The complex having lowest Δ _O value among the given complexes is :

The correct answer is Option (4) → \([CrCl_6]^{3-}\)

The crystal field splitting Δ_o depends on the strength of the ligand (spectrochemical series) and on the metal ion. In the spectrochemical series

    Cl⁻ < \( \ce{H2O} \) < \( \ce{NH3} \) < \( \ce{CN^{-}} \)

\( \ce{Cl^{-}} \) is a weak-field ligand at the low end of the series, so \( \ce{[CrCl6]^{3-}} \) has the smallest Δ_o of the four complexes.

Why the other options are incorrect

• Option (1) \([Co(NH_3)_6]^{3+}\) — Incorrect. \( \ce{NH3} \) is a fairly strong ligand and \( \ce{Co^{3+}} \) gives a large splitting (the complex is low spin), so Δ_o is large.

• Option (2) \([Cr(H_2O)_6]^{3+}\) — Incorrect. Same metal ion as option 4, but \( \ce{H2O} \) is a stronger ligand than \( \ce{Cl^{-}} \), so Δ_o is larger.

• Option (3) \([Co(CN)_6]^{3-}\) — Incorrect. \( \ce{CN^{-}} \) is one of the strongest-field ligands; this complex has the largest Δ_o of the four.

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:
I^– < Br^– < SCN^– < Cl^– < S^2– < F^– < OH^– < C₂O₄^2– < H₂O < NCS^– < edta^4– < NH₃ < en < CN^– < CO
Such a series is termed as spectrochemical series.”