Consider the following complex ions.
`[CrCl_(6)]^(3-)" "[Cr(H_(2)O)_(6)]^(3+)`
`[Cr(NH_(3))_(6)]^(3+)" "[Cr(CN)_(6)]^(3-)`
The correct order of `triangle_(0)` is :

Options

A. `P gt Q gt Rgt S`
B. `P lt R lt Q lt S`
C. `P lt Q lt R lt S`
D. `P lt Q lt S lt R`

Explanation

To determine the correct order of the crystal field splitting energy (Δ₀) for the given complex ions, we will analyze the ligands and their strengths, as well as the oxidation state of the chromium ion in each complex.

### Step-by-Step Solution:

1. **Identify the Complex Ions**: We have four complex ions:
- [CrCl₆]³⁻
- [Cr(H₂O)₆]³⁺
- [Cr(NH₃)₆]³⁺
- [Cr(CN)₆]³⁻

2. **Determine the Oxidation State of Chromium**:
- For [CrCl₆]³⁻: Let the oxidation state of Cr be x. The equation is x + 6(-1) = -3, which gives x = +3.
- For [Cr(H₂O)₆]³⁺: x + 6(0) = +3, gives x = +3.
- For [Cr(NH₃)₆]³⁺: x + 6(0) = +3, gives x = +3.
- For [Cr(CN)₆]³⁻: x + 6(-1) = -3, gives x = +3.

All complexes have Cr in the +3 oxidation state.

3. **Identify the Ligand Strength**: The strength of ligands can be categorized based on the spectrochemical series:
- CN⁻ (strong field ligand)
- NH₃ (moderate field ligand)
- H₂O (weak field ligand)
- Cl⁻ (weak field ligand)

4. **Rank the Ligands**: Based on the spectrochemical series, we can rank the ligands from strongest to weakest:
- CN⁻ > NH₃ > H₂O > Cl⁻

5. **Determine the Order of Δ₀**: Since all complexes have the same metal in the same oxidation state, the order of Δ₀ will depend solely on the ligand strength:
- [Cr(CN)₆]³⁻ > [Cr(NH₃)₆]³⁺ > [Cr(H₂O)₆]³⁺ > [CrCl₆]³⁻

6. **Final Order of Δ₀**: Therefore, the correct order of Δ₀ is:
- [Cr(CN)₆]³⁻ > [Cr(NH₃)₆]³⁺ > [Cr(H₂O)₆]³⁺ > [CrCl₆]³⁻

### Conclusion:
The correct order of Δ₀ is:
**[Cr(CN)₆]³⁻ > [Cr(NH₃)₆]³⁺ > [Cr(H₂O)₆]³⁺ > [CrCl₆]³⁻**