Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?

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Hey everyone in this example. We need to draw 12 P orbital and 13 D. Orbital. We need to explain how these two orbital's compared to their counterparts in higher energy levels such as three P. And four D. Before we draw our orbital's we should recall a few facts. The first being that L. Representing our angular quantum number will range from zero all the way to three and it corresponds to our sub levels. And that would be our letters of our orbital's. So the angular quantum number zero corresponds to the S sublevel. The angular quantum number one corresponds to the P sublevel. The angular quantum number two corresponds to D. Sub level and the angular quantum number three corresponds to our F sub level. We also want to recall that in order to draw our orbital's we need to consider how many nodes we have total. And to recall total nodes we're going to take our energy level which again is represented by N. And subtracting that from one. We also want to figure out our number of angular notes that we would draw in and that would correspond to our angular quantum number L. And then lastly we want to recall our number of radial notes to draw in our orbital and that would correspond to our energy level minus one minus our angular quantum number L. So beginning with drawing out our two p orbital, we should recall that our peace sub level is going to be dumbbell shaped. And because we're only at the second energy level. Given by our name of our orbital 2, 2 p. We can go ahead and draw this dumbbell to be pretty small here. So we have our dumbbell and for our total number of nodes we should draw in. We're going to take our energy level two and subtract that from one. So two minus one would give us one node. Now, which note would it be? Would it be our angular node or radial node? So for the angular node we again want to consider our angular quantum number represented by L. And so because we Recall that we have the two p orbital as our sub level, we're going to look at the piece sub level and see that that corresponds to the angular quantum number one. And so this means we have one angular node. So we can draw in our angular node by this vertical line here in the middle of our dumb bill. And this would represent the single node in our two p orbital. As you can see, we only have an angular node, We do not have a radial node and we can tell that also because we would take our energy level to subtract that from one, which would give us one and then we know our angular quantum number is one because we're in the p sub level. So that would be one minus one giving us zero radial notes. So we can say we have no radial notes For our two piece sub level not to draw our three D orbital. We're going to follow the same steps. So we should recall that R. D orbital because it's the D sublevel is going to be more clover shaped. So we can go ahead and draw in our clovers and we're going to make them a bit bigger than our two p orbital because it's higher in energy at the third energy level. So we'll draw in the four clovers to represent our D sub level here And to figure out our total number of nodes we would draw in, we take our energy level, which again is the third energy level -1. So that means that we would have two nodes total when we take N -1. So to figure out which of these two nodes you would have, we would consider first our angular notes. So looking at our angular nodes that corresponds to our angular quantum number L. Because we know that we're in the d sub level, we would see that this will correspond to two angular notes. So we can draw in again our angular nodes as these vertical lines here and recall that our nodes represent the areas in our sub levels where we have a zero possibility of finding electrons. So I'm just going to label this as our angular notes. Next. We want to draw in our second type of node, which is our radial notes. So we're going to take our energy level. Which because we know we're in the three D sub level, we take three minus one that gives us two And then 2 -1 or sorry two minus L. Which is our angular quantum number for our D sub level that corresponds to two. So two minus two gives us zero. So we will have zero radial nodes in our three D orbital. So we would also say no radial nodes here for the three D sub level. And now let's go ahead and draw their counterparts, The three p sub level And the 40 sub level. So for first hour three p sub level, we're still going to have a dumbbell shape because it's the P sub level and because we know that it's the three pay sub level which is the third energy level. We're going to make our dumbbells quite bigger. So we'll make them about this big. Now for our orbital here, we need to figure out first total number of notes. So we would take our energy level three -1 and that would give us two total nodes for our three piece orbital. So first let's go ahead and figure out how many angular nodes we would draw in. That corresponds to our angular quantum number. So because we're in the three p orbital, we look at the piece sub level and that will give us our angular quantum number of one and this means we would draw in one angular node, which we can draw in as this vertical line here. Next we want to go ahead and figure out what our second type of note is which is our radial node. So we're going to take our energy level which we again know is three. We subtract that from one that gives us two and then we take that value minus L. So because we're in the P sub level or angular quantum number, L. Is one. So that would be two minus one which gives us one radial node. And we can draw in our radial node surrounding our dumbbell. So we would go ahead and draw it in surrounding our dumbo like this To represent our single angular node in our three piece sub level. So this is our angular node and the vertical line is our radial node. Or sorry what we just drew or surrounding our dumbbells is our radial node. And then the vertical line in the middle is our angular node. And now we can move on and draw our four D. Sub shell. So because this is the fourth energy level in the D sub level compared to the three D. One. We're going to make this a lot bigger. So we're going to draw our clover shape even bigger than before. And now we want to figure out total number of notes. So that would be 4 -1 giving us a total of three notes. So first we would find our angular nodes which corresponds to our angular quantum number. We know we're in the D sublevel for four D. So we look and we see that corresponds to two as our angular quantum number, meaning we should have two angular notes. And so we would go ahead and first draw the first angular node in as a vertical line here and then the second angular node across. Next. We want to go ahead and figure out our third node which would be our radial node. So we would take our and value our energy level four. Subtract that from one. That would give us three minus our angular quantum number because we know we're in the D sub level that quantum number is two. So that would be three minus two which gives us one radial node and we can draw that radial node in in the center of our clover shaped orbital's. And so as you can see, We have a total of three notes For our four D sub shell and we have a total of two nodes, four Hour 3 P sub shell. We can go ahead and say that therefore to answer this question, the two P and three D orbital's have the same shape as their counterpart orbital's but the counterparts being at higher energy levels are larger orbital's, we can say also the three P and four D orbital's have more notes as we said above. The three p orbital has two notes and the four D orbital has three notes. whereas our three D orbital only contained To angular notes and R two p orbital contained just one angular node. So to complete this example, our final answer is explained here in these two sentences, and this will be our final answer to complete this question. So if you have any questions, please leave them down below. But I hope I was able to help you understand and I'll see everyone in the next practice video.

Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?

Verified Solution

Key Concepts

Atomic Orbitals

Quantum Numbers

Energy Levels and Electron Configuration