In which of the following octahedral complexes will the magnitude of `triangle_(0)` be the highest

Options

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

Answer

To determine which octahedral complex has the highest magnitude of crystal field splitting energy (Δ₀), we need to analyze the ligands involved in the complexes. The crystal field splitting energy is influenced by the nature of the ligands surrounding the metal ion in the octahedral complex.

### Step-by-Step Solution:

1. **Understand Crystal Field Splitting Energy (Δ₀)**:
- Δ₀ is the energy difference between the higher energy \(E_g\) orbitals and the lower energy \(T_{2g}\) orbitals in an octahedral complex.

2. **Identify Factors Affecting Δ₀**:
- The magnitude of Δ₀ is primarily influenced by the strength of the ligands. Strong field ligands cause a larger splitting of the d-orbitals, resulting in a higher Δ₀ value.

3. **Refer to the Spectrochemical Series**:
- The spectrochemical series ranks ligands based on their ability to split the d-orbitals:
- Weak field ligands (lower Δ₀): \(I^- < Br^- < Cl^- < F^- < OH^- < H_2O < NH_3 < NO_2^- < CN^- < CO\)
- From this series, we can see that \(CN^-\) is a strong field ligand, while \(C_2O_4^{2-}\) (oxalate ion) is a weak field ligand.

4. **Compare the Ligands in the Given Complexes**:
- If the complexes include ligands such as \(CN^-\), \(NH_3\), \(H_2O\), and \(C_2O_4^{2-}\), we can rank them:
- \(CN^-\) (strongest field ligand)
- \(NH_3\) (moderate field ligand)
- \(H_2O\) (weaker field ligand)
- \(C_2O_4^{2-}\) (weakest field ligand)

5. **Determine the Complex with the Highest Δ₀**:
- Since \(CN^-\) is the strongest field ligand, the octahedral complex containing \(CN^-\) will have the highest Δ₀ value.
- Therefore, the complex with \(CN^-\) will have the highest magnitude of Δ₀.

### Conclusion:
The octahedral complex with the highest magnitude of Δ₀ is the one that contains the \(CN^-\) ligand.