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. a.
`II gt I gt III`
B. b. `I gt II gt III`
C. c. `III gt I gt III`
D. 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 ligands present in each complex and their relative strengths.

### Step-by-Step Solution:

1. **Identify the Ligands**:
- Complex I: Contains Cl (chloride) and NH3 (ammonia).
- Complex II: Contains NH3 and H2O (water).
- Complex III: Contains only NH3.

2. **Rank the Ligands by Strength**:
- According to the spectrochemical series, ligands can be ranked based on their field strength:
- Strongest: NH3 (ammonia)
- Intermediate: H2O (water)
- Weakest: Cl (chloride)

3. **Determine the Energy Absorption**:
- Stronger ligands cause greater splitting of the d-orbitals, leading to the absorption of higher energy light (shorter wavelength).
- Conversely, weaker ligands result in lower energy absorption (longer wavelength).

4. **Assign Wavelengths to Each Complex**:
- Complex III `[Co(NH3)6]^(3-)`: Contains only NH3 (strongest ligand), thus absorbs light at the shortest wavelength.
- Complex II `[Co(NH3)5H2O]^(3+)`: Contains NH3 and H2O (intermediate strength), thus absorbs light at a longer wavelength than Complex III but shorter than Complex I.
- Complex I `[CoCl(NH3)5]^(2+)`: Contains Cl (weakest ligand), thus absorbs light at the longest wavelength.

5. **Order of Wavelengths Absorbed**:
- From the analysis, we can conclude:
- Wavelength absorbed by Complex III < Wavelength absorbed by Complex II < Wavelength absorbed by Complex I.
- Therefore, the order of wavelengths absorbed is:
- Complex III (NH3 only) < Complex II (NH3 + H2O) < Complex I (NH3 + Cl).

### Final Answer:
The correct order of the wavelength of light absorbed by the complexes is:
**[Co(NH3)6]^(3-) < [Co(NH3)5H2O]^(3+) < [CoCl(NH3)5]^(2+)**.