# 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 Δ_{0}

b. lowered in energy by 0.4 Δ_{0}

c. raised in energy by 0.5 Δ_{0}

d. lowered in energy by 0.6 Δ_{0}