Three octahedral complexes of Co³⁺ formed separately with the ligands CN^- , en , and F^- absorb light at wavelengths ₁ , ₂ , and ₃ respectively, such that ₁ < ₂ < ₃ . If X is the complex that absorbs light at wavelength ₃ , then the spin-only magnetic moment of X is ________ B.M. (Nearest integer)

Step-by-step solution

The energy of absorbed light is inversely proportional to its wavelength ( ₀ 1 ). According to the spectrochemical series, the ligand field strength is in the order: CN^- > en > F^- . Therefore, the crystal field splitting energy ( ₀ ) follows the order: [Co(CN)₆]³⁻ > [Co(en)₃]³⁺ > [CoF₆]³⁻ . Thus, the absorbed wavelengths will follow the reverse order: _ CN^- Given ₁ In [CoF₆]³⁻ , the central metal ion is Co³⁺ , which has a 3d^6 electronic configuration. Since F^- is a weak field ligand, it forms a high-spin compl