In the linear crystal-field shown here, the negative charges are on the z-axis. Using Figure 23.28 as a guide, predict which of the following choices most accurately describes the splitting of the d orbitals in a linear crystal-field? [Find more in Section 23.6.]                                                                                                                                                

Video transcript

Hello everyone today. By the following problem, the negative charges are on the X and waxes of the following crystal field. The representation of the splitting of the D orbitals in the crystal field. So the orbitals with the lobe closest to the negative charge of the approaching login will have the highest energy because it will experience the greatest repulsion. So we have five of these crystal field diagrams that we can showcase of these D orbitals. With one being, we have the z axis, we have the X axis and we have the y axis and each will represent each arrowhead represent a negative charge save for the Z. So this will be our DXY orbital and it will have the following configuration. And then we have a second crystal field diagram with the same axis. And this one will be our DXZ or diagram which will have this configuration. We have it yet. They another one when the orbitals have a more distinct appearance and this specific orbital diagram will be our DYZ diagram. And then we have two more with our fourth one having a more flat appearance. And then we have one last final diagram wherein we will have our donut shaped orbital. So as we stated previously, the orbitals with the lobe closest to the negative charge of the approaching L in will have the highest energy because of the great of greater repulsion. And the same can be said for the opposite. So if we look at our last orbiter that we drew, and this is actually our DX squared. And the fourth one we drew is DX squared minus Y squared. If you look at the X squared minus Y squared orbital, these point directly at the charges. And so this will have the highest energy as for the DXY or first orbital, we diagram that we drew. These don't directly point at the negative charges, but it is closer. So it will have a higher energy than the rest as for the DZ squared orbital, this will have higher energy than the DXZ and the Dyz orbital because of the, or the D the DX word because of the doughnut part of the orbital that is in the xy plane. And then lastly for our DXZ and Dyz, these have orbitals that are pointing in the direction of the YNX axis. However, they're not as prominent as the DX squared minus y squared orbital diagram. So these will have lower energies lower energies then the DX squared orbital. And so if we were to draw this out to show the splitting, we would have two orbitals at the bottom, we would have our DXZ orbital and our DYZ orbital because they have the lower lowest energies. And this will be followed by DX squared, which is then followed by the DXY orbital. And then lastly, we have our DX squared minus Y squared that have the highest energy. And so with that, we have solved the problem overall, I hope it's helped. And until next time.