In which of the following coordination entites the magnitude of `Delta_(0)` (CFSE in octehedral field) will be maximum.
`(At. No .Co = 27)`

Options

A. `[Co(H_(2)O)_(6)]^(3+)`
B. `[Co(NH_(3))_(6)]^(3+)`
C. `[Co(CN)_(6)]^(3-)`
D. `[Co(C_(2)O_(4))_(3)]^(3-)`

Explanation

To determine which coordination entity has the maximum magnitude of \(\Delta_0\) (the crystal field splitting energy in an octahedral field), we need to consider the strength of the ligands involved. The splitting energy is influenced by the nature of the ligands surrounding the central metal ion.

### Step-by-Step Solution:

1. **Identify the Coordination Entities**:
We need to examine the coordination entities provided in the question. For example, let’s assume the options are:
- A: \([Co(NH_3)_6]^{3+}\)
- B: \([Co(CN)_6]^{3-}\)
- C: \([Co(OH)_6]^{3-}\)
- D: \([Co(H_2O)_6]^{3+}\)

2. **Determine the Ligand Strength**:
The strength of ligands can be classified into strong field and weak field ligands. The order of ligand strength is as follows:
- Strongest: CN\(^-\) > CO > NH\(_3\) > H\(_2\)O > OH\(^-\) > F\(^-\) > Cl\(^-\) > Br\(^-\) > I\(^-\)

3. **Analyze Each Coordination Entity**:
- **A: \([Co(NH_3)_6]^{3+}\)**: NH\(_3\) is a moderate field ligand.
- **B: \([Co(CN)_6]^{3-}\)**: CN\(^-\) is a strong field ligand.
- **C: \([Co(OH)_6]^{3-}\)**: OH\(^-\) is a weak field ligand.
- **D: \([Co(H_2O)_6]^{3+}\)**: H\(_2\)O is also a weak field ligand.

4. **Compare the Ligands**:
Based on the strength of the ligands:
- CN\(^-\) (in option B) is the strongest ligand, leading to the largest \(\Delta_0\).
- NH\(_3\) (in option A) is stronger than OH\(^-\) and H\(_2\)O but weaker than CN\(^-\).
- OH\(^-\) and H\(_2\)O are weak field ligands.

5. **Conclusion**:
Since the magnitude of \(\Delta_0\) is greatest for the strongest ligand, the coordination entity with the maximum \(\Delta_0\) is \([Co(CN)_6]^{3-}\).

### Final Answer:
The coordination entity with the maximum magnitude of \(\Delta_0\) is \([Co(CN)_6]^{3-}\).