Ep. 323: Isotopes

The number of protons defines an element, but the number of neutrons can vary. We call these different flavors of an element isotopes, and use these isotopes to solve some challenging mysteries in physics and astronomy. Some isotopes occur naturally, and others need to be made in nuclear reactors and particle accelerators.

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This episode is sponsored by: Swinburne Astronomy Online, 8th Light

Show Notes

  • Basics of an atom — HowStuffWorks
  • Gluons — GSU
  • Isotopes — Colorado University
  • Introduction to Nuclear Processes — University of Cambridge
  • Radiocarbon dating — NOVA
  • Atomic Number and Mass Number – Iowa State
  • Element Isotopes
  • Isotopes info — David Darling
  • Periodic Table by Number of Stable Isotopes – Wiki
  • Determining the ages of stars through studying isotopes — (Ancient Nearby Star is Nearly as Old as the Universe) Universe Today
  • Astronomers Discovery Unusual Stars with Extremely High Concentrations of Lead in their Atmospheres — SciTechDaily
  • Transcript

    Transcription services provided by: GMR Transcription

    Female Speaker: This episode of Astronomy Cast is brought to you by Swinburne Astronomy Online, the world’s longest-running online astronomy degree program. Visit astronomy.swin.edu.au for more information.

    Fraser Cain: Astronomy Cast Episode 323: Isotopes

    Welcome to Astronomy Cast, our weekly facts-based journey through the cosmos. We hope you understand not only what we know but how we know what we know.

    My name is Fraser Cain. I’m the publisher of Universe Today and with me is Dr. Pamela Gay, a professor at Southern Illinois University, Edwardsville, and the director of CosmoQuest.

    Hey, Pamela. How are you doing?

    Dr. Pamela Gay: I’m doing well. How are you doing, Fraser?

    Fraser Cain: Good.

    And you’re back from your epic Indonesian adventure.

    Dr. Pamela Gay: I am. Last week I was at the Southeast Asian Young Astronomers Conference, where I gave a workshop that I’m going to be blogging about on CosmoQuest and I gave a talk about CosmoQuest. It was amazing.

    It was, I think, the first conference I’ve been to in my life where the number of contributed talks by women was the same, if not more, than the number by men. Invited speakers were equal numbers. The food was amazing. I gained a kilogram while I was there.

    Yeah, it was – it was, in every way: The science was great, the comradery was great. The spiders were the biggest spiders I’ve ever seen.

    Fraser Cain: I saw your pictures on Google Plus. You looked terrified. Your hand next to the spider and they were the same size.

    Dr. Pamela Gay: Yes, yes. It was a huge spider. It was awesome.

    Fraser Cain: Yeah.

    Dr. Pamela Gay: Yeah. So, I highly recommend Indonesia and I think I’m going to be attempting to convince my husband it’s worth going there for a vacation at some point.

    Fraser Cain: Ahh. That sounds great.

    So, one thing that maybe we want to get people’s help doing. If you’re listening to this and you subscribe to us through iTunes. If you could take a second and give us a review on iTunes, that would be terrific. We’d really appreciate it. Let other people know what you think of the show and so they can find it and decide whether they should subscribe as well.

    So, the best place to do that is in iTunes. You can just do a search for Astronomy Cast and then there’s “Reviews” and you can rate the show and give us a review and we’d really appreciate that. That’s super helpful.

    Okay. Let’s get on with the show, then.

    Female Speaker: This episode of Astronomy Cast is brought to you by 8th Light, Inc. 8th Light is an agile software development company. They craft beautiful applications that are durable and reliable. 8th Light provides disciplined software leadership on demand and shares its expertise to make your project better.

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    Fraser Cain: So, the number of protons defines an element but the number of neutrons can vary. We call these different flavors of an element isotopes and use these isotopes to solve some challenging mysteries in physics and astronomy. Some isotopes occur naturally and others need to be made in nuclear reactors and particle accelerators.

    Okay, Pamela. So let’s – I guess we need to have that kind of basic chemistry/physics lesson about the atom, what’s inside the atom. So, let’s go with that basic, sort of building block of the atom and then we’ll get into the isotopes.

    Dr. Pamela Gay: So, you basically have three different particles that make up an atom. You know – the electrons, which are inconsequential for the discussion today. They orbit in a cloud. Not in nice, neat orbits like planets but in a cloud around the atomic nuclei.

    The nuclei itself is made up of protons that desperately want to repel each other via the electromagnetic force but are held together with the strong force and buffering them is a set, in many cases, of neutrons and those neutrons – the whole thing is held together, again, via the strong force and, if you really care, the particle that is conducting this force is the gluon. And I just love the fact that nuclei are glued together with gluon.

