Question

Which of the following are true about the energy of the given d-orbitals of a tetrahedral complex?

A. $d_{xy} = d_{yz}>d_{x^2-y^2}$
B. $d_{xy} = d_{yz}>d_{z^2}$
C. $d_{x^2-y^2}>d_{z^2}>d_{xz}$
D. $d_{x^2-y^2} = d_{z^2}<d_{xz}$

• A. A, B and D only
• B. A and B only
• C. B and D only
• D. B, C and D only

Hint:

In tetrahedral splitting, the t2 set (xy, yz, xz) is higher in energy than the e set (z^2, x^2-y^2).

Answer 1

The Correct Option is A

In a tetrahedral crystal field, the ligands approach the metal ion from directions that lie between the coordinate axes (x, y, and z). This results in a splitting of the five degenerate d-orbitals into two distinct energy levels, which is the inverse of the octahedral splitting pattern.

1. The set of orbitals that point between the axes ($d_{xy}, d_{yz}, d_{xz}$), known as the $t_2$ set, experience greater repulsion from the ligands and are consequently raised in energy.
2. The set of orbitals that point along the axes ($d_{x^2-y^2}, d_{z^2}$), known as the e set, experience less repulsion and are lowered in energy.

Therefore, the energy relations are:
- Energy of $t_2$ set>Energy of e set.
- Within each set, the orbitals are degenerate (equal in energy):
$$E(d_{xy}) = E(d_{yz}) = E(d_{xz})$$
$$E(d_{x^2-y^2}) = E(d_{z^2})$$

Now, let's evaluate the given statements:
A. $d_{xy} = d_{yz}>d_{x^2-y^2}$: This is true because $d_{xy}$ and $d_{yz}$ belong to the higher energy $t_2$ set, and $d_{x^2-y^2}$ belongs to the lower energy e set.
B. $d_{xy} = d_{yz}>d_{z^2}$: This is true for the same reason as above ($t_2>e$).
C. $d_{x^2-y^2}>d_{z^2}>d_{xz}$: This is false because $d_{x^2-y^2}$ and $d_{z^2}$ have equal energy, and $d_{xz}$ (a $t_2$ orbital) actually has higher energy than the e orbitals.
D. $d_{x^2-y^2} = d_{z^2}<d_{xz}$: This is true because the two e orbitals have equal energy and are lower in energy than the $t_2$ orbital $d_{xz}$.

Thus, statements A, B, and D are correct.