Part 4 of our article, in which we hope to develop an understanding of atomic structure and the periodic table, from the beginning of secondary school/junior-high level, to first/second year undergraduate physics/chemistry, via one fictional conversation. Find the first three parts on our blog page: sciencebydegrees.com/blog. Sigrid has just asked Sally how fluorine bonds ionically with sodium…
SIGRID: The fluorine atom can take sodium’s ‘extra one’. But then sodium doesn’t have a full outer shell – it has an empty one!
SALLY: Ah, don’t worry about that. A sodium atom is 2.8.1 – the third shell is the outer shell. But when it loses that 1, and becomes 2.8, then the second shell becomes the outer shell. Empty shells don’t count.
SIGRID: Good, because otherwise we’d have to keep track of all the empty shells all the time.
SALLY: OK, so what happens if fluorine is reacting with an element whose atoms also want to gain electrons? Then everything involved wants to gain more electrons.
SIGRID: They could share?
SALLY: Yes! And that’s called covalent bonding. In fact, chemical bonding is more complicated than what we have described, but we’ll need to leave that for another conversation.
SIGRID: Yeah, you always say that. Well, let’s get back to atomic structure then. I feel like there is a big shock on the way. I mean – you keep showing me the first three rows of the periodic table, and this book I’ve got just talks about the electronic configuration for the first 20 elements. I’m thinking something weird must happen at element 21.
SALLY: What would you expect to happen?
SIGRID: Well, element 20 (calcium) has electronic configuration 2.8.8.2, and we fill electron shells from the inside outwards, so the 21st element must be 2.8.8.3?
SALLY: And that’s a perfectly reasonable thing for you to think, based on what we know. What did that book tell you about the number of electrons that the shells hold?
SIGRID: The first holds two, the second holds 8, the third holds 8 before the fourth starts to fill…
SALLY: That’s a clever use of words so that the explanation can be ‘contained’ at a certain level! Do you see the trick? Nobody has said that the third only holds 8!
SIGRID: Just that once you put 8 in it, then the fourth shell starts to fill. There could still be ‘room’ in the third shell.
SALLY: There is! n=3 is NOT full with 8 electrons in it. It can take 18.
SIGRID: So the electronic configuration for scandium (number 21) wouldn’t be 2.8.8.3 because the 21st electron goes into the third shell. It would be 2.8.9.2.
SALLY: That’s right. So look at your periodic table – see that block of elements from scandium to zinc?
SIGRID: As we go across that row, the third shell is filling up, and they still have two in the outer shell.
SALLY: What’s the electronic configuration of zinc then?
SIGRID: 2.8.18.2. And then the third shell really is full, and we go back to adding electrons to the outer (n=4) shell.
SALLY: Find gallium.
SIGRID: Next to zinc.
SALLY: So gallium is in group 3, under boron and aluminium because, like them, it has 3 in the outer shell.
SIGRID: And then all the noble gases will have 8 in the outer shell because even though some of their outer shells can take more than 8, we are actually filling inner shells first.
SALLY: Exactly. That’s called the ‘octet rule’ – 8 in the outer shell is particularly stable, even though it’s not necessarily a full outer shell once we get past neon.
SIGRID: How many can the fourth shell take?
SALLY: 32.
SIGRID: There must be a pattern here. I know some maths that might help – don’t worry if you can’t follow it – this is my area of expertise! Give me a minute, and I’ll work it out…
SIGRID: OK, so that means the nth shell can take 2n2 electrons.
SALLY: Well done.
SIGRID: How does that work on the periodic table? We had scandium to zinc because we had to fit in an extra 10 elements…
SALLY: …That’s right – and that led to the rectangular block that we call the transition metals…
SIGRID: …Yeah, but further down the table, we are going to need to fit in more than 10 extras, because of 2n2.
SALLY: Well spotted.
SIGRID: So where do they go?
SALLY: Have you spotted the lanthanides and actinides?
SIGRID: What are they?
SALLY: All these elements down in a separate block at the bottom of the periodic table.
SIGRID: I’ve often wondered why they are separate, but to be honest I hardly notice them – I’m always too busy concentrating on the top half of the table! Actually, there’s loads of them!
SALLY: Yes, they are comparatively rare, so you tend not to deal with them much in school science. But they really aren’t separate in the way they appear! Look – the lanthanides are numbers 57 – 71. They belong between barium and hafnium.
SIGRID: And the actinides are numbers 89 – 103, and so go between radium and rutherfordium. So why don’t we draw them there?
SALLY: Well we could, but then the periodic table would look like this.
It would be ‘more accurate’ or ‘less misleading’ if you like. But it also wouldn’t fit on the average page of a book or a website.
SIGRID: That’s the only reason for putting them down there? Wow. And you know the next question… Why 2n2? In other words, why can you fit 2 in the first, 8 in the second, 18 in the third, and so on?
SALLY: Well, we can answer that, but it’s going to need a whole new approach. Welcome to the world of ‘orbitals’. So far we have drawn the atom like a solar system, with electrons in definite orbits around the nucleus, like planets around the Sun. But it’s not really like this. Planets have well defined trajectories through space. Electrons not so much.
SIGRID: But they must be orbiting. Bohr said so. And all of our drawings show them orbiting.
SALLY: Have you heard of the Heisenberg Uncertainty Principle?
SIGRID: Heard of it. But no idea what it means.
SALLY: The uncertainty principle says that there are pairs of quantities that we cannot know to arbitrary accuracy.
SIGRID: Because we can’t measure them well enough?