    Fraser Cain: Best name ever.

    Dr. Pamela Gay: Yes.

    Fraser Cain: Yeah.

    Okay. So we’ve got the protons, the neutrons, the electrons. Forget about the electrons. We don’t care about them. Protons – that’s the number which gives us the –

    Dr. Pamela Gay: Atom.

    Fraser Cain: It’s the atomic number, right?

    Dr. Pamela Gay: Yes. And then you take the number of the protons and the number of the neutrons and that specifies which isotope you’re dealing with and each particular isotope is referred to as a nucleotide. So –

    Fraser Cain: Okay.

    Dr. Pamela Gay: One atom has many isotopes. Each individual isotope is a nucleotide.

    Fraser Cain: Okay. Now – and this is the thing, right – is that, while the number of protons really defines that element – if we have 12 protons, we’re looking at carbon – but we can have different amounts of neutrons. So how – how do you get these different flavors, these different isotopes?

    Dr. Pamela Gay: You add or subtract neutrons.

    Fraser Cain: How?

    Dr. Pamela Gay: It’s – well, when a mommy and daddy proton get together –

    No, seriously though, it’s one of these things where you can get to them through a whole variety of different ways. You can get to them in the outskirts of a star, by having neutrons slowly bombarding atomic nuclei in the atmospheres of stars and you build up – you can get various isotopes of carbon that way, for instance.

    During supernovae reactions, you can have the fast process or the slow process taking place. So, that’s the more positive direction to go.

    On the more negative way to go, you can have nuclear decay processes. Either what’s called an alpha process, where you have happy little atoms sitting there and, all of a sudden, it – well, for lack of a better word – excretes a helium atom. So, off flies two protons and two neutrons that are tied together via the strong force. They go flying away but by alpha particle, hello new isotope that is actually a completely different atom because you got rid of two protons.

    We also have beta decay processes where either a proton spontaneously turns into a neutron and a positron or you have a neutron spontaneously turns into a proton and an electron and there’s other things like neutrinos involved.

    But, all these different processes change the identity of an atom in various ways.

    Fraser Cain: But you said, like in the outsides of stars, in supernova. I mean, are the methods of creating the different flavors of, say, carbon fairly extreme places? I mean, are you just gonna get, say, a carbon atom get – I don’t know – like, get hit by a piece of hydrogen and then turn into Carbon 14 or is it – do you need like really powerful, extreme events to happen?

    Dr. Pamela Gay: It depends on which direction you’re going. If you’re building things up, yes. That’s going to be some sort of something is in an extreme environment. You need some sort of a neutron stream that is hammering away, slowly but surely, producing that neutron flow that the nuclei is able to get bombarded and, over time, build up, build up, build up.

    But the decay process can happen anywhere. So, we have here on earth, Carbon 14. It’s a radioactive form of carbon and plants absorb it. So, throughout their life, they’re going to absorb Carbon 14 and the stable forms of Carbon 12 and 13 in particular ratios. And, once the plant dies, it’s clearly no longer processing carbon out of the atmosphere because it’s dead. So that dead plant will then perhaps turn into charcoal through a fire; it will perhaps simply become, well, a fossilized piece of wood.

    And as you look at its ratio over time, we can do carbon dating. Carbon dating also works on – well, we’re eating those plants. So we’re, by consuming plants, we’re consuming that ratio of carbon, 12, 13 to 14. And so, when you do radio carbon iso – radio carbon dating, you’re looking at the ratios of the isotopes that basically go back to the plants we ate, the plants we use to make our clothes, the plants we use to make our fire. If there is a plant involved, we can carbon date it.

    Fraser Cain: Right. I see. So, you’ve got these plants. They’re – there’s a – the atmosphere has a certain ratio of Carbon 14 to Carbon 12 to Carbon 13 and they’re breathing it in –

    Dr. Pamela Gay: Yes.

    Fraser Cain: The carbon dioxide. They’re turning it into plant material and they’re incorporating that Carbon 14 into their structure. It works exactly the same? Like, if you can use a Carbon 14 just like you can use a Carbon 12?

    Dr. Pamela Gay: Yeah. Chemically, as far as chemical reactions are concerned, a carbon is a carbon is a carbon. Doesn’t really matter, for all intents and purposes – doesn’t really matter which isotope it is. And so, when we’re digesting things, when we’re weaving things, when we’re burning things, all carbon is treated the same. But then, over the eons, well the Carbon 14 is going to decay. So, that ratio is going to change over time. And by looking to see how the ratio has changed, we can figure out how old something is.

