The complex ion [Mn(CN)6]^3- is a low spin octahedral complex. In an…

The correct answer is Option (4) → −1.6Δ_o

The crystal field stabilisation energy (as defined in the question) adds −0.4Δ_o for every t_2g electron and +0.6Δ_o for every e_g electron. In a low spin complex Δ_o > P, so the electrons pair in the t_2g set before any enters e_g.

• Oxidation state of Mn: x + 6(−1) = −3, so x = +3.

• Mn (Z = 25): [Ar] 3d⁵ 4s²; losing the two 4s electrons and one 3d electron gives Mn³⁺: [Ar] 3d⁴.

• Low spin (CN⁻ is a strong field ligand): the fourth electron pairs in t_2g, giving \( t_{2g}^{4}e_{g}^{0} \), with two unpaired electrons.

• \( \text{CFSE} = 4(-0.4\Delta_o) + 0(+0.6\Delta_o) = -1.6\Delta_o \)

NCERT (2026-27 edition):
5.5.4 Crystal Field Theory – “…Thus, the energy of the two e_g orbitals will increase by (3/5) Δ_o and that of the three t_2g will decrease by (2/5)Δ_o.”

“(ii) If Δ_o > P, it becomes more energetically favourable for the fourth electron to occupy a t_2g orbital with configuration t_2g⁴e_g⁰. Ligands which produce this effect are known as strong field ligands and form low spin complexes.”

5.5.2 Magnetic Properties of Coordination Compounds – “…[Mn(CN)₆]^3– has magnetic moment of two unpaired electrons while [MnCl₆]^3– has a paramagnetic moment of four unpaired electrons.”