitals).

2. **Identify the Condition**:
We are given that Δ₀ < P. This means that the energy required to pair electrons in the lower energy orbitals (t₂g) is greater than the energy difference between the t₂g and eₕ orbitals.

3. **Filling the Electrons**:
Since the splitting energy is less than the pairing energy, electrons will occupy the available orbitals singly before pairing occurs. This is in accordance with Hund's rule, which states that electrons will fill degenerate orbitals singly first.

4. **Electronic Configuration for d⁴**:
For a d⁴ system, we have four electrons to place:
- The first three electrons will fill the three t₂g orbitals (t₂g³).
- The fourth electron will go into one of the eₕ orbitals (eₕ¹).

5. **Final Configuration**:
Therefore, the electronic configuration for the d⁴ system under the condition Δ₀ < P will be:
- t₂g³ eₕ¹

### Conclusion:
The correct electronic configuration for a d⁴ system when Δ₀ < P is **t₂g³ eₕ¹**.