Final answer:
In an octahedral complex, the five d orbitals of a metal cation split into two sets of differing energy levels: the t2g orbitals with lower energy, and the eg orbitals with higher energy. The correct options are B and D.
Step-by-step explanation:
When a metal cation forms an octahedral complex, the arrangement of its d orbitals changes due to the crystal field splitting. Initially, the five d orbitals in a metal ion are degenerate, which means they have the same energy level. However, in the presence of an octahedral arrangement of ligands, this changes.
The dz2 and dx2-y2 orbitals, which are collectively referred to as eg orbitals, increase in energy because they point directly towards the ligands. Consequently, the energy of an electron in the eg orbitals is higher due to increased electrostatic repulsions. On the contrary, the other three d orbitals, dxy, dxz, and dyz orbitals, are termed t2g orbitals and are oriented at a 45° angle to the coordinate axes, pointing between the ligands, which results in a lower energy than the eg orbitals.
Therefore, the correct statements that describe the arrangement of the d orbitals in a metal cation after forming an octahedral complex are: B. There will be three lower energy d orbitals designated t2g orbitals. and D. There will be two higher energy d orbitals designated eg orbitals. It is also important to note that although there's a splitting in energies, the average energy of the five d orbitals remains the same.