The absolute difference in the squares of the spin-only magnetic moments of the complex ions [Fe(H₂O)₆]²⁺ and [Ru(H₂O)₆]²⁺ is ________ (in BM ^2 ).

Step-by-step solution

For [Fe(H₂O)₆]²⁺ : The central metal ion is Fe²⁺ , which has a 3d^6 electronic configuration. Since H₂O acts as a weak field ligand for 3d series metals, the crystal field splitting is small ( _o The electronic arrangement is t_ 2g ^4 e_g^2 , giving 4 unpaired electrons ( n = 4 ). The square of the spin-only magnetic moment is ₁^2 = n(n+2) = 4(4+2) = 24 BM ^2 . For [Ru(H₂O)₆]²⁺ : The central metal ion is Ru²⁺ , which belongs to the 4d series and has a 4d^6 configuration. For metals of the 4d and 5d series, the crys