In octahedral coordination entities:

\(t_{2g}\) set has lower energy than \(e_g\) set

The correct answer is option 2. \(t_{2g}\) set has lower energy than \(e_g\) set.

To understand why option 2 is correct we need to know about the Crystal Field Octahedral Complexes.

Crystal Field Theory for Octahedral Complexes

The ligand is represented by modest negative charges in the octahedral complex ion, while the metal ion is represented by positive change.

Repulsion between the ligands and the d-orbitals occurs in octahedral complexes as the ligands approach metal ions, raising their energy relative to the free ion. The ligands repel \(d_{x^2–y^2}\) and \(d_{z^2}\) orbitals more strongly than the remaining three d-orbitals, \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\). As a result, the energies of the dxy, dxz, and dyz orbitals are lower than the energies of the dx2–y2 and dz2 orbitals.

Lower-energy \(d_{xy}\), \(d_{xz}\), and \(d_{yz}\) orbitals are known as \(t_{2g}\) orbitals, while higher-energy \(d_{x^2–y^2}\),\(d_{z^2}\)orbitals are known as \(e_g\) orbitals. Crystal field splitting energy or crystal field stabilisation energy is the difference in energy between the two sets of d- orbitals (CFSE). It is denoted by the letter \(Δ_O\), which stands for the octahedral complex.

The eg orbitals have an energy level of \(+0.6 Δ_0\) or \(3/5 Δ_0\) above the average, whereas the \(t_{2g}\) orbitals have an energy level of \(–0.4 Δ_0\) or \(–2/5 Δ_0\) below the average.

Strong field ligands have a high \(Δ_0\) value and are low spin complexes in octahedral complexes. \([Fe(CN)_6]^{4–}\) and \([Co(NH_3)_6]^{3+}\) are two examples. The weak field ligands are high spin complexes with a low \(Δ_0\) value.