So i was going through my 1st year engineering chemistry textbook as a i have test in about a few weeks. So my textbooks says:
"Repulsion by six ligands in an octahedral complex splits the d orbitals on the central metal into t2g and eg levels. It follows that there is a corresponding repulsion between the d electrons and the ligands. If the d electrons are symmetrically arranged, they will repel all six ligands equally. Thus the structure will be a completely regular octahedron."
So i understood the first 2 lines. Basically what my understanding says is that in an octahedral complex the ligands usually approach the central metal along the x, y and z axis. So obviously the orbitals which lie along the axis (dx2-y2 and dz2) will rise in energy which is your eg level than compared to the orbitals which lie in between the axis ( dxy, dyz, dxz) which your t2g levels. What i am not able to understand is the part where they say "If the d electrons are symmetrically arranged, they will repel all six ligands equally". The electrons in eg level rise in energy because they face more repulsion from the ligands right? so how is it possible that the d electrons will repel all ligands equally? Shouldn't the electrons in the eg level repel them more than the electron in the t2g level? I even tried to make my self understand by taking an example of a d5 configuration(which is symmetrically arranged) in the presence of a weak field ligand where two of your electrons would be in eg and the other 3 electrons would be in t2g level, but still I wasn't able to understand how is it that the d electrons are repelling the ligands equally?