Energy Associated with t2g and eg Orbitals for Octahedral Complexes

Energy Associated with of t_2g and e_g Orbitals for Octahedral Complexes

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

Let 'x' and 'y' be the energy of each electron in t_2g and e_g 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, 3x + 2y = 0 -----Equation-2
Because the degeneracy value for t_2g and e_g are 3 and 2 respectively.
Multiplying the equation-1 by 3 and adding to equation-2, we get-

3y − 3x = 30Dq
3x + 2y = 0
------------------
5y = 30Dq
or, y = +6Dq
Now putting the value of 'y' in equation-1 we get-
6 − x = 10Dq
x = −4Dq
So, we have the energy associated with t_2g and e_g Orbitals for Octahedral Complexes are −4Dq and +6Dq per electron respectively.

In an octahedral crystal field, the t_2g orbitals are

a. raised in energy by 0.4 Δ₀
b. lowered in energy by 0.4 Δ₀
c. raised in energy by 0.5 Δ₀
d. lowered in energy by 0.6 Δ₀

Energy Associated with of t₂ and e Orbitals for Tetrahedral Complexes