Orbitals – Introduction to Chemistry

00:01 As I mentioned, the shells themselves can be divided into orbitals, each of which contains two electrons.

00:08 Orbitals are characterized by shape that is produced when the region surrounding the nucleus is plotted in which it’s typically regarded that a 95% chance exists of finding the electrons.

00:22 The orbital shapes that we will come across are s, p, d and f.

00:29 We’re mostly going to focus on s, p and d orbitals.

00:35 The analogy to use is that each shell unlocks if you like an additional orbital type.

00:40 So, in other words, for the first shell you can only get the s-type orbital.

00:45 For the second shell you can get the s- and the p-type orbitals.

00:49 And for the third shell you can get s, p and d.

00:53 And for the fourth it’s possible to have access to all four, bearing in mind each individual orbital can only contain two electrons.

01:05 And we’ll talk about this in more depth a little later.

01:08 The orbital quantum numbers are given for s orbitals as 0, 1, 2 and 3.

01:16 And the nomenclature in quantum mechanics, where n was for principal quantum number, is that the orbital quantum number carries the letter l.

01:26 So, as we’ll see, it’s possible to actually assign the specific designation of an electron just using quantum numbers.

01:39 The simplest orbital, as you can see here, is where l, or the orbital quantum number, is equal to 0.

01:46 And it is spherical.

01:48 Here you can see three particular types of shells of orbitals: the 1s, the 2s and the 3s.

01:58 Each of these is spherical but, as you can see, each of these is of a different size.

02:03 As of course we move further away from the nucleus, of course the electrons themselves or the probability of finding them is also more distant from the nucleus.

02:14 Also bear in mind it’s spherical and so the x, y and z axes there demonstrate the three dimensionality of this species, and the fact that there is a 95% probability of finding electrons within this region.

02:29 Note of course that, if you go back to the basic quantum mechanics, the theoretical chance of finding electrons in the nucleus is, of course, 0.

02:40 So, going from left to right, 1s is an s orbital, which is a spherical orbital which actually stands for ‘sharp’ rather than ‘spherical,’ which is rather counterintuitive.

02:52 The 2s is an s orbital in shell 2 and the 3s is an s orbital in shell 3.

02:59 And each of these – the 1s, the 2s and the 3s – can formally contain two electrons.

03:08 p orbitals – these are ‘principal’ orbitals and this is where you have an orbital quantum number of 1 or l equals 1 – are more complex.

03:20 And remember what I said: as you move up the shells, it’s possible to accommodate more and more electrons.

03:26 The only way to do this of course is to have more and more different types of orbital.

03:31 And here we can see three of these: the 2py, the 2px and the 2pz.

03:38 Note that the number prior to the py, px and pz correlates to the principal quantum number which, in this case, is the lowest one for p orbitals of two.

03:52 It is, of course, possible to get 3p and 4p orbitals but, of course, not possible to get 1p.

03:59 You haven’t unlocked them at that point.

04:02 Note the similarities between these guys.

04:04 They are dumbbell shaped.

04:07 It’s often the shape that’s considered.

04:09 And their orientation is along the three component axes – that is the y axes, the x axes and the z axes as shown in this particular slide.

04:26 Crucially, if we look in the center where the node is formed, where we have the tiny spot in the center is where the nucleus is.

04:38 And there we have an electron density of 0.

04:43 Now, the question you may be asking is: well why are they shaded differently? And this is what I’m going to come to in a moment.

04:55 A p orbital has two regions where electrons may be found on either side.

04:59 Note what I’ve done is we’ve got a plane through the node of the p orbital as shown here.

05:07 And, along that plane, there exists no electron density as it contains the nucleus.

05:14 But, again, what is the significance of the negative and the positive charges? And this is to do with the phase of electrons.

05:26 Now remember what I said: we tried to discount the idea of treating electrons as particles because it created a lot of theoretical problems for us.

05:37 In fact, we understand that electrons exist in shells and it can only go up or down those shells by absorbing or giving off quanta of energy.

05:47 Equally, we talked about electrons existing in waves.

05:50 That’s why we can only talk about the probability of finding them in particular parts of an atom.

05:57 And this is the same analogy because, in this case, we’re talking about wave coherence.

06:03 We’re talking about whether or not an electron exists as the peak here of the trough that we’re showing here, the sine wave, or as the trough.

06:16 Right. So, as I mentioned, it’s possible for us to treat electrons as waves as well as as particles.

06:24 And, in the context of the p orbital, this is very important.

06:28 So, if we look at this wave form here, we can see that it is analogous to the dumbbell shape of our p orbital whereas we see in the center node, the chances of finding an electron are 0.

06:42 but the chances of finding an electron either side are reasonably high.

06:48 So, if we think of an electron as a wave with positive and negative regions, we can think about the ideas of coherence, i.e. constructive or destructive interference.

07:03 So, as there are three p orbitals, there needs to be a way of telling them apart because, if you look here, you can see that they are degenerate.

07:12 By that, what I’m talking about here is the idea that you could superimpose one on the other by a simple rotation, around 90 degrees.

07:21 And so a way of defining an electron in a given p orbital is via the magnetic quantum number or ml, Okay, not to be confused with ms.

07:31 That is a different one which we’ll come onto a little later.

07:34 So this helps us to define the direction of an orbital as well as its type.

07:42 So here we can see we’ve got the orbital running along the y axis and across the x axis and then, finally, along the z axis.

07:52 So, d orbitals.

07:55 These have a more complex set of shapes and they have the orbital quantum number of 2.

08:02 The d in the orbital stands for ‘diffuse’ and they have two nodal planes and come in sets of five.

08:11 The ml, or magnetic orbital number, can be -2, -1, 0, 1 or 2.

08:20 And don’t just take it and accept it as read.

08:22 There is actually an equation which we’ll come onto in the next lecture which explains how you can determine this yourselves.

08:31 The lowest energy shell containing d orbitals is n = 3.

08:36 Prior to that, they haven’t been unlocked.

08:42 Degeneracy.

08:43 This is what I alluded to in the case of the p orbitals and, as we’ll see a little later on, in the d orbitals.

08:51 These are orbitals with the same energy.

08:54 When they have the same energy and they have the same orientation, they’re regarded as degenerate.

09:00 In other words, they’re superimposable onto each other.

09:04 And this is the case for p and also some of the d orbitals.

09:09 And degeneracy is based on the idea that, whilst they have the same energy and the electrons – or the probability of finding them – is the same distance from the nucleus, they point in different directions.

09:23 By rotating them 90 degrees in the three axes, however, they would all be identical.

09:30 They’re all superimposable and therefore they’re termed degenerate.