Arrange the following complexes in decreasing order of absorption of…

The correct answer is Option (1) → (B), (C), (D), (A)

In an octahedral complex the ligands split the d orbitals of the metal into a lower t_2g set and an upper e_g set. The energy gap is the crystal field splitting, Δ_o. The colour of the complex comes from an electron absorbing light whose energy equals this gap, so the wavelength absorbed is inversely related to Δ_o:

    \( \displaystyle \Delta_o = \frac{hc}{\lambda} \)

All four complexes contain the same ion, \( \ce{Co^3+} \), so Δ_o depends only on the ligand. The spectrochemical series orders ligands by the splitting they produce:

    \( \displaystyle \ce{F-} \lt \ce{H2O} \lt \ce{NH3} \lt \ce{CN-} \)

• (B) \( \ce{[CoF6]^3-} \): \( \ce{F-} \) is the weakest of the four, so Δ_o is smallest and the wavelength absorbed is the longest.

• (C) \( \ce{[Co(H2O)6]^3+} \): water produces a larger splitting than \( \ce{F-} \).

• (D) \( \ce{[Co(NH3)6]^3+} \): ammonia is stronger than water.

• (A) \( \ce{[Co(CN)6]^3-} \): \( \ce{CN-} \) is the strongest field ligand, so Δ_o is largest and the wavelength absorbed is the shortest.

In decreasing order of the wavelength absorbed:

    \( \displaystyle \ce{[CoF6]^3-} \gt \ce{[Co(H2O)6]^3+} \gt \ce{[Co(NH3)6]^3+} \gt \ce{[Co(CN)6]^3-} \)

Shortcut: The fluoro complex absorbs the longest wavelength and the cyano complex the shortest, so the order starts with (B) and ends with (A); only Option (1) does both.

NCERT (2026-27 edition):
Crystal Field Theory – “… In general, ligands can be arranged in a series in the order of increasing field strength as given below:

    \( \ce{I^- \lt Br^- \lt SCN^- \lt Cl^- \lt S^{2-} \lt F^- \lt OH^- \lt C2O4^{2-} \lt H2O \lt NCS^- \lt edta^{4-} \lt NH3 \lt en \lt CN^- \lt CO} \)

Such a series is termed as spectrochemical series. It is an experimentally determined series based on the absorption of light by complexes with different ligands.”