    Fraser Cain: But aren’t there forms – so, I mean, you said that we can use carbon just in any shape or form. You know, I could eat a hamburger made of all Carbon 14 and it would taste exactly the same as a Carbon 12 hamburger.

    Dr. Pamela Gay: Yes.

    Fraser Cain: But I know that, for example, hydrogen fusion wants deuterium, right? And that’s a heavier form of hydrogen.

    Dr. Pamela Gay: And that’s not a chemical process.

    Fraser Cain: Ahh.

    Dr. Pamela Gay: So this is where we have to look. So, chemistry – that’s the electromagnetic force. That’s what bonds my coffee cup happily together with, I think it’s mostly ionic bonds – but don’t trust me on that. I’m a physicist not a chemist.

    So, as far as covalent bonds, ionic bonds, your general chemical reactions care, it’s all about the atomic number. It’s all about the number of electrons. For chemistry, the number of electrons does matter. That’s the ion.

    But when it comes to quantum mechanics, then you start to worry about – well, what’s the neutron number? And, in fact, one of the things that I actually did as research in graduate school was the molecule magnesium hydride can be made up with magnesium atoms that have different numbers of neutrons in them and, depending on what the magnesium hydride is made of, the color at which it absorbs light is going to be ever-so-slightly different because those protons in the center are repelling one another in slightly different ways, they’re attracting the electrons in slightly different ways. It’s all mediated by those neutrons being there.

    And so, when we look at the light of stars, if we have a high enough resolution spectrograph, if we’re able to split the light apart with fine enough details, we can actually start to see how the photons interact differently with each of those different types of atoms, how the electrons are thus in slightly different orbital [inaudible] [00:12:24] reaction.

    And the same is true with nuclear reactions. If you have an atom that has a different binding energy to the core, it’s that binding energy that plays such a big role in nuclear reactions. Well, if something’s just on the verge of falling apart because it either has too few neutrons or too many neutrons, well something that’s about ready to fall apart anyways is going to be much easier to use in a nuclear reaction.

    This is where we start to worry about countries that are enriching uranium. Well, enriching uranium generally means you’re bombarding that sucker with more and more neutrons, getting it to a higher and higher ratio of the – well, easier to use in nuclear bombs, nuclear burning. So, we worry about neutron number.

    And, as I said, it can worry – it can be a worry in both directions. If you have too few, it’s ready to fall apart in one direction. If you have too many, it’s ready to fall apart in another direction.

    Fraser Cain: Is there a limit? Like, if I – Say I took my hamburger and bombarded it with neutrons and made a high-neutron burger, you know – would there be some kind of limit on how many – how many neutrons a carbon atom can hold –

    Dr. Pamela Gay: Yes.

    Fraser Cain: Until it just goes, “Kaboom”.

    Dr. Pamela Gay: Yeah, and in this case, what you’re more looking at is what is the rate of the two reactions? What is the rate at which you’re bombarding that sucker with neutrons compared to the rate at which it’s capable of essentially switching identities? So, as you’re bombarding that poor, innocent, undeserving hamburger with neutrons, how quickly are those neutrons able to undergo beta decay to become protons and become something else entirely different?

    If your rate of bombardment is slower than the reaction rate, it’s just going to switch identities and become something stable. Now, if you’re able to bombard those carbon atoms so fast that they’re not able to undergo beta decay, you’re going to end up with these very unwieldy carbon atoms. But the reality is those unwieldy carbon atoms are going to quite happily undergo different decay processes and you probably can’t bombard it that quickly.

    But this does get at what are stable versus unstable isotopes and the magical way it sometimes feels like nuclear physicists are constantly pushing the boundaries of the periodic table, constantly trying to create heavier and heavier atoms and what they’re doing in most cases is bombarding things with neutrons to, well, get them to eventually undergo this beta decay to create the heavier atoms because, well, in some cases, that’s a lot easier than bombarding with protons and trying to get the protons to stick.

    Both processes get used.

    Fraser Cain: Yeah. In preparing for this episode, I saw there was a number that – there was 3 – I think 3,000 artificial isotopes had been created –

    Dr. Pamela Gay: There’s a poster –

    Fraser Cain: Above and beyond just the natural isotopes that we’ll have in the universe, right?

