Orbitals – Introduction to Chemistry

by Adam Le Gresley, PhD

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    00:00 As I mentioned, the shells themselves can be divided into orbitals, each of which contains two electrons. Orbitals are characterised 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. The orbital shapes that we will come across are s, p, d and f. We’re mostly going to focus on s, p and d orbitals.

    00:40 The analogy to use is that each shell unlocks if you like an additional orbital type. So, in other words, for the first shell you can only get the s-type orbital. For the second shell you can get the s- and the p-type orbitals. And for the third shell you can get s, p and d. And for the fourth it’s possible to have access to all four, bearing in mind each individual orbital can only contain two electrons. And we’ll talk about this in more depth a little later. The orbital quantum numbers are given for s orbitals as 0, 1, 2 and 3. And the nomenclature in quantum mechanics, where n was for principal quantum number, is that the orbital quantum number carries the letter l. So, as we’ll see, it’s possible to actually assign the specific designation of an electron just using quantum numbers. The simplest orbital, as you can see here, is where l, or the orbital quantum number, is equal to 0. And it is spherical.

    01:52 Here you can see three particular types of shells of orbitals: the 1s, the 2s and the 3s. Each of these is spherical but, as you can see, each of these is of a different size. 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. 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. 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. 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. The 2s is an s orbital in shell 2 and the 3s is an s orbital in shell 3. And each of these – the 1s, the 2s and the 3s – can formally contain two electrons. 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.

    03:23 And remember what I said: as you move up the shells, it’s possible to accommodate more and more electrons. The only way to do this of course is to have more and more different types of orbital. And here we can see three of these: the 2py, the 2px and the 2pz. 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. It is, of course, possible to get 3p and 4p orbitals but, of course, not possible to get 1p. You haven’t unlocked them at that point. Note the similarities between these guys.

    04:10 They are dumbbell shaped. It’s often the shape that’s considered. 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. Crucially, if we look in the centre where the node is formed, where we have the tiny spot in the centre is where the nucleus is.

    04:43 And there we have an electron density of 0. 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.

    04:57 A p orbital has two regions where electrons may be found on either side. Note what I’ve done is we’ve got a plane through the node of the p orbital as shown here. And, along that plane, there exists no electron density as it contains the nucleus. But, again, what is the significance of the negative and the positive charges? And this is to do with the phase of electrons. 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. 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.

    05:51 Equally, we talked about electrons existing in waves. That’s why we can only talk about the probability of finding them in particular parts of an atom. And this is the same analogy because, in this case, we’re talking about wave coherence. 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. Right. So, as I mentioned, it’s possible to treat electrons as waves as well as particles. And, in the context of the p orbital, this is very important. So, if we look at this wave form here, we can see that it is analogous to the dumbbell shape of our p orbital where we see in the centre node the chances of finding an electron are 0 but the chances of finding an electron either side are reasonably high. 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. 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. 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°.

    07:25 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. That is a different one which we’ll come onto a little later. So this helps us to define the direction of an orbital as well as its type. 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.

    07:55 So d orbitals: these have a more complex set of shapes and they have the orbital quantum number of 2. The d in the orbital stands for ‘diffuse’ and they have two nodal plans and come in sets of five. The ml, or magnetic orbital number, can be -2, -1, 0, 1 or 2.

    08:25 And don’t just take it and accept it as read. There is actually an equation which we’ll come onto in the next lecture which explains how you can determine this yourselves.

    08:35 The lowest energy shell containing d orbitals is n = 3. Prior to that, they haven’t been unlocked. Degeneracy: 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. These are orbitals with the same energy. When they have the same energy and they have the same orientation, they’re regarded as degenerate. In other words, they’re superimposable onto each other. And this is the case for p and also some of the d orbitals. 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. By rotating them 90° in the three axes, however, they would all be identical.

    09:33 They’re all superimposable and therefore they’re termed degenerate.

    About the Lecture

    The lecture Orbitals – Introduction to Chemistry by Adam Le Gresley, PhD is from the course Chemistry: Introduction.

    Included Quiz Questions

    1. It is a mathematical function which gives the probability of occurrence of an electron at a specific region around the nucleus
    2. It is a mathematical function which gives the amount of charge on an electron in an atom
    3. It is a mathematical function which gives the amount of effective charge on an electron
    4. It is a mathematical function which gives the number of attractive forces between an electron and the nucleus of the atom
    5. It is a mathematical function which gives the velocity of an electron revolving around the nucleus in an atom
    1. It determines the orbital angular momentum and gives an estimation regarding the shape of an orbital
    2. It determines the negative charge of the electrons present in particular orbitals
    3. It helps in determining the location and velocity of an electron around the nucleus with accuracy at a given time frame
    4. It helps in determining the magnetic spin of two electrons present in two distant orbitals
    5. It helps in the calculation of the total effectiveness of nuclear charge on the electrons present at a particular spatial point in an atom
    1. 0, 1, 2
    2. 1, 2, 3
    3. -2, -1, 0, +1, +2
    4. -1, 0, +1
    5. -3, -2, -1, 0, +1, +2, +3
    1. 14
    2. 10
    3. 12
    4. 16
    5. 18
    1. Spherical
    2. Dumbbell
    3. Cloverleaf
    4. Diffused
    5. Cubic
    1. -2, -1, 0, +1, +2
    2. -3, -2, -1, 0, +1, +2, +3
    3. 0, 1, 2, 3
    4. 1, 2, 3
    5. -1, 0, +1
    1. …are filled evenly by Hund’s rule before moving to higher energy orbitals
    2. …are filled by Aufbau principle before moving to the other orbitals present in an atom
    3. …usually contain excited state electrons
    4. …provide an extra space for the accommodation of neutrons.
    5. …provide an additional space for the accommodation of protons

    Author of lecture Orbitals – Introduction to Chemistry

     Adam Le Gresley, PhD

    Adam Le Gresley, PhD

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