# Energy Associated with t_{2} and e Orbitals for Tetrahedral Complexes

The d-orbitals splitted in tetrahedral field is shown below-

Let 'x' and 'y' be the energy of each electron in e' and 't_{2} orbitals respectively. Then we have-

y − x = 10Dq -----Equation-1

The splitting of d-orbital takes place according to the Bary center or center of gravity rule-

so, 2x + 3y = 0 -----Equation-2

Because the degeneracy value for t_{2g} and e_{g} are 3 and 2 respectively.

Multiplying the equation-1 by 2 and adding to equation-2, we get-

2y − 2x = 20Dq

3y + 2x = 0

------------------

5y = 20Dq

or, y = +4Dq

Now putting the value of 'y' in equation-1 we get-

4 − x = 10Dq

x = −6Dq

So, we have the energy associated with e and t_{2} Orbitals for tetrahedral Complexes are −6Dq and +4Dq per electron respectively.

We know that-

Δ_{tet} = (4/9)Δ_{oct}

so, for 'e' orbital- −6 x 4/9 = −24/9 = −2.67Dq

similarly, for t_{2} orbital- +4 x 4/9 = 16/9 = +1.78Dq.

## Energy Associated with of t_{2g} and e_{g} Orbitals for Octahedral Complexes

### Why in the tetrahedral splitting, terms e and t_{2} are used, whereas, in octahedral splitting, terms as e_{g} and t_{2g} are used ?

A. Due to the approach of the ligands from the axis

B. Due to the approach of the ligands in between the axis

C. Due to the symmetry present in the octahedral system

D. Due to the symmetry present in the tetrahedral system

Explanation: The word 'g' stands for gerade (German word) which means symmetry. If the sign of the lobes remains the same, we call it a gerade orbital and if the signs are changed, the orbital is ungerade. In gerade, the centre of inversion symmetry is present.

Tetrahedral complexes have no centre of symmetry so, its orbital do not have 'g' term in it. While in an octahedral system, 'g' term is included because it is symmetric. Therefore, in the tetrahedral splitting, terms e and t_{2} are used, whereas, in octahedral splitting, terms as 'e_{g}' and 't_{2g}' are used.