In this video, we're going to talk about orbitals, energy levels, sublevels, quantum numbers, and things like that. Now, an orbital is simply the most probable location to find an electron. So let's say this is a nucleus. We're going to consider the Bohr model of the atom. So I'm going to draw circular orbits.
So this is going to be the first energy level, n equals 1. And here we have the second energy level, n equals 2. And here's the third energy level, n equals 3. An electron that occupies the third energy level has more energy than one that occupies the second energy level. n represents the principal quantum number. It describes the size and the energy of that orbital. So as n increases, the distance from the nucleus increases as well. So electrons that are closer to the nucleus exist at lower energy levels.
Electrons that are further away from the nucleus exist at higher energy levels. So that's the first quantum number that you need to be familiar with. So, n is the principal quantum number.
So, keep in mind, n is associated with the energy level. L is the angular momentum quantum number. And it describes the shape of the orbital. So when L is 0, what you have is the s orbital. And so this orbital looks like a sphere.
When L is 1, you have the p orbital, which looks like a dumbbell. And when L is 2, you have the d orbital, which is... a cloverleaf for the most part.
And when L is 3, you have the f orbital, which looks pretty strange, which I'm not going to draw in this video. So just keep that in mind. L describes the shape of the orbital, and n, the principal quantum number, describes the size and the energy level of that orbital.
By the way, s also corresponds to the sublevel. It describes the shape of the orbital, but you can also think of it as the sublevel. Now let's talk about the relationship between n and l. l is always less than or equal to n-1. So when n is 1, you can only have one value for l, that's 0, which corresponds to the s sublevel.
Now when n is 2, l can be 0 or 1, but not 2. So in the second energy level, you can have the s sub-level and the p sub-level. In the third energy level, l can be 0, 1, or 2. So the third level can have the s sub-level, the p sub-level, and the d sub-level. So if you look at the electron configuration of certain elements, you'll see that there's 1s, there's no such thing as 1p.
In the second angel level, you have 2s and 2p, but 2d doesn't exist. In the third angel level, you have 3s, 3p, 3d, but 3f is impossible. Now for the fourth energy level, you have four sublevels.
L can be 0, 1, 2, or 3. So this is going to be S, P, D, F. So in the fourth energy level, you have the 4S sublevel, the 4P sublevel, the 4D sublevel, and the 4F sublevel. So notice that the n value is always equal to the number of sublevels. So when n is 6, you should expect 6 sublevels. When n is 3, we have 3 sublevels. S, P, and D.
Now the next quantum number that you need to know is the magnetic quantum number. M sub L. So M sub L describes the orientation of the orbital relative to other similar orbitals in that atom.
So how do we describe this? Well we know that the s sub level has only one orbital. The p sub level, if you draw the orbital diagram, has three orbitals.
Now for S, we know that L is 0. For P, L is 1. ML will always vary between negative L and L. So in this example, L is 0, so ML has to be 0. Now for P, L is 1, so ML is going to vary between negative 1 and 1, including 0. So notice that ML describes each orbital in the P sub-level. The P sub-level has three orbitals.
You have Px, Py, and Pz. So Px is basically along the x-axis. PY is along the y-axis and then you have PZ which is along the z-axis And so these three orbitals within the P sub-level has different orientations.
So one of these numbers corresponds to Px, one of them corresponds to Py, and the last one corresponds to Pz. It doesn't have to be in that order, but each orbital corresponds to one of these designations. Now let's talk about the D sub-level. For the D sub-level, we said that L is 2. And D has 5 orbitals.
And ML, we know it's between negative L and L. If L is 2, then ML has to vary between negative 2 and 2. So we can place 5 ML values for each orbital. And so ML describes the orientation of the orbital.
So each box that you see here has a certain ML value. Now the last quantum number that you need to be familiar with is the electron spin. And there's only two possibilities. An electron can only spin in the clockwise direction or in the counterclockwise direction. And so that's why there's two possibilities.
It can be positive 1 half, or it can be negative 1 half. And within an orbital, you can place the electron with an up arrow or with a down arrow. So when the spin is up, ms is plus 1 half.
When the spin is down, it's negative 1 half. So according to Pauli's exclusion principle, every electron within an atom has a unique set of four quantum numbers. So you can think of those four quantum numbers as the address of each electron within an atom.
So let's say if we want to talk about the 2p5 electron. What are the four quantum numbers that describes the 2p5 electron? So what's n, l, ml, and m sub s that correlates to this electron?
n, the principal quantum number, corresponds to the number that you see in front. So n is 2. That means this electron is in the second energy level. L is based on the sublevel P. Now if you recall, S has an L value of 0, P has an L value of 1, D has an L value of 2, and F has an L value of 3. So L is 1. Now we need to find the ML value.
So what you want to do is draw the orbitals that's found in the P sublevel. Keep in mind, P has three orbitals. Now because L is 1, ML is going to vary between negative 1 and 1. Now we need to focus on the fifth electron in the P sub-level.
So here's the first one, the second, the third, the fourth, and the fifth. So the fifth electron is found in this orbital, which has an ML value of 0. Now the electrons spin based on what we have here. We have a down arrow, so the spin is minus 1 half. So that's a quick and simple way in which you can find the four quantum numbers that corresponds to a specific electron. So let's try one more example.
Go ahead and find the four quantum numbers that corresponds to the 3d5 electron. You can pause the video if you want to. Now the easiest one to see is the number in front of the d sub level.
So n is stream. This number corresponds to the energy level. Now, what is the L value for the D sub-level?
Keep in mind, L is 0 for S, L is 1 for P, and for the D sub-level, L is equal to 2. Now, within the D sub-level, we have 5 orbitals, and if L is 2, ML is going to vary between negative L and L. So it's going to vary between negative 2 and positive 2. So now we're looking for the fifth electron. So this is going to be the first one, the second, the third, the fourth.
So here's the fifth one. So the fifth electron is in this orbital, where ML has a value of 2. Now, notice that we're dealing with an up arrow. So the electron spin... is positive 1 half.
So that's it for this video. If you want to get more examples on this stuff, I've created other videos on YouTube entitled quantum numbers, how to calculate the maximum number of electrons, and other stuff like that. So you can look it up on YouTube, or you can go to my channel and check out my chemistry video playlist, and find more videos on this stuff as well. So thanks again for watching, and have a good day.