The complex ion having minimum magnitude of `Delta_0 (CFSE)` is

Options

A. `[Co(Cl)_6]^(3-)`
B. `[Cr (CN)_6]^(3-)`
C. `[Cr(H_2O)]^(3+)`
D. `[Co(NH_3)_6]^(3+)`

Explanation

To determine the complex ion with the minimum magnitude of `Δ₀ (CFSE)`, we need to understand the concept of Crystal Field Stabilization Energy (CFSE) and how it relates to the splitting of d-orbitals in transition metal complexes.

### Step-by-Step Solution:

1. **Understanding Crystal Field Splitting Energy (Δ₀)**:
- In transition metal complexes, the d-orbitals split into different energy levels when ligands approach the metal ion. The energy difference between these levels is known as Crystal Field Splitting Energy (Δ₀).
- The magnitude of Δ₀ depends on the nature of the metal ion, its oxidation state, and the type of ligands surrounding it.

2. **Identifying Factors Affecting CFSE**:
- The CFSE is calculated based on the arrangement of electrons in the split d-orbitals.
- In a high-spin complex, the electrons occupy the higher energy orbitals to minimize pairing, leading to a lower CFSE.
- In a low-spin complex, electrons pair up in the lower energy orbitals, leading to a higher CFSE.

3. **Determining the Minimum CFSE**:
- To find the complex with the minimum CFSE, we need to look for a high-spin complex, as high-spin configurations generally lead to lower stabilization energy.
- Complexes with weak field ligands (like I⁻, Br⁻, etc.) tend to be high-spin and thus have lower CFSE.

4. **Evaluating Options**:
- If given multiple options for complex ions, identify which ones are likely to be high-spin complexes based on their ligands.
- For example, complexes with ligands such as Cl⁻ or F⁻ are typically high-spin, while those with ligands like CN⁻ or CO are low-spin.

5. **Conclusion**:
- The complex ion with the minimum magnitude of `Δ₀ (CFSE)` will be the one that is a high-spin complex with weak field ligands.

### Final Answer:
The complex ion having the minimum magnitude of `Δ₀ (CFSE)` is the one with weak field ligands leading to a high-spin configuration.