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Step-by-Step Explanation
Step 1: Identify the Complexes and Their Ligands
We have three cobalt(III) complexes:
(I) [CoCl(NH3)5]2+
(II) [Co(NH3)5H2O]3+
(III) [Co(NH3)6]3+
Each complex absorbs visible light, and we need to arrange them according to the wavelength of the light they absorb.
Step 2: Recall the Concept of Ligand Field Splitting
In octahedral complexes, ligands split the d orbitals of the metal ion into two sets with different energies. Stronger-field ligands produce a larger splitting ($\Delta_0$), thereby requiring a higher energy (and thus a lower wavelength) of light for the d–d transition.
Step 3: Relate Ligand Strength to Wavelength of Absorption
The energy of the absorbed light is inversely proportional to its wavelength:
$ E \propto \frac{1}{\lambda} $
A stronger ligand field means larger splitting ($\Delta_0$) and higher energy of absorption, which in turn corresponds to lower wavelength of light.
Step 4: Order of Ligand Strength
The general order of ligand field strength (from weaker to stronger field) for the ligands present is:
$ \text{Cl}^- < \text{H}_2\text{O} < \text{NH}_3 $
Hence the splitting ($\Delta_0$) follows:
$ \text{(Cl}^-)\, < \text{(H}_2\text{O})\, < \text{(NH}_3) $
Step 5: Apply to Each Complex
• Complex (I) [CoCl(NH3)5]2+ contains Cl⁻, which is a weaker ligand than H2O and NH3. Therefore, it causes smaller splitting and absorbs light of longer wavelength.
• Complex (II) [Co(NH3)5H2O]3+ has H2O as the ligand apart from NH3. H2O is a stronger ligand than Cl⁻ but weaker than NH3.
• Complex (III) [Co(NH3)6]3+ has NH3 only, which is a relatively strong ligand, causing the largest splitting and hence the lowest wavelength absorbed.
Step 6: Arrive at the Correct Order of Wavelengths
Combining these ideas, the correct decreasing order of absorbed wavelength is:
(I) > (II) > (III).
This matches the principle that a weaker ligand field leads to lower energy of absorbed light, meaning a higher wavelength.