    Dr. Pamela Gay: There’s a poster that you can see in the background of one of the hallways in The Big Bang Theory that’s a poster we actually had in graduate school and I deeply regret that I’ve never bought this poster and I just tried to find it online, prepping for this show, and couldn’t. And it’s this poster that, when you look at it, there’s a diagonal line and that’s the line of stable atoms. Not stable atoms – stable nucleotides, stable isotopes – and off of it is different colors that represent different forms of unstable.

    So, there’s things that are stable for short periods; things that are stable for long periods; things that decay via beta process, either through proton creation or through neutron creation; and things that decay via the alpha process, by spitting out helium atoms.

    This poster, when you get really close to it, allows you to look and see, “Oh! This is thorium of this species. It’s going to bounce down here to aecidium, go back up to a different form of thorium.”

    And you can trace through all of the different forms of decay processes that it goes through. And it’s actually really neat to see how things linger at one state before finally decaying all the way down to, well, their end stable atom or atoms.

    Fraser Cain: You kind of imagine – I imagine this, like, a cliff with different little things jutting out of the cliff, little sub-cliffs, and these things are falling down and they are rolling and then they fall again and they roll for a bit and then, you know, as they move through this process.

    Dr. Pamela Gay: Well, what’s kind of awesome is the way they go up and down. So the particular reaction I’m thinking of is, you have Thorium 232 that will give off a helium nuclei. So, ditches two protons and two neutrons, becomes Radium 228. It then goes through an inverse beta decay process. So then, one of its neutrons becomes a proton. It’s now aecidium, which I know I have never in my life pronounced completely right. It then goes and switches another neutron to a proton, goes back up to thorium. Now it’s Thorium 228. Now it bounces down to radium again, then francium, then radon. Eventually, it gets all the way down to an unstable form of lead.

    And I just love the idea that this metal we rely on isn’t always stable. So, it becomes Lead 212. It then undergoes inverse beta decay, bounces up to bismuth. Goes through another inverse beta decay, goes up to polonium. And so you have things that are going up and down in proton number.

    So, in terms of how big an atom they are in the way that we think of atoms when we’re taking chemistry in 10th grade, you have things that go up the cliff but they’re also losing neutrons. So, it’s this crazy, how do you judge whether something is bigger or smaller? Well, you have to look at that combined neutron plus proton number.

    Fraser Cain: Right. So you add up the protons and the neutrons and – Because each time that it’s doing some kind of decay, it’s shooting off neutrons away from the atom itself. Right? They’re gone.

    Dr. Pamela Gay: Well, it’s either shooting off a neutron or – shooting off is the wrong word. So –

    Fraser Cain: Emitting?

    Dr. Pamela Gay: No, no. So, it will sometimes shoot off an alpha particle, which is two protons and two neutrons, but the rest of the time, it’s shooting off either an electron or a positron as it converts a proton to a neutron or a neutron to a proton.

    So, what we have is this case of protons and neutrons having essentially the same mass but a difference in charge. So, you have to conserve charge, which is either an electron or a proton goes away. You have to conserve other things. So, there’s neutrinos involved. But, as things bounce back and forth, the Radium 228, the Aecidium 228, the Thorium 228; all three of those things are different atoms. You get between them by converting neutrons to protons. They have the same atomic number but they’re completely different atoms.

    Fraser Cain: So, I’m just gonna have to take your word for it here, that – I’m sure the math, every time, every step – that if you add up all the positrons and take away all the electrons and convert the neutrons into protons and the protons into neutrons, that it all balances out –

    Dr. Pamela Gay: And you need the binding energy of the atom. So –

    Fraser Cain: Right. And the alpha particles come away. That in the end, each step, the math balances out again.

    Dr. Pamela Gay: And it is a matter if you have to conserve charge, you have to conserve a bunch of other stuff you learn about in quantum mechanics, you have to figure out: Okay, so, the atomi nuclei has a certain binding energy. What happens to that energy?

    But, in the end, for the most part, everything is conserved. There’s a few exceptions that you learn about in advanced quantum mechanics. If they didn’t exist, our universe wouldn’t exist. So, we’re grateful for the exceptions and annoyed by them, but it’s really a fascinating process to learn about. And, the amazing thing is, how much of this we can calculate, how much of this we can predict.

    And so there’s this great pairing of – once we started to figure it out, people could go on mad predictions of, “Okay, there should be stability right here!” Spin up the linear accelerator, spin up the neutron stream and build away.

    Fraser Cain: And so right now, I mean, is the limit of, like, the isotopes that we can build purely the amount of energy that we can – the amount of neutrons that we can slam in? Because, like, I can imagine you’ve got this situation where you’re slamming neutrons into your atom to try and build it up but then it’s trying to decay off neutrons faster and faster and it’s just, like, how fast and how much energy can you throw at this problem, right?

