The wavelength of light absorbed for the following complexes are in the order
[Co(NH₃)₆]³⁺, ;, [Co(H₂O)₆]³⁺, ;, [Co(CN)₆]³⁻, ;, [Co(NH₃)₅(H₂O)]³⁺, ;, [CoF₆]³⁻; (I), (II), (III), (IV), (V)

Solution

Chemistry ma’am · 3 steps

Rank the ligands by field strength first; the biggest splitting absorbs the shortest wavelength.

1. Same metal ion. All five complexes contain octahedral Co³⁺, so only the ligands change the splitting Δₒ. The spectrochemical series gives their strength: F⁻ < H₂O < NH₃ < CN⁻.
2. Splitting and wavelength. The absorbed photon carries exactly the energy Δₒ. Energy and wavelength are inversely related, so a larger Δₒ means a shorter wavelength.

   Δₒ = hc/λ ⇒ λ ∝ 1/Δₒ

   Complex	Ligand set	Δₒ	λ absorbed
   III	6 CN⁻	largest	shortest
   I	6 NH₃	second	second shortest
   IV	5 NH₃ + 1 H₂O	a little below I	a little longer than I
   II	6 H₂O	fourth	second longest
   V	6 F⁻	smallest	longest

3. So. Swapping one NH₃ for the weaker H₂O puts IV between I and II, and F⁻ gives the smallest splitting. The order is III < I < IV < II < V, option (c).

The idea to keep. For the same metal ion, strong-field ligands give a big Δₒ and absorb short wavelengths. A mixed-ligand complex falls between its two parent complexes.

Answer from the NTA final answer key. Solution by PrepWiser.