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

Options

A. `[Cr(H_2O)_6]^(+2) gt [Cr(H_2O)_6]^(+3)`
B. `[Fe(CN)_6]^(-4) gt [Fe(CN)_6]^(-3)`
C. `[Rh(NH_3)_6]^(+3) gt [Co(NH_3)_6]^(+3)`
D. `[CrF_6]^(-3) gt [Cr(CN)_6]^(-3)`

Answer

To determine the correct order of values of Δ₀ (crystal field splitting energy) for the given pairs of coordination compounds, we need to analyze the factors that affect Δ₀, which include the nature of the central metal atom, its oxidation state, and the type of ligands involved.

### Step-by-Step Solution:

1. **Understanding Δ₀**:
- Δ₀ is the energy difference between the split d-orbitals in an octahedral field. It is influenced by the central metal atom, its oxidation state, and the ligands.

2. **Identifying Factors Affecting Δ₀**:
- **Central Metal Atom**: The atomic number of the metal affects Δ₀. A higher atomic number typically leads to a greater Δ₀.
- **Oxidation State**: A higher oxidation state of the metal increases Δ₀ because it leads to greater ligand field strength.
- **Nature of Ligands**: Strong field ligands (like CN⁻) produce a larger Δ₀ compared to weak field ligands (like F⁻ or H₂O).

3. **Analyzing the Given Options**:
- **Option A**: Compare two complexes with the same metal but different ligands. The ligand strength will determine Δ₀.
- **Option B**: Compare complexes with the same metal but different oxidation states. Higher oxidation state will lead to a greater Δ₀.
- **Option C**: Compare complexes with different metals. The metal with the higher atomic number will generally have a greater Δ₀.

4. **Evaluating Each Option**:
- For **Option C**: If we have rhodium (higher atomic number) compared to cobalt, then Δ₀ for rhodium will be greater than for cobalt. This option is likely correct.
- For **Option B**: If both complexes have chromium but one is in the +2 oxidation state and the other in +3, the +3 state should have a greater Δ₀. If the statement claims otherwise, it is incorrect.
- For **Option A**: If comparing a strong field ligand with a weak field ligand, the strong field ligand will yield a greater Δ₀.

5. **Conclusion**:
- After analyzing the options based on the factors affecting Δ₀, we conclude that **Option C** is correct, as it correctly identifies the relationship between the atomic number of the metals and Δ₀.

### Final Answer:
The correct order of values of Δ₀ is for **Option C**.