The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (c) What is the largest possible value of the magnetic quantum number, ml?

Question

Accepted Answer

Welcome back everyone in this example, we need to determine which of the below illustrations shows a D. Orbital oriented in the xy plane with the correct shape and orientation. So as the prompt states, the orientation should be on the xy plane and the shape should be for a D. Orbital. So looking at choice A. Or illustration A. We see that we have two lobes that are oriented in the Y. Direction or on the Y axis. And so we should recognize that this is a dumbbell shape. And so we should recall that this shape is described for a p orbital and this is specifically oriented as we stated along the Y axis. And so this is specifically a P. Y orbital illustration. So we can rule out choice A. Because this is going to be the wrong shape as well as the wrong orientation. Again, orientation would be on the Y axis and shape would be for a p orbital because it's a dumbbell shaped. So, moving on to illustration B, we have a flower shaped orbital with four lobes and these lobes are oriented where we have a box in our illustration telling us the orientation being along the X. Y axis. And so we should recall that when we have a flower shape for orbital, this corresponds to the shape of a D. Orbital and as far as the orientation here, that is again given by the box surrounding our orbital here and it's oriented along the X. Y axis. And so we can say that therefore this is going to be the D. X. Y orbital. So here we can confirm that we have the correct shape as well as the correct orientation. And so we would confirm that so far. Choice B is looking as a good prospect as an answer choice. Moving on to choice C. Or illustration C. We have again a flower shaped orbital which definitely does match the correct shape for a p orbital. So we can confirm that we have the flower shape which describes our D orbital. So right now we do agree that we have the correct shape. And sorry, this should have a dash in the name. So D dash orbital. Right now, the box around the shape of our orbital here represents the access at which this orbital is lying on. And we can confirm that this box is describing that this access is oriented or we can say it. It lies along the XZ plane. And so here we have the incorrect orientation due to the fact that we have a D orbital, which is the right shape, but it's oriented along planes X and Z. Or axes X and Z. So we would rule out choice C. Because again, it's the incorrect orientation. And we need the orientation to be on the X. Y axis as stated in the prompt. So that leaves us with choice D as the last choice to consider where we should recognize that we have a dumbbell shape oriented along the access for Z, which is surrounded by a ring oriented in the axes for why? Sorry, access for why. And so we should recall that when we have a dumbbell shape. Sorry, this is the wrong pen. So when we have a dumbbell shape surrounded buy a ring where in the center this ring is surrounding our nucleus. So this blue dot represents our nucleus. This shape corresponds to also a D orbital. So we can't rule choice D out because this actually is another way to draw a D orbital. But when we look at the orientation of this D orbital here, we see that because we have two lobes which are oriented along the Z axis. We have a D. Z. Two orbital here because we have two lobes oriented along the Z axis and we have a ring oriented along the Y axis. So right now we have the correct shape but we have the incorrect orientation. And so we would rule out choice D. And so that leaves us with choice B. As the only correct illustration and answer choice. To complete this example for a D orbital oriented along the X. Y axis. So I hope that everything that I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video

The accompanying drawing shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital. (b) What is the value of the angular momentum quantum number, l?

Verified Solution

Key Concepts

Quantum Numbers

Angular Momentum Quantum Number (l)

Orbital Shapes and Types