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 energy (CFSE), we can follow these steps:

### Step 1: Understand the relationship between absorption maxima and CFSE
The crystal field splitting energy (CFSE) is inversely proportional to the wavelength of light absorbed (λ_max). This means:
\[ \text{CFSE} \propto \frac{1}{\lambda_{\text{max}}} \]
Thus, a smaller λ_max corresponds to a larger CFSE.

### Step 2: List the given complexes and their λ_max values
We have the following complexes and their absorption maxima:
1. \( \text{Co(NH}_3\text{)}_6^{3+} \) - λ_max = 475 nm
2. \( \text{Co(CN)}_6^{3-} \) - λ_max = 310 nm
3. \( \text{Co(H}_2\text{O)}_6^{3+} \) - λ_max = 490 nm

### Step 3: Identify the minimum λ_max value
Now, we need to find which of these complexes has the minimum λ_max value:
- For \( \text{Co(NH}_3\text{)}_6^{3+} \): 475 nm
- For \( \text{Co(CN)}_6^{3-} \): 310 nm
- For \( \text{Co(H}_2\text{O)}_6^{3+} \): 490 nm

The minimum λ_max is 310 nm for \( \text{Co(CN)}_6^{3-} \).

### Step 4: Determine the CFSE order
Since λ_max is minimum for \( \text{Co(CN)}_6^{3-} \), it will have the maximum CFSE. We can now order the complexes based on their CFSE:
1. \( \text{Co(CN)}_6^{3-} \) - Maximum CFSE
2. \( \text{Co(NH}_3\text{)}_6^{3+} \) - Intermediate CFSE
3. \( \text{Co(H}_2\text{O)}_6^{3+} \) - Minimum CFSE

### Conclusion
The crystal field splitting is maximum for \( \text{Co(CN)}_6^{3-} \).

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