The ratio of spin-only magnetic moment values μ _ eff [Cr ( CN ) _...

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

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

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

${\mu}_{\text{eff}}$ of ${\left[Cr ( CN{)}_{6}\right]}^{- 3} = \sqrt{15}\text{B.M.}$

${\mu}_{\text{eff}}$of ${\left[Cr\left({H}_{2}O\right)\right]}_{6}^{+ 3} = \sqrt{15}\text{B.M.}$

Ratio $= 1$