SALLY: It’s worse than that. Even in principle they can’t be simultaneously known, even with the best not-yet-invented measurement process imaginable. Two such quantities are momentum \(p\) and position \(x\). The uncertainty principle is then written \(\Delta p \Delta x \geq \frac{\hbar}{2}\). It means that when you multiply the uncertainty in the two quantities, it can’t be less than the right hand side – don’t worry about the h-bar – it’s just a very small number.
SIGRID: So the better you know one of the quantities, the worse you know the other, because the product of their uncertainties has to fit that rule.
SALLY: That’s it.
SIGRID: The ‘delta’ symbol \(\Delta\) means ‘uncertainty in’, right?
SALLY: Yes, sorry – should have said that. This level of uncertainty is tiny (because h-bar is a very small number) and it makes no difference for macroscopic moving objects like birds, ice hockey players, or planets.
SIGRID: But what’s all this got to do with atoms?
SALLY: Atoms are tiny, and on that scale that level of uncertainty does make a difference. As far as the electrons are concerned, you can think of \(x\) as ‘where it is’ and \(p\) as ‘where it’s going’. The combination of those two things maps out its trajectory in space.
SIGRID: Then the uncertainty principle is saying that even in principle we can’t know an electron’s trajectory, and our picture of an atom is wrong?
SALLY: It’s a useful picture, and it has got us this far. And in some situations you don’t need anything more. But yes – the orbits are a bit misleading.
SIGRID: What’s an orbital then, as compared to an orbit? And why is the uncertainty principle involved?
SALLY: Well, if we can’t know the electron’s path, then its position becomes a matter of probability. An orbital is a region of space with a high probability of containing an electron. Often 95 % is the ‘high probability’ specified.
SIGRID: OK, but the picture of the atom is just going to look the same as before, but drawn a bit more 3D and with some probabilities on it!
SALLY: And some electrons do behave like that. But not all electrons have spherical orbitals. Spherical orbitals are called ‘s’ orbitals.
SIGRID: ‘s’ for spherical – I like it!
SALLY: Actually ‘s’ stands for ‘sharp’, but we are not going to worry about the etymology of the orbital names. Just go with the idea that there are orbitals called s, p, d and f. And they all have different shapes.
SIGRID: For example?
SALLY: Well, what we call the 2p orbital is dumbbell shaped, like this.
SIGRID: But that makes no sense. Every time an electron goes from one lobe of the dumbbell into the other, it will crash into the nucleus.
SALLY: You need to stop thinking of these pictures as the paths of electrons – they are regions where electrons are likely to be.
SIGRID: Hmm, maybe. Although I feel you have tricked me here in a way I can’t quite put my finger on.
SALLY: No, really, not this time! It makes literally no sense to consider the trajectory of an electron in an atom – remember the uncertainty principle!
SIGRID: But things do have trajectories! Stuff moves from A to B!
SALLY: Macroscopically, yes. But microscopically, in the world of quantum physics, not so much! Heisenberg’s approach was to let the maths do all the work and make the predictions, and not worry too much about what was ‘really going on’. Maybe our minds are not cut out for thinking about what is ‘really going on’ at that scale.
SIGRID: No wonder there’s that quote about how ‘anyone who says they understand quantum mechanics, hasn’t’ or something.
SALLY: I know how you feel.
SIGRID: Anyway, how does this help us understand electronic configurations?
SALLY: For this stuff, you’ll need to move on to your next book – one level up, as it were.
SIGRID: OK, here we are. Electronic configurations… Let’s see – here we are.
- The first shell (corresponding to n=1) can only contain one s-orbital.
- The second shell (n=2) can have one s-orbital and three p-orbitals
- The third shell (n=3) can have one s-orbital, three p-orbitals and five d-orbitals (and the d-orbitals have a more complicated shape than the p-orbitals)
- The fourth shell can have one s-orbital, three p-orbitals, five d-orbitals and seven f-orbitals
And that will do for now…
SALLY: OK – we’re getting somewhere. The different types of orbitals are sometimes called ‘subshells‘ – so for example the n=2 shell has an s subshell, and a p subshell, and within the p subshell are three p-orbitals. And the orbitals, as well as a certain shape, have a certain orientation to each other. I’m not going to get you to draw this – have a look at this one from chemistryonline.
SIGRID: You said that n=1 can take two electrons, but it only has one orbital. And we know that n=2 can take 8 electrons, whereas it has 4 orbitals – an s and 3 p-orbitals. So does that mean that each orbital can contain two electrons?
SALLY: That’s exactly what it means… Did you know that electrons ‘spin’?
SIGRID: What? Oh, it says that here, but it calls it ‘intrinsic angular momentum’.
SALLY: Good! And do you know what angular momentum is?
SIGRID: Yes! Linear momentum is the product of mass and velocity. And angular momentum is an analogous quantity for rotational motion, given by the product of mass, velocity and radius of motion.
SALLY: Exactly! Well, on an atomic scale the angular momentum of electrons consists of two parts. Angular momentum due to its orbit…
SIGRID: …I thought we couldn’t determine the trajectory of an electron in an atom?
SALLY: We can’t – but we can know its orbital angular momentum… And it also has ‘intrinsic angular momentum’ – angular momentum that is just a property of the electron and doesn’t depend on what it is doing. That’s what we call ‘spin’. All electrons have the same amount of spin and it can be in two orientations, which we call ‘up’, labelled ↑, and ‘down’, labelled ↓.
SIGRID: OK, so what has spin got to do with electron configurations?
To be continued…