Three complexes, `[CoCl(NH_(3))_(5)]^(2+) (I), [Co(NH_(3))_(5)H_(2)O]^(3+) (II) [Co(NH_(3))_(6)]^(3-) (III)` absorb light in the visible region. The correct order of the wavelength of light absorbed by them is:

Options

A. `II gt I gt III`
B. `I gt II gt III`
C. `III gt I gt III`
D. `III gt II gt I`

Explanation

To determine the correct order of the wavelength of light absorbed by the complexes `[CoCl(NH₃)₅]²⁺ (I)`, `[Co(NH₃)₅H₂O]³⁺ (II)`, and `[Co(NH₃)₆]³⁻ (III)`, we need to analyze the nature of the ligands in each complex and their positions in the spectrochemical series.

### Step-by-Step Solution:

1. **Identify the Ligands**:
- Complex I: `[CoCl(NH₃)₅]²⁺` has one chloride ion (Cl⁻) and five ammonia (NH₃) ligands.
- Complex II: `[Co(NH₃)₅H₂O]³⁺` has five ammonia (NH₃) ligands and one water (H₂O) ligand.
- Complex III: `[Co(NH₃)₆]³⁻` has six ammonia (NH₃) ligands.

2. **Determine the Ligand Strength**:
- According to the spectrochemical series, ligands can be ranked based on their ability to split the d-orbitals:
- Cl⁻ (halide donor) is a weak field ligand.
- H₂O (oxygen donor) is a moderate field ligand.
- NH₃ (nitrogen donor) is a strong field ligand.
- Therefore, the order of ligand strength is:
- NH₃ > H₂O > Cl⁻

3. **Relate Ligand Strength to Wavelength Absorption**:
- Strong field ligands cause a larger splitting of d-orbitals, which corresponds to higher energy transitions and thus absorb shorter wavelengths of light.
- Conversely, weak field ligands cause smaller splitting, leading to lower energy transitions and longer wavelengths of light absorption.

4. **Assess Each Complex**:
- Complex I: Contains Cl⁻ (weak field), absorbs longer wavelengths.
- Complex II: Contains H₂O (moderate field), absorbs intermediate wavelengths.
- Complex III: Contains only NH₃ (strong field), absorbs shorter wavelengths.

5. **Order of Wavelength Absorption**:
- Based on the ligand strength and the corresponding wavelength absorption:
- Complex III (NH₃) absorbs the shortest wavelength (highest energy).
- Complex II (H₂O) absorbs an intermediate wavelength.
- Complex I (Cl⁻) absorbs the longest wavelength (lowest energy).
- Therefore, the order of wavelengths absorbed is:
- λ(III) < λ(II) < λ(I)

### Final Answer:
The correct order of the wavelength of light absorbed by the complexes is:
\[ \text{Complex III} < \text{Complex II} < \text{Complex I} \]