Among the following pairs of complexes, in which case the `Delta_(0)` value is higher for the first one?

Options

A. `[Co(NH_(3))_(6)]^(3+) and [Co(CN)_(6)]^(3-)`
B. `[CoF_(6)]^(3-) and [Co(NH_(3))_(6)]^(3+)`
C. `[Co(H_(2)O)_(6)]^(2+) and [Co(H_(2)O)_(6)]^(3+)`
D. `[Rh(H_(2)O)_(6)]^(3+) and [Co(H_(2)O_(6)]^(3+)`

Explanation

To determine in which pair of complexes the `Delta_(0)` value is higher for the first complex, we need to analyze the factors that influence the value of `Delta_(0)`. The `Delta_(0)` value, which represents the crystal field splitting energy, depends on:

1. The oxidation state of the central metal ion.
2. The nature of the ligands (strong field vs weak field).
3. The effective nuclear charge (Z effective) experienced by the d-electrons in the metal ion.

Let's analyze the given pairs of complexes step by step:

### Step 1: Analyze the Ligands
- **Identify the ligands in each pair** and their relative strengths based on the spectrochemical series. Stronger ligands cause greater splitting of d-orbitals, leading to a higher `Delta_(0)` value.

### Step 2: Compare the Oxidation States
- **Determine the oxidation states** of the central metal ions in each complex. A higher oxidation state typically results in a higher `Delta_(0)` value due to increased electrostatic attraction between the metal ion and the ligands.

### Step 3: Evaluate the Effective Nuclear Charge (Z effective)
- **Consider the Z effective** of the metal ions. A higher Z effective means that the d-electrons are held more tightly, which can lead to a larger splitting of the d-orbitals.

### Step 4: Compare Each Pair
- For each pair of complexes, compare the ligands, oxidation states, and Z effective values to determine which complex has a higher `Delta_(0)` value.

### Example Analysis:
1. **First Pair:** Amine vs. Cyano
- Cyano is a stronger ligand than amine. Thus, `Delta_(0)` for the second complex (Cyano) will be higher.

2. **Second Pair:** Fluoro vs. Amine
- Amine is a stronger ligand than fluoro. Thus, `Delta_(0)` for the first complex (Amine) will be higher.

3. **Third Pair:** Aqua (Oxidation state +3) vs. Aqua (Oxidation state +2)
- The complex with the +3 oxidation state will have a higher `Delta_(0)` value.

4. **Fourth Pair:** Rhodium vs. Cobalt (both with oxidation state +3)
- Rhodium has a higher Z effective than cobalt, leading to a higher `Delta_(0)` value for Rhodium.

### Conclusion:
Based on the analysis, the pairs where the first complex has a higher `Delta_(0)` value are:
- The second pair (Fluoro vs. Amine).
- The third pair (Aqua with +3 vs. Aqua with +2).

The final answer is that the **second option (Fluoro vs. Amine)** and **third option (Aqua with +3 vs. Aqua with +2)** are the cases where the first complex has a higher `Delta_(0)` value.