Amongst FeCl₃.3H₂O, K₃[Fe(CN)₆] and [Co(NH₃)₆]Cl₃, the spin-only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is ____________ B.M. [nearest integer]

Solution

Chemistry ma’am · 3 steps

Shortest wavelength, largest Δₒ: among inner-orbital complexes, go for the strongest ligand.

1. Shortest wavelength. Absorbed energy is E = hc/λ, so the shortest wavelength means the largest energy gap. In crystal field theory that gap is Δₒ, and a stronger-field ligand makes Δₒ larger.

   Compound	Metal ion	Ligand field	Hybridisation	Unpaired e⁻
   FeCl₃.3H₂O	Fe³⁺, 3d⁵	weak (Cl⁻, H₂O), high spin	sp³d², outer orbital	5
   K₃[Fe(CN)₆]	Fe³⁺, 3d⁵	very strong (CN⁻), low spin	d²sp³, inner orbital	1
   [Co(NH₃)₆]Cl₃	Co³⁺, 3d⁶	strong (NH₃), low spin	d²sp³, inner orbital	0

2. Pick the complex. Two complexes are inner-orbital. Both metals are +3, and CN⁻ sits above NH₃ in the spectrochemical series, so [Fe(CN)₆]³⁻ has the larger Δₒ and absorbs at the shorter wavelength.

   μ = √n(n+2) = √(1 × 3) = 1.73 B.M.

3. So. Low-spin 3d⁵ is t_(2g)⁵ with one unpaired electron, so μ = 1.73 B.M., which rounds to 2.

The common slip: 0. Choosing [Co(NH₃)₆]³⁺ as the shortest-wavelength absorber gives 0, but CN⁻ is a stronger-field ligand than NH₃, so the iron complex has the larger Δₒ.

The idea to keep. Shortest wavelength absorbed means the largest Δₒ, so look for the strongest-field ligand. Then count unpaired electrons in the low-spin arrangement and use √n(n+2).

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