In the give complexes
(i). `[Co(NH_(3))_(5)(H_(2)O)]^(3+)`
(ii). `[Co(NH_(3))_(5)Cl]^(2+)`
(iii). `[Co(NH_(3))_(6)]^(3+)`
The decreasing order of `lamda` absorbed is

Options

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

Answer

To determine the decreasing order of λ (wavelength) absorbed for the given complexes, we need to analyze the ligands involved and their field strengths. The ligands will influence the splitting of the d-orbitals in the metal complex, which in turn affects the wavelength of light absorbed.

### Step-by-Step Solution:

1. **Identify the Ligands**:
- For complex (i) `[Co(NH3)5(H2O)]^(3+)`, the ligands are NH3 and H2O.
- For complex (ii) `[Co(NH3)5Cl]^(2+)`, the ligands are NH3 and Cl^-.
- For complex (iii) `[Co(NH3)6]^(3+)`, the ligand is NH3.

2. **Determine the Field Strength of Ligands**:
- The field strength of the ligands can be ranked based on their ability to split the d-orbitals:
- NH3 (ammonia) is a strong field ligand.
- H2O (water) is a moderate field ligand.
- Cl^- (chloride) is a weak field ligand.
- The order of field strength is:
- NH3 > H2O > Cl^-

3. **Relate Splitting Energy to Wavelength**:
- The splitting energy (Δ) is inversely proportional to the wavelength (λ) absorbed:
- Higher splitting energy (Δ) → Lower wavelength (λ)
- Lower splitting energy (Δ) → Higher wavelength (λ)

4. **Determine the Splitting Energy for Each Complex**:
- For `[Co(NH3)5(H2O)]^(3+)`, the presence of NH3 (strong field) and H2O (moderate field) suggests a higher splitting energy than complexes with Cl^-.
- For `[Co(NH3)5Cl]^(2+)`, NH3 is strong, but Cl^- is weak, leading to moderate splitting energy.
- For `[Co(NH3)6]^(3+)`, only NH3 is present, resulting in high splitting energy.

5. **Rank the Complexes by Wavelength Absorbed**:
- Since NH3 has the highest field strength, it will result in the lowest wavelength absorbed.
- Cl^- has the lowest field strength, leading to the highest wavelength absorbed.
- Therefore, the order of λ absorbed is:
- Cl^- (highest λ) > H2O > NH3 (lowest λ)

6. **Final Order**:
- The decreasing order of λ absorbed is:
- `[Co(NH3)5Cl]^(2+)` > `[Co(NH3)5(H2O)]^(3+)` > `[Co(NH3)6]^(3+)`

### Conclusion:
The final answer for the decreasing order of λ absorbed is:
1. `[Co(NH3)5Cl]^(2+)`
2. `[Co(NH3)5(H2O)]^(3+)`
3. `[Co(NH3)6]^(3+)`