Part 3 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. Missed Parts 1 and 2? Find them here and here! Sigrid has just asked Sally what ‘n’ is…
SALLY: n is just a label for the energy level. n=1 means the first (lowest) energy level. n=2 is the second lowest, and so on. n is the first ‘quantum number’ you have met – it is called the principal quantum number. A quantum number describes the value of a quantity that is constrained to have only certain values. n describes the energy levels of the atom.
SIGRID: What’s the biggest number for n?
SALLY: In theory n can be any value up to infinity, but the energy levels get closer and closer together (we have stopped at 5 to stop the picture getting squashed), so that the energy does not increase forever – it has a maximum labelled 0 on the graph. If you give the atom enough energy to get to 0 the electron will not be ‘excited’ – instead it will leave the atom altogether, and the atom will be ‘ionised’.
SIGRID: Why are the energies negative? I didn’t think negative energy was a thing?
SALLY: Don’t worry about that. It’s just a convention. It’s like the contours on a map. We plot the altitudes in metres relative to sea level, and that way we are currently at 250 m and the summit of Everest is 8850 m. The Dead Sea is 430 m below sea level, which we would call an altitude of -430 m. But we could call Everest 0, and label the contours to describe places’ ‘depth’ relative to Everest.
SIGRID: Then sea level would be -8850 m and we would be at -8600 m.
SALLY: Yes. And physics would still work. Going from here to the sea would still be a reduction in altitude of 250 m, and a corresponding reduction in gravitational potential energy.
SIGRID: It doesn’t much matter where you zero the scale, then, provided it is always differences you are interested in.
SALLY: That’s a quite profound general truth.
SIGRID: You said that Bohr had experimental evidence that led to him coming up with this theory?
SALLY: Yes – there was quite a bit, but we’ll focus on one particular instance. Do you know the meaning of the term ‘emission spectrum?’
SIGRID: I know that if you pass white light through a prism it separates all the different wavelengths out and we see the colours of the rainbow, and we call it a spectrum.
SALLY: An emission spectrum is like that, but without most of the colours. In fact only a few colours are present. You can make one by passing electricity through a gas at low pressure. Here’s the emission spectrum for atomic hydrogen.
SIGRID: Do other gases have a spectrum like this?
SALLY: Yes, but they tend to be more complicated for reasons you’ll understand before the night is through. Why do you think only certain well-defined colours are present?
SIGRID: Well, if the electricity is exciting the hydrogen atoms into an excited state and they spontaneously fall back to lower energy levels, they will give out photons of specific energies – each energy corresponds to light of a specific colour.
SALLY: The emission spectrum is really closely linked to the energy level diagram we saw a few minutes ago. Do you think you could find a way to draw the two combined so the link is really clear? One thing to note is that downwards electron transitions don’t have to go directly to n=1. They can ‘stop off’ at intermediate levels, and return to the ground state in a series of jumps, rather than just one.
SIGRID: I’ll have a go. Back in a bit…
SALLY: That’s really good. I like the way your transitions are at the appropriate place on the wavelength scale!
SIGRID: Thanks! But if this agrees so well with experiment, is this the endpoint of our learning about atoms.
SALLY: Well, we certainly know quite a bit now about the hydrogen atom. But why is hydrogen unique?
SIGRID: It’s the simplest. But that doesn’t make it unique, because ‘simplest’ is a relative term. Hmm… Oh! It’s the only element with a single electron in its atoms.
SALLY: Yes, all the other elements have more than one. Some have a lot more than one!
SIGRID: But that will be easy. Pick an element.
SALLY: Gold.
SIGRID: Let’s see. Gold’s atomic number is 79. So an atom of gold has 79 electrons. They’ll all just crowd down into the n=1 orbit and behave just like the hydrogen electrons.
SALLY: Ah, it turns out they don’t! What does that book tell you about ‘electronic configurations’?
SIGRID: Hmm. It says that you can only fit two electrons in the n=1 shell, and 8 in the second (n=2). I assume a ‘shell’ here is what we have described as an ‘energy level’.
SALLY: Yes. What does it say about the third shell?
SIGRID: It says it can take 8 before the n=4 shell starts filling up.
SALLY: OK, hold that thought. Now, does it give any examples?
SIGRID: Yes! It says that the electron configuration of carbon is 2.4.
SALLY: And what do you think that means?
SIGRID: Well, I know a carbon atom has 6 electrons. I suppose it means that it has two electrons in its first shell, and the second shell takes the remaining four.
SALLY: Precisely, so can you work out the electronic configurations of fluorine and potassium? You’ll need to look at your periodic table.
SIGRID: OK! Fluorine is element number 9, so it’s electron configuration will be 2.7. And potassium is number 19. So, going by the rules in this book, it will have 2 in the first shell, 8 and the second, and 8 in the third. That’s 18 so far, so the 19th and final electron will start a brand new fourth shell, n=4. So the answer is 2.8.8.1.
SALLY: Good. Now it is really important to realise that what you have described is the ground states of the atoms. Just like our discussion of the hydrogen emission spectrum, if you give the atom enough energy, electrons can jump into higher shells, and you have an excited state.
