The colour of the coordination compounds depends on the crystal field splitting . What will be the correct order of absorption of wavelength of light in the visible region, for the complexes, `[Co(NH_(3))_(6)]^(3+)`, `[Co(CN)_(6)]^(3-)` and `[Co(H_(2)O)_(6)]^(3+)`?

Options

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

Explanation

To determine the correct order of absorption of wavelength of light in the visible region for the coordination compounds \([Co(NH_3)_6]^{3+}\), \([Co(CN)_6]^{3-}\), and \([Co(H_2O)_6]^{3+}\), we need to analyze the ligands involved and their strength in terms of crystal field splitting.

### Step 1: Identify the ligands and their strengths
- **Cyanide (CN⁻)**: This is a strong field ligand.
- **Ammonia (NH₃)**: This is a moderate field ligand.
- **Water (H₂O)**: This is a weak field ligand.

### Step 2: Understand crystal field splitting
In coordination compounds, ligands cause the degenerate d-orbitals to split into different energy levels. The extent of this splitting depends on the strength of the ligand:
- Strong field ligands (like CN⁻) cause a larger splitting of the d-orbitals.
- Weak field ligands (like H₂O) cause a smaller splitting.

### Step 3: Relate crystal field splitting to absorption of light
The energy difference \(\Delta E\) between the split d-orbitals is related to the wavelength (\(\lambda\)) of light absorbed by the complex using the formula:
\[ \Delta E = \frac{hc}{\lambda} \]
Where:
- \(h\) is Planck's constant,
- \(c\) is the speed of light,
- \(\lambda\) is the wavelength.

From this relationship, we can see that:
- A larger \(\Delta E\) (stronger ligand) corresponds to a shorter wavelength (higher energy light absorbed).
- A smaller \(\Delta E\) (weaker ligand) corresponds to a longer wavelength (lower energy light absorbed).

### Step 4: Determine the order of absorption
Based on the ligand strengths:
1. **Cyanide (CN⁻)**: Strongest ligand → Largest \(\Delta E\) → Shortest wavelength absorbed.
2. **Ammonia (NH₃)**: Moderate ligand → Intermediate \(\Delta E\) → Intermediate wavelength absorbed.
3. **Water (H₂O)**: Weakest ligand → Smallest \(\Delta E\) → Longest wavelength absorbed.

Thus, the order of absorption of wavelength (from longest to shortest) is:
\[ [Co(H_2O)_6]^{3+} > [Co(NH_3)_6]^{3+} > [Co(CN)_6]^{3-} \]

### Final Answer
The correct order of absorption of wavelength of light in the visible region for the complexes is:
\[ [Co(H_2O)_6]^{3+} > [Co(NH_3)_6]^{3+} > [Co(CN)_6]^{3-} \]