The ratio of crystal field stabilization energies of ${\left[V{\left(H_{2}O\right)}_6\right]}^{+2}/{\left[Mn{\left(H_{2}O\right)}_6\right]}^{+3}$ is ________

${\left[V{\left(H_{2}O\right)}_6\right]}^{+2}V-3d^{3}4s^2$

$V^{2+}=3d^{3}4s^0,t2g^{3}e{g}^0$

$CFSE=[-0.4\times 3+0.6\times 0]{\Delta }_0=-1.2{\Delta }_0$

${\left|Mn{\left(H_{2}O\right)}_6\right|}^{3+}Mn-3d^{5}4s^2$

$M{n}^{3+}=3d^{4}4s^0,t2g^{3}e{g}^1 H_{2}O$ - weak field ligand

$CFSE=(-0.4\times 3+0.6\times 1)={\Delta }_0=-0.6{\Delta }_0$

$\therefore \frac{{\left[V{\left(H_{2}O\right)}_6\right]}^{+2}}{{\left(Mn{\left(H_{2}O\right)}_6\right)}^{+3}}=\frac{-1.2{\Delta }_0}{-0.6{\Delta }_0}=2{\Delta }_0$