The ratio of spin-only magnetic moment values μ eff Cr ( CN ) 6 3 - / μ eff Cr H 2 O 6 3 + is…

In case of ${\mathrm{Cr}}^{3+}$ ion , the valence shell electronic configuration is same whether the ligand is strong field or weak field.

The spin only magnetic moment , ${\mathrm{\mu }}_{\mathrm{eff}}=\sqrt{\mathrm{n}\left(\mathrm{n}+2\right)}\mathrm{BM}$

The valence shell electronic configuration of ${\mathrm{Cr}}^{3+}$ is $3{\mathrm{d}}^3$, hence, it has three unpaired electrons.

${\mu }_{\text{eff }}$ of ${\left[\mathrm{Cr}(\mathrm{CN}{)}_6\right]}^{-3}=\sqrt{15}\text{ B.M. }$

${\mu }_{\text{eff }}$of ${\left[\mathrm{Cr}\left({\mathrm{H}}_2\mathrm{O}\right)\right]}_6^{+3}=\sqrt{15}\text{ B.M. }$

Ratio $= 1$