For a given metal ion and set of ligands, is the crystal-field splitting energy larger for a tetrahedral or an octahedral geometry?

Video transcript

All right. Hello everyone. So this question says that for a specific transition metal and set of ligands, which geometry has a lower crystal field splitting energy or delta. Option A says octahedral and option B says tetrahedral. So here recall first and foremost that the crystal field spitting energy that's delta is the difference in energies between the higher level D orbitals and the lower energy orbitals. Now the splitting patterns for de orbitals depend on geometry. And it's also worth mentioning that orbitals with stronger ligand interactions have higher energy associated to them. And so here I went ahead and I pre drew some energy level diagrams for the octahedral complex or un octahedral complex on the left and a tetrahedron complex on the right. So let's focus our attention on the octahedral complex first. So here let me go ahead and move this upwards. But in any case, recall that in an octahedral crystal field, ligands are going to lie on or along the X the Y and the Z axis. This means that the strongest interactions are going to take place with the orbitals that lie on or along the axes themselves. There are two that meet this criteria. That's the DX squared subtracted by Y squared and the DZ squared because of this in the octahedral complex, those two orbitals are high energy and are at the top of the energy diagram. This means that the remaining three are lower energy. This means that on the other hand, the weakest interactions are going to take place with the D orbitals that lie in between the axes that's DXYDYZ and DXZ. And so from here, it's also worth mentioning that when compared to a tetrahedral crystal field, an octahedral crystal field simply has more ligand point charges and more point charges means more interactions with these de orbitals. Also, these point charges are going to point directly at the D orbitals of the metal, which makes that interaction stronger. Still this means that the overall crystal field splitting energy is higher for an octahedron crystal field. So lets compare this now to the tetrahedral crystal field. In this particular case in the tetrahedral field, I should say the ligands are going to lie in between the xy and Z axes. This means that the greatest interactions are going to occur with the orbitals that lie in between the axes themselves. So that's DXYDYZ and DXZ. Therefore, these three orbitals are higher energy and are at the top of the energy diagram. Therefore, the lowest interactions are going to occur with orbitals that lie on or along the axes themselves, meaning that the DX squared subtracted by Y squared and DZ squared orbitals are going to be lower energy. So now compared to the octahedral crystal field, there are going to be fewer ligand point charges, there are fewer ligand point charges that interact with the D orbitals in a tetrahedral crystal field. This means that overall the value for the crystal field spitting energy is simply going to be lower for the tetrahedral crystal field. And so going back to the question at hand asking which geometry has a lower crystal field splitting energy. The answer is going to be the tetrahedral. So that's option B in the multiple choice and there you have it. So with that being said, thank you so very much for watching and I hope you found this helpful.