The complex having minimum `Delta_(0)` value is :

Options

A. `[Co(NH_(3))_(6)]^(3+)`
B. `[Cr(H_(2)O)_(6)]^(3+)`
C. `[Cr(CN)_(6)]^(3-)`
D. `[CoCl_(6)]^(3-)`

Explanation

To solve the question regarding the complex having the minimum Δ₀ value (crystal field splitting energy), we will follow these steps:

### Step 1: Understand Δ₀ (Crystal Field Splitting Energy)
Δ₀ is the energy difference between the higher energy d-orbitals (E_g) and the lower energy d-orbitals (T_2g) in an octahedral complex. It is influenced by the nature of the ligands surrounding the metal ion.

**Hint:** Remember that Δ₀ is affected by the strength of the ligands; strong field ligands lead to larger Δ₀ values, while weak field ligands lead to smaller Δ₀ values.

### Step 2: Identify the Ligands
We need to identify the ligands in the given complexes and classify them based on their strength. The spectrochemical series ranks ligands from strong field to weak field:
- CN⁻ (strong field)
- NH₃ (moderate field)
- H₂O (weak field)
- Cl⁻ (weak field)

**Hint:** Use the spectrochemical series to determine the strength of the ligands in the complexes.

### Step 3: Determine the Type of Complexes
For each ligand, we need to determine whether they form high spin or low spin complexes:
- Strong field ligands (like CN⁻) lead to low spin complexes with higher Δ₀ values.
- Weak field ligands (like Cl⁻) lead to high spin complexes with lower Δ₀ values.

**Hint:** High spin complexes are formed by weak field ligands, resulting in lower Δ₀ values.

### Step 4: Compare Δ₀ Values
From the ligands identified:
- CN⁻ → High Δ₀ (low spin complex)
- NH₃ → Moderate Δ₀ (can be high or low spin depending on the metal)
- H₂O → Lower Δ₀ (high spin complex)
- Cl⁻ → Lowest Δ₀ (high spin complex)

Since Cl⁻ is the weakest field ligand, it will have the minimum Δ₀ value.

**Hint:** The weakest field ligand corresponds to the lowest Δ₀ value.

### Step 5: Conclusion
The complex with the minimum Δ₀ value is the one that contains Cl⁻ as a ligand, which forms a high spin complex.

**Final Answer:** The complex having minimum Δ₀ value is the one containing Cl⁻ (option number four).