Question

What can be inferred from the magnetic moment values of the following complex species?

Example	Magnetic Moment (BM)
$K_4\left[Mn\right(CN{)}_6]$	$2.2$
$\left[Fe\right(H_{2}O{)}_6{]}^{2+}$	$5.3$
$K_2\left[MnC{l}_4\right]$	$5.9$

Answer 1

Magnetic moment ($\mu$) is given as $\mu =\sqrt{n(n+2)}$

$n=1,\mu =\sqrt{1(1+2)}=\sqrt{3}=1.732;n=2,\mu =\sqrt{2(2+2)}=\sqrt{8}=2.83$

$n=3,\mu =\sqrt{3(3+2)}=\sqrt{15}=3.87;n=4,\mu =\sqrt{4(4+2)}=\sqrt{24}=4.899$

$n=5,\mu =\sqrt{5(5+2)}=\sqrt{35}=5.92$

$K_4\left[Mn\right(CN{)}_6]$
$M{n}^{2+}:3d^5$
From magnetic moment of 2.2, presence of 1 unpaired electron can be infered. This is possible for inner orbital or low spin complexes with configuration, $t_{2g}^5$.
$\left[Fe\right(H_{2}O{)}_6{]}^{2+}$
$F{e}^{2+}:3d^6$
From magnetic moment of 5.3, presence of 4 unpaired electrons can be infered. This is possible for outer orbital or high spin complexes with configuration, $t_{2g}^4{e}_g^2$.
$K_2\left[MnC{l}_4\right]$
$M{n}^{2+}:3d^5$
From magnetic moment of 5.9, presence of 5 unpaired electrons can be inferred. This is possible for tetrahedral complexes (as d orbitals are not disturbed) with configuration, $e_g^2{t}_{2g}^3$.