For which pair of complexes is the order of values of `Delta_0` correct?

Options

A. `[Rh(NH_(3))_(6)]^(3+) gt [Co(NH_(3))_(6)]^(3+)`
B. `[Fe(CO)_(6)] gt [Fe(CN)_(6)]^(3-)`
C. `[Cr(H_(2)O)_(6)]^(2+) gt [Cr(H_(2)O)_(6)]^(3+)`
D. `[CrF_(6)]^(3-) gt [Cr(CN)_(6)]^(3-)`

Explanation

To solve the question regarding the correct order of values of Δ₀ (crystal field splitting energy) for given pairs of complexes, we will analyze each option based on the principles of crystal field theory and the spectrochemical series.

### Step-by-step Solution:

1. **Understanding Crystal Field Splitting Energy (Δ₀)**:
- Δ₀ is influenced by the nature of the central metal ion, its oxidation state, and the type of ligands surrounding it.
- Generally, Δ₀ increases with the increase in the oxidation state of the metal ion and the strength of the ligands.

2. **Analyzing the First Option**:
- The first option compares two complexes with cobalt (3d series) and rhodium (4d series).
- For transition metals, the order of Δ₀ is typically 5d > 4d > 3d due to the increasing effective nuclear charge and the associated ligand field strength.
- Since both complexes have the same ligands and coordination number, the order of Δ₀ is correct as given in the option.

3. **Analyzing the Second Option**:
- This option compares complexes with carbonyl (neutral ligand) and cyanide (strong field ligand).
- The oxidation state of the central atom affects Δ₀. The complex with cyanide will have a higher oxidation state than that with carbonyl, leading to a higher Δ₀.
- Therefore, this option is incorrect as the Δ₀ for the cyanide complex should be greater than that for the carbonyl complex.

4. **Analyzing the Third Option**:
- This option compares chromium complexes with water (neutral ligand) and a complex with a higher charge.
- The complex with a higher charge will have a higher Δ₀ due to the increased electrostatic attraction between the metal ion and the ligands.
- Thus, this option is also incorrect as the Δ₀ for the second complex should be greater.

5. **Analyzing the Fourth Option**:
- This option compares chromium complexes with fluorine (weak field ligand) and cyanide (strong field ligand).
- Since cyanide is a strong field ligand, it will cause a greater splitting of the d-orbitals compared to fluorine.
- Therefore, this option is also incorrect as the Δ₀ for the cyanide complex will be greater than that for the fluorine complex.

### Conclusion:
The only correct order of Δ₀ is found in the first option, which states that Δ₀ for rhodium (4d) is greater than that for cobalt (3d).