Predict the crystal field energy-level diagram for a square pyramidal ML₅ complex that has two ligands along the axes but only one ligand along the z axis. Your diagram should be intermediate between those for an octahedral ML₆ complex and a square planar ML₄ complex.

Video transcript

Hi, everyone take a look at our next question. The crystal field energy level diagram for a square parameter complex formula ML five is known to be intermediate between an octahedral complex ML six and a square planar complex Ml four. Does the crystal field energy level diagram below correspond to a square parameter, ML five complex with one ligand along the plus or minus Z axis two along the plus or minus Y axis and two along the plus or minus Y axis. So we're given a diagram that shows the xy and Z axis X axis going vertically on the screen, the Z axis going horizontally and the y axis coming out of the plane of the screen in front and behind. And then the diagram of the structure of that given square planar complex, we have four ligands in a square plane on the X and Y axis. So the plane xy plane and then one ligand along the z axis. Our crystal fill energy level diagram we're given has the highest level at X squared minus Y squared orbital. Next, the Z squared orbital, next, the xy orbital. And finally, at the same energy level, the Xzmyz orbitals. And our answer choices are a yes, it does correspond to the crystal field energy level diagram of a square parameter complex ML five with one ligand along the cluster minus z axis. It goes on to describe all of them M and or choice B no, it does not correspond to the crystal field energy level diagram of this complex. So let's think about the shapes of the different de orbitals and how they are with where they are with relation to our complex. And use that to determine what this energy level splitting should look like. So we'll start with the most distinctive of them. And that most distinctive orbital is of course, the DZ squared orbital that has that sort of doughnut shape in the middle and then the two lobes extending outward along the Z axis. So let's draw and I'll draw in red little dots to show where our different ligands will be. And we can think about how this affects the energy level. So we have two ligands each on the X and y axis. So an X and Y axis and just one on the Z axis. So we can't say a lot about this in isolation. Um we want to look at other orbitals but we see that this does have some direct interaction with that z the um or excuse me, the ligand along the z axis. But again, remembering there's just the one ligand, it's only interacting directly with that. So we'll kind of set that aside and look at some of our other orders. So next, we'll look at our other sort of exceptional D orbital, the DX squared minus Y squared orbital. And of course, it has the sort of four leaf clover shape that most of our de orbitals do. But unlike the three others that point in between the axes, this one is directly along the X and Y axis. So this is a clear front runner for our highest energy level because of course, we have four ligands that it's going to point directly at along the X and y axis. So that's definitely higher than the DZ squared where you just have the one li in on the z axis that it's pointing directly at. However, when we think about all our other orbitals, we know they're all in between the axes and therefore none of them will point directly at any ligands. So we've got our two top energy levels and that would correspond with our diagram where we see X squared minus Y squared as the top energy level and Z squared as the second. So now we're on a little more straightforward ground because we just have our three left that go in between the axes and we have Xyxz and YZ and we could take out the diagrams, but we don't really need to because we just would know that Xy would be expected to be a bit higher than XY or YZ, because there are two ligands along each of these axes. While in the two lowest energy levels, Xz and YZ, we have one ligand along the Z axis and of course, two ligands along either the X or Y axis. So that's pretty easy to just logically figure out and we can confirm that those final energy levels are correct. So our given diagram here with X squared minus Y squared, then Z squared then Xy and then at the bottom XZ and YZ together does indeed correspond to what we'd expect of the energy level diagram of a square parameter complex with one ligand along the Z plus or minus Z axis two along the plus or minus X and two along the plus or minus Y. So our answer is choice a that yes, it does correspond. See you in the next video.