# Electron Structure Notation

by Jared Rovny

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00:02 There's a different naming convention that we have for these different orbital shapes that we have to be familiar with.

00:07 Because we'll be using these naming conventions as we go forward.

00:10 Specially when we get into the context of the periodic table.

00:13 These names for historical reasons are starting with l equals 0.

00:17 That circular shape.

00:18 Moving to l equal to 1 the lobed shape.

00:20 And then getting to more and more complex shapes the l equals 2 and the l equals 3 shapes have these names that you can see on the bottom here.

00:27 Which are s for the l equals 0 shape.

00:30 You can remember that may be as s being for sphere something that's very simplest, l equals 0 shape.

00:36 And then we move up to p and then d and then f, for the l equals 1, 2 and 3 shapes respectively.

00:42 We could in principle keep going to higher and higher numbers and letters.

00:47 But in fact with just these 4 different shapes we can describe the entirety of the periodic table as we know it.

00:54 And since we only have 4 quantum numbers.

00:56 And we have 4 different letters for the different types of shapes that can describe again the whole periodic table.

01:02 It's well worth your time to make sure you go over what we've introduced so far until it's very intuitive it makes a lot of sense to you.

01:09 Because you can describe so, so much with so little.

01:12 So let's see how these work in the context of the notation for the periodic table.

01:18 So first let's introduce this notation.

01:20 If I gave you an atom and it had electrons orbiting it all around, we would need some way to describe where those electrons were, what their orientation was relative to the atom.

01:30 And so we have a naming or notation convention for the electron configuration and it looks like this.

01:36 If I wrote 1s2, what I mean is, I'm in the 1 energy level, the n equals 1 energy level.

01:44 I'm in the s shape which we just described l equals 0 or the spherical shape.

01:50 And the 2 that's above the s there is saying, that I have 2 electrons in that particular shape.

01:56 So for the atom you can see here, it would be describing exactly this picture.

02:00 You are in the first or the ground state energy level.

02:03 You're in the first or the 0th, the original shape, the spherical shape and you have 2 electrons in that shape, in that particular orbital.

02:12 And there's one last thing I could ask you about these electrons.

02:15 I could ask you what are the spins of these two electrons.

02:18 And you would know by the Pauli Exclusion principle that one must be spin up and the other one must be spin down.

02:23 Because otherwise they would have the same 4 quantum numbers.

02:26 So this is one example of how we could use this particular notation.

02:30 Let's look at another one and see how this works.

02:32 If I instead said I was in the n equals 2 energy level and I had the same orbital shape, the s the circle, the spherical shape and also had 2 electrons, it would look something like this shape here.

02:45 Again we are in the n equals 2 energy levels, so we are in that excited shape.

02:49 We pick an orbital, since we could picked either these spherical l equals 0 orbital or we could pick the lobed orbitals.

02:55 But we picked the spherical one here.

02:57 The s one.

02:58 And then we say that we have 2 electrons in that particular orbital.

03:02 And again we know that by the Pauli Exclusion principle, one of these electrons must be spin up and the other electron must be spin down.

03:10 Now you could ask yourself at this time, "Well is it always going to be the case that this last number and these notations are going to be a little two because we only have spin up and spin down." And in fact that's not quite the case because we have one intricacy here.

03:22 So for example, what if I went to the p orbital, the lobed shape.

03:27 So I could say I was in n equals 2 energy level.

03:30 The p orbital or the p shape this lobed shape which is l equals 1.

03:35 But now I can fit 6 electrons.

03:37 But how do I fit 6 electrons in an orbital.

03:39 Well, it looks like this.

03:40 Don't forget that for the p shape, this lobed shape we don't just have one orientation.

03:45 We now have three different possible orientations for that shape.

03:49 For each orientation, for each one of these m sub l shapes that we have, we have two electrons per orientation.

03:57 Because each one can be spin up and then spin down.

04:00 So again be careful with this notation.

04:02 Notice the notation has three symbols in it.

04:06 One number, a letter and then a number.

04:08 And these three symbols tell us n, l and the number of electrons.

04:13 But you notice that in our notation that we don't have m sub l anywhere.

04:16 It doesn't say anything about the orientation of the orbitals.

04:18 So we know we are in the p orbital.

04:21 But we don't have anything in the notation telling us which orientation of the p orbital we're in.

04:26 So we have to count these electrons sort of on our own.

04:29 We know that we're in the l shape or the l equals 1 shape, the p or lobed orbital.

04:34 And therefore we know that for each of the three orientations we can fit 2 electrons.

04:39 One spin up and one spin down.

04:41 So for that reason, for the lobed shape, the l equals 1 shape with 3 orbitals, we have 3 times 2, 2 for each spin of the electron or 6 electrons total that could fit in that p shape.

04:55 So let's summarize the number of electrons.

04:58 We just talked about how we can fit certain numbers of electrons in each orbital shape.

05:02 We saw that for the s shape that's spherical shape, there's only one possible orientation for this sphere.

05:08 Because again that could turn the sphere any which way and it always look like a sphere.

05:12 So since we only one possible orientation, we can only fit two electrons.

05:17 One spin up and one spin down.

05:20 For the p shape which we saw has this lobed structure, we have 3 different orientations.

05:25 And so again for each orientation we can fit 2 more electrons, one spin up and one spin down.

05:31 So 2 electrons with the different spins.

05:33 One for each of the three shapes gives us 6 total electrons which is drawn in the picture here.

05:39 As we go up we haven't talked about the particular shapes for the d or f orbitals or the particular orientations that they can have.

05:48 But you can do this yourself and go back to the equations that we have that defined l which is the shape and m sub l which is the orientation.

05:56 And you can see if you can remember our equation for m sub l, m sub l starts at negative l.

06:01 And then counts integers up to l.

06:04 And so what you'll have is two l, l for either side of the 0 of your axis going to minus l and going to positive l.

06:12 So you have 2 l but then you need a plus 1.

06:15 So you have the 0 as well.

06:17 And so just using this method and go back to the definitions for the quantum numbers that we described, you can count for yourself how many m sub l possibilities you have.

06:26 And then just remember that for each m sub l possibility, you have two spins.

06:30 So you'll just double that number.

06:32 In this case after doubling that number for the d orbital or the l equals 0 1 2.

06:37 So the l equals 2 orbital we would have 10 electrons.

06:41 Finally for the f orbital which we just said just using these 4 we can describe the whole periodic table.

06:46 So this is the last and most complicated orbital.

06:48 For this f orbital we could fit 14 electrons using the exact same sort of analysis.

The lecture Electron Structure Notation by Jared Rovny is from the course Electronic Structure.

### Included Quiz Questions

1. Names for the electron orbital shapes, l = 0, 1, 2, 3
2. Names for the electron energy levels, n = 0, 1, 2, 3
3. Names for the electron orbital orientations, ml = 0, 1, 2, 3
4. Names for the electron spins, ms = 0, 1, 2, 3
5. The row of the periodic table occupied by the atom.
1. 3p6
2. 1p2
3. 2d1
4. 1m4
5. 0s2
1. Each of its three orbitals, ml, can hold two electrons.
2. The Pauli Exclusion Principle does not apply to higher orbitals.
3. Both of the energy levels can hold three electrons.
4. Its angular momentum quantum number, l, can range from one to six.
5. Each energy level can hold twice as many electrons as the prior level.
1. 3d5
2. 3p2
3. 3s10
4. 3p5
5. 3d10

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