SIGRID: And the atom will then spontaneously return to the ground state and emit a photon.
SALLY: Right.
SIGRID: So the ground state doesn’t mean n=1. Well it did for hydrogen, because it had just the one electron so it can fit in the first shell. But the ground state of potassium, for example, involves electrons in four shells.
SALLY: Right again. So to summarise here’s a picture of the top three rows of the periodic table, but with electronic configurations added.
SIGRID: Wow, so elements in the same column have the same number of electrons in the outer shell. Those in the first column have 1 in the outer shell…
SALLY:…The columns of the periodic table are called groups, so they are called Group 1 elements.
SIGRID: OK, and Group 2 elements have two in the outer shell.
SALLY: What about the final column?
SIGRID: Hmm, that’s weird – they don’t all have the same number in the outer shell. Helium only has 2, and the others have 8. But they do all have a full outer shell, so they still belong together I guess.
SALLY: Well done. I’ve cheated a bit, and led you to this conclusion by showing only the first three rows. And we’ll come back to this later. But at this stage of your atomic education, we can go with that…
SIGRID: Then the periodic table is arranged by chemical properties and by atomic number as we said before, but it’s also arranged according to electronic configuration. That’s a lot of information in one table!
SALLY: It is pretty amazing. But it’s no coincidence, because the atomic number determines the electronic configuration, and that in turn goes a very long way towards determining the chemical properties.
SIGRID: Those elements in the final group with the full outer shell. They are the noble gases aren’t they? They hardly take part in chemical reactions at all – I mean argon, for instance, is deliberately used as an inert atmosphere when you want to prevent chemical reactions, generally with oxygen. So how does a ‘full outer shell’ lead to that kind of behaviour?
SALLY: Good question. We say the noble gases are particularly ‘stable’, which means they don’t react much. The reason for that goes back to the energy discussion we had before. The electronic configurations of the noble gases are particularly low energy states.
SIGRID: So when fluorine reacts, what happens to its electronic configuration?
SALLY: Well, one version of fluorine reacting has it gaining an extra electron. The electronic configuration then turns into that of neon – it goes from 2.7 to 2.8 – but that doesn’t mean the atom becomes a neon atom. It’s still fluorine because nothing has happened to the number of protons. That’s still 9.
SIGRID: And why are the noble gas electronic configurations particularly stable?
SALLY: Well, that’s a pretty technical question. At this stage though we can have a quick go at answering it by comparing a noble gas with its neighbouring elements. Pick a noble gas and tell me its electronic configuration.
SIGRID: OK, let’s go with our old friend neon. It is element number 10 – so the electronic configuration is 2.8.
SALLY: And now find the two elements either side – elements 9 and 11.
SIGRID: We’ve met fluorine before – that’s element 9, it’s 2.7. And element 11 is sodium, so 2.8.1.
SALLY: Now see if you can work out why neon’s electronic configuration would be the most stable of the three. It might help to think of it in the terms ‘more strongly bound electrons’ equals ‘lower energy configuration’. You can think of the boulder as being ‘more strongly bound’ to the earth at the bottom of the valley than the top of the hill. In other words it will take an input of energy to move it back up, whereas it will spontaneously fall down. There’s another thing to consider, too. And that is the idea of ‘shielding’. Inner electrons can ‘shield’ the outer electrons from the attraction of the nucleus, making the outer electrons less tightly bound than they would otherwise be.
SIGRID: OK… Well, fluorine’s outer electrons are in the same shell as neon’s, so there will be roughly the same amount of shielding, but the nucleus of fluorine has less positive charge than that of neon. So fluorine’s outer electrons will be less strongly attracted, and less tightly bound, and be in a higher energy state than neon’s. In other words an atom of neon will be more chemically stable than an atom of fluorine.
SALLY: Good! A similar argument can be made to explain why it’s harder to add an electron to fluorine, as well as remove one, but let’s not get sidetracked. And what about comparing neon with sodium?
SIGRID: Well, sodium’s outer electron is less tightly bound to the nucleus because it’s further from it. And even though there are more protons in the nucleus attracting the outer electron, there is also an extra inner shell to provide shielding from the nucleus. So again, sodium’s outer electron will be less tightly bound than neon’s, and an atom of neon will be more chemically stable than an atom of sodium. Right, that’s a lot to take in. I might need to draw a summary picture of this.
SALLY: Remember we said that spontaneous processes tend to happen so as to minimise energy? Well, you can think of a lot of chemical reactions as happening when atoms move towards the electronic configuration of a noble gas.
SIGRID: I’ve heard people say that when chemical reactions take place, the elements are ‘trying to get a full outer shell’.
SALLY: What they mean is that processes take place that lead to lower energy configurations, and the noble gas electronic configurations, what we are for now calling a ‘full outer shell’, are such low energy configurations.
SIGRID: Fluorine has 7 electrons in its outer shell (2.7), and so it ‘needs one more’. And this is why it can bond by receiving an electron from another atom?
SALLY: Exactly – that’s called ionic bonding. So what happens if fluorine bonds with sodium (1 in the outer shell)?
To be continued…