Order of wavelength of absorbed radiation for the below given complexes is

(a) [Co(NH₃)₆]³⁺
(b) [Co(NH₃)₅H₂O]³⁺
(c) [CoF₆]³⁻
(d) [Co(CN)₆]³⁻

The correct answer is d < a < b < c.

To determine the order of the wavelength of absorbed radiation for the given complexes, we can use Crystal Field Theory (CFT) and the spectrochemical series.

Step 1: Understand the relationship between Energy and Wavelength
The energy of the absorbed radiation is inversely proportional to its wavelength. This relationship is represented by the formula:

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

Here, $h$ is Planck's constant and $c$ is the speed of light. Therefore, a larger crystal field splitting energy (${\Delta }_o$) corresponds to the absorption of radiation with a shorter (smaller) wavelength ($\lambda$).

Step 2: Compare ligand strength using the Spectrochemical Series
The spectrochemical series arranges ligands in order of increasing field strength (their ability to split the d-orbitals):
F^- < H₂O < NH₃ < CN^-

Now, let us analyze the given complexes and their ligands:
(a) [Co(NH₃)₆]³⁺ contains six NH₃ ligands.
(b) [Co(NH₃)₅H₂O]³⁺ contains five NH₃ ligands and one weaker H₂O ligand.
(c) [CoF₆]^3- contains six weak-field F^- ligands.
(d) [Co(CN)₆]^3- contains six strong-field CN^- ligands.

Step 3: Order of Crystal Field Splitting Energy (Δ_o)
Based on the ligand field strength, the order of crystal field splitting energy is:
[CoF₆]^3- < [Co(NH₃)₅H₂O]³⁺ < [Co(NH₃)₆]³⁺ < [Co(CN)₆]^3-

In terms of the given letters, the energy order is:
c < b < a < d

Step 4: Order of Wavelength of Absorbed Radiation (λ)
Since the wavelength of absorbed radiation is inversely proportional to the crystal field splitting energy, the order of the wavelength is the exact reverse of the energy order:
c > b > a > d

Which is written as:
d < a < b < c