Match List I with List II LIST – I (Complex ion) LIST – II...

The ${t}_{2g}$ (triplet, lower energy) orbitals are the ${d}_{xy}, {d}_{xz}$ and ${d}_{yz}$ orbitals. The ${e}_{g}$ (doublet, higher energy) orbitals are the $d{z}^{2}$ and ${d}_{{x}^{2} - {y}^{2}}$ orbitals. These split d-orbitals are called ${t}_{2g}$ and ${e}_{g}$because they are split by the effect of the surrounding ligand ions in a crystal field.

${\left[Cr{\left({H}_{2}O\right)}_{6}\right]}^{3 +}$ Contains ${Cr}^{3 +}: \left[Ar\right]3{d}^{3}: {t}_{2g}^{3}{e}_{g}^{o}$
${\left[Fe{\left({H}_{2}O\right)}_{6}\right]}^{3 +}$ Contains ${Fe}^{3 +}: \left[Ar\right]3{d}^{5}: {t}_{2g}^{3}{e}_{g}^{2}$
${\left[Ni{\left({H}_{2}O\right)}_{6}\right]}^{2 +}$ Contains ${Ni}^{2 +}: \left[Ar\right]3{d}^{8}: {t}_{2g}^{6}{e}_{g}^{2}$

${\left[V{\left({H}_{2}O\right)}_{6}\right]}^{3 +}$ Contains ${V}^{3 +}: \left[Ar\right]3{d}^{2}: {t}_{2g}^{2}{e}_{g}^{o}$