The absorption maxima of several octahedral complex ions are as follows:
`{:("S.No","Compound",lamda_(max)nm,),(1,[Co(NH_(3))_(6)]^(3+),475,),(2,[Co(CN)_(6)]^(3-),310,),(3,[Co(H_(2)O)_(6)]^(3+),490,):}`
The crystal field SQPlitting is maximum for :

Options

A. `[Co(H_(2)O)_(6)]^(3+)`
B. `[Co(CN)_(6)]^(3-)`
C. `[Co(NH_(3))_(6)]^(3+)`
D. All the complex ions have the same SQPlitting `Delta_(0)`,

Answer

To determine which octahedral complex ion has the maximum crystal field splitting (CFSC), we can analyze the provided absorption maxima (λ_max) values for each complex. The relationship between the crystal field splitting energy (Δ) and the wavelength of light absorbed is given by the formula:

\[ E = \frac{hc}{\lambda} \]

Where:
- \( E \) is the energy of the absorbed light,
- \( h \) is Planck's constant,
- \( c \) is the speed of light,
- \( \lambda \) is the wavelength of light absorbed.

### Step-by-Step Solution:

1. **Identify the Compounds and their Wavelengths**:
- [Co(NH₃)₆]³⁺: λ_max = 475 nm
- [Co(CN)₆]³⁻: λ_max = 310 nm
- [Co(H₂O)₆]³⁺: λ_max = 490 nm

2. **Determine the Energy for Each Complex**:
Using the formula \( E = \frac{hc}{\lambda} \), we can see that a smaller wavelength corresponds to a higher energy. Therefore, we can compare the wavelengths directly to determine which complex has the highest energy and consequently the highest CFSC.

3. **Compare the Wavelengths**:
- [Co(NH₃)₆]³⁺: 475 nm (Energy is lower than [Co(CN)₆]³⁻)
- [Co(CN)₆]³⁻: 310 nm (Highest energy)
- [Co(H₂O)₆]³⁺: 490 nm (Energy is lower than [Co(NH₃)₆]³⁺)

4. **Identify the Strongest Ligand**:
- Among the ligands (NH₃, CN⁻, and H₂O), CN⁻ is the strongest ligand, followed by NH₃, and then H₂O. Stronger ligands cause greater crystal field splitting.

5. **Conclusion**:
Since [Co(CN)₆]³⁻ has the lowest λ_max (310 nm), it corresponds to the highest energy and thus the maximum crystal field splitting (CFSC).

### Final Answer:
The crystal field splitting is maximum for [Co(CN)₆]³⁻.