Sketch the shape and orientation of the following types of orbitals: (c) dx2 - y2.

Question

Accepted Answer

welcome back everyone in this example. We need to draw the shape of a D. Z squared orbital and include the X, Y and Z axis. So what we should recall first is what an atomic orbital is. And we should recall that this tells us a region around and Adam's nucleus where electrons are likely to be found. So we'll start off by drawing out our axes. So beginning with our Z axis, we'll draw that first, then we have our X axis, we'll label that and then last. We have our y axis. So we label that here. And so according to the prompt, we have to draw the DZ squared orbital. So recalled that a D orbital can either be clover shaped like this or it can just be a dumbbell with a ring around it. And in this case we want to go with scenario to hear. So that's what we're going to draw in our diagram. So I'll just erase this. So what we want to do is draw in the first lobe and according to the prompt, are lobes of our orbital here, should be oriented along the Z axis. So we'll draw our first lobe in the positive direction of Z. So that would be up here and then we'll draw our second lobe in the negative direction of Z. Like this. And then to complete this orbital, we must have a ring and we'll draw on the ring as follows. So, and we can actually draw that over because it's going to surround both of our orbital's. So this ring is crucial to add because this ring and we'll write a note here. The ring creates electron density along the xy plane. And we can also expand this by also recognizing that because we have our lobes of our atomic orbital here, in the direction of our Z axis. As we've drawn in, we would recognize that the lobes create electron density along the Z axis. So we also have electron density there, meaning we are likely to find an electron in any of these regions. Now, we also want to recognize that we have the presence of a node or nodes in our diagram to draw in as well and we want to recall what a note is. And that would be a region around the nucleus of our atom where We have zero electron density. So we'll underline this in red. So we can distinguish it in our diagram here. So to draw in our node, we should recognize that because we have this ring in our D Z squared orbital. We would have a node that surrounds both of our lobes along the Z axis. And so it would be in a cone type shape here. So, drawing that in this would represent our note here. So we have a cone surrounding the first slope and will accurately draw that all the way to the end of the lobe. And then we have the same thing going on for our lobe in the negative direction here where we have another cone here representing our note. And so this here represents specifically what we want to recall as an angular node and it's an angular node because it's in a cone shape due to that ring in our D. Z. Squared orbital. And so in these regions we have zero electron density or zero probability of finding an electron. And so this actually would complete this example because this is going to be our depiction of our and sorry about that of our D. D. Z squared orbital. And again, just so we're clear that too in our name here is just a part of our name, but it just tells us that our lobes of our atomic orbital are oriented along our Z axis and we have two of these lobes oriented along the Z axis as we've depicted in our picture here. And so I'll just box in our diagram here because this entire image that we've drawn out with our labels for axis is our final answer. So I hope that everything that I reviewed was clear. If you have any questions, please leave them down below. And I will see everyone in the next practice video

Sketch the shape and orientation of the following types of orbitals: (c) dx2 - y2.

Verified Solution

Key Concepts

Atomic Orbitals

d-Orbitals

Orbital Orientation