In an ocahedral crystal field, the `t-(2g)` orbitals are

Options

A. lower in energy by `0.4 Delta_(@)`
B. raised in energy by `0.4 Delta_(@)`
C. lowered in energy by `0.6 Delta_(@)`
D. raised in energy by `0.6 Delta_(@)`

Answer

A

Explanation

The `d_(x^(2)-y^(2))` and `d_(z^(2))` orbitals a directed along a set of mutually perpendicular x, y and z axes. As a group, these orbitals are called `e_(g)` orbitals. The `d_(xy)` , `d_(yz)` and `d_(xz)` orbitals, collectively called `t_(2g)` orbitals, lie between the axes. The ligand donor atoms approach the metal ion along the axes to form octahedral complexes. The approach of the six donor atoms (point charges) alon the axes sets up an electrical field called the crystal field. Electrons on the ligands repel electrons in `e_(g)` orbitals on the metal ion more strongly then they repel those tn `t_(2g)` orbitals.

This removes the degeneracy of the set of d orbitals and split them into two sets, the `e_(g)` set higher energy and the `t_(2g)` set of lower energy. This splitting of the degenerate levels due to the presence of ligands in a denfinite geometry between the two sets of d orbitals in the energy difference between the two sets of d orbitals in the octahedral field is called the crystal field splitting energy, denoted by `Delta_("ocatahedral")`, or `Delta_(oct)` or `Delta_(o)`. The sum of the orbital energies equals the dengenerate energy (sometimes called Bair centure). Thus, the energy of the two (higher energy) `e_(g)` orbitals is `3//5 Delta_(oct)` and the energy of the three (lower energy) `t_(2g)` orbitals is `-2//5 Delta_(oct)` below the mean.