The spin only magnetic moment of Hexacyanidomanganate(II) ion is ____…

The correct answer is Option (2) → 1.73

The spin only magnetic moment depends only on the number of unpaired electrons, n:

    \( \displaystyle \mu=\sqrt{n(n+2)}\ \text{BM} \)

Hexacyanidomanganate(II) is \( \ce{[Mn(CN)6]^4-} \), with manganese in the +2 state. Mn (Z = 25) is [Ar]3d⁵4s²; losing the two 4s electrons gives \( \ce{Mn^2+} \): 3d⁵.

\( \ce{CN-} \) is a strong field ligand. It splits the d orbitals so widely that the five electrons pair up in the lower t_2g set instead of entering e_g (low spin):

    t_2g: [↑↓] [↑↓] [↑ ]    e_g: [  ] [  ]

This leaves one unpaired electron:

    \( \displaystyle \mu=\sqrt{1(1+2)}=\sqrt{3}=1.73\ \text{BM} \)

So the spin only magnetic moment is 1.73 BM.