1. Identify the type of transition

These octahedral cobalt complexes absorb visible light mainly due to $d$-$d$ transitions. The energy absorbed is approximately proportional to the crystal field splitting, $\Delta_o$.

$E = \frac{hc}{\lambda}$

So,

• larger $\Delta_o \Rightarrow$ higher energy absorbed
• higher energy absorbed $\Rightarrow$ smaller wavelength $\lambda$

Hence, the order of wavelength absorbed is inverse of the order of $\Delta_o$.

2. Compare ligands using spectrochemical series

Relevant ligands here:

$Cl^- < H_2O < NH_3$

So ligand field strength increases in the order:

$Cl^- < H_2O < NH_3$

This means replacing $Cl^-$ by $H_2O$ or $NH_3$ increases $\Delta_o$.

3. Examine each complex

(I) $[CoCl(NH_3)_5]^{2+}$

Let oxidation state of Co be $x$:

$x + (-1) + 5(0) = +2 \Rightarrow x = +3$

So this is a $Co^{3+}$ complex with one weak ligand $Cl^-$.

(II) $[Co(NH_3)_5H_2O]^{3+}$

$x + 5(0) + 0 = +3 \Rightarrow x = +3$

Again $Co^{3+}$, but now the sixth ligand is $H_2O$, which is stronger than $Cl^-$.

(III) $[Co(NH_3)_6]^{3+}$

$x + 6(0) = +3 \Rightarrow x = +3$

This has all six ligands as $NH_3$, strongest among the three sets.

4. Order of crystal field splitting

Since metal ion and oxidation state are same in all three, only ligand strength matters:

$\Delta_o(\text{I}) < \Delta_o(\text{II}) < \Delta_o(\text{III})$

because

• (I) contains $Cl^-$
• (II) contains $H_2O$
• (III) contains only $NH_3$

5. Convert to order of wavelength absorbed

Since

$\lambda \propto \frac{1}{\Delta_o}$

therefore,

$\lambda(\text{I}) > \lambda(\text{II}) > \lambda(\text{III})$

So the correct order is:

$\boxed{(I) > (II) > (III)}$

6. Match with options

This corresponds to Option C.