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