Amongst FeCl3.3H2O, K3 $\left[Fe{\left(CN\right)}_6\right]and\left[Co{\left(N{H}_3\right)}_6\right]C{l}_3,$ the spin- only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is ________ B.M [nearest integer]

FeCl₃. 3H₂O i.e. [Fe (H₂O)₃], K₃ [Fe (CN]₆ and [Co (NH₃)₆]Cl₃ the last two complex are inner-orbital complex due to presence of strong ligand.

$\therefore {\Delta }_{0}of{K}_3\left[Fe{\left(CN\right)}_6\right]>{\Delta }_{0}of\left[Co{\left(N{H}_3\right)}_6\right]C{l}_3$

Because CN^- is strong ligand

$\therefore {\Delta }_0\propto \frac{1}{\lambda }$

More ${\Delta }_0$ smaller value of absorbed $\lambda$

$K_3\left[Fe{\left(CN\right)}_6\right]\to F{e}^{+3}=4s^{0}3d^{5}4p^0$

$\therefore u.e=1$

$\therefore \mu =\sqrt[]{1*\left(1+2\right)}B.M=\sqrt[]{3}B.M$

= 1.732 B.M

$\approx$ 2