    Dr. Pamela Gay: It ends up becoming – so, depending on if you’re building things up by using a proton stream or a neutron stream, it really becomes a matter of how fast, how dense can you get it so that you can overcome the desire of the protons to repel; the rate at which the neutrons are trying to decay. There’s all of these different things. It becomes a rate-bounded problem.

    Fraser Cain: Right. Is there – do you think there’s any limit? Do you think there’s some point where you just can’t make a heavier atom and things will just start bouncing off?

    Dr. Pamela Gay: This is one of those things that theorists struggle with. You periodically see papers and the literature that it’s thought that if we can just get big enough, we’re going to hit another stable point.

    But, when you look out across the universe, well our universe does a pretty good job at creating all sorts of accelerators. We don’t see any evidence that there’s atomic lines, in-stellar spectra or any other type of spectra for that matter, that those atoms actually exist.

    So, I am dubious about there being another plateau of stable atoms but I suspect that we can build larger and larger atoms as technology gets better and better. The suckers are just going to decay so fast, that there’s always going to be the, “Did you catch it?” “Okay, caught it.”

    And so, yes. We’ll be able to keep building things bigger that last for bazillionths of a second before decaying away. It sort of starts to become the nuclear physicist’s challenge of, “Look what I did!”

    And it’s kind of an awesome challenge. Yeah, it’s really expensive and fun.

    Fraser Cain: Right. We gotta build bigger and bigger particle accelerators to get your –

    But I just imagine, you know, someone might get enough energy, hammer it together and, like, pop! You’ve got something that’s got, you know, 400 quadrillion protons. Just one big – one big atom. You could, like, pick it up and hold it. And you’re like, it’s one atom.

    Dr. Pamela Gay: Yeah. The issue starts to become – the strong force works over a very small distance and the electromagnetic force, which is forcing those protons to try and fling each other apart, it doesn’t care. It happily works over any distance. So when your atomic nuclei gets bigger than what the strong force can act over, it just wants to fall apart.

    And so there are limits based strictly on the fact that, while the strong force over short distances is strong enough to hold nuclei together, it only works over very short distances.

    Fraser Cain: Now we talked a bit about isotopes and how they’re used for radioactive carbon dating, where we look at the ratios of Carbon 14 to Carbon 13, Carbon 12. What are some other uses, specifically in astronomy, that astronomers will use these different isotopes as a research tool?

    Dr. Pamela Gay: Well, it’s not just carbon that we use for dating. There’s an entire field of cosmochemistry, where we use the different isotopes to understand – well, how old is the gas in the outskirts of that star? Because, well, these different nucleotides, they’re formed in supernovae. The supernovae then – the material from the supernovae then get gravitationally swept up and turned into new stars.

    And so you can start to date – well, what is the limit on the age of this star’s composition? And that starts to give us a sense of how long the stars have been around. We can use it for dating likely when our solar system formed, by looking at the ratios of isotopes in different asteroid fragments. And then there’s just basically the fact that, well, stars wouldn’t burn if it wasn’t from tritium and deuterium, which burn much easier than your standard hydrogen does.

    So, when we’re trying to define what’s the difference between a star and a planet, we’re looking for – well, did the tritium get dense enough in the center? That’s a hydrogen atom that has multiple neutrons. Did it get hot enough that it would burn and you’d end up with nuclear burning? Well, in that case, this was a star, however short a period of time it burned.

    And then the uses go on and on. Different species of uranium and plutonium are easier to use in nuclear reactions. We use different isotopes for treating cancers. The uses go on and on. There’s radium – nuclear radium in fire detectors.

    Fraser Cain: That’s really cool. I mean, I know that, for example, like, is it lead? Astronomers were looking for lead in the atmospheres of stars to date stars, right?

    Dr. Pamela Gay: Yeah, that’s one of the uses.

    Fraser Cain: Yeah. And so, if we’re looking for plants, we look at carbon. And if we’re looking at the age of stars, we use lead. And there is a – there is an isotope that we can use to date almost anything out there. It’s just –

    Dr. Pamela Gay: How long is that sucker stable?

    Fraser Cain: Yeah. What’s its half-life? How long do we want to do that?

    So, I guess one last question.

    Dr. Pamela Gay: Mm-hmm.

    Fraser Cain: Is everything decaying down eventually to just one proton? Like, will every atom –

    Dr. Pamela Gay: No.

    Fraser Cain: No. So are things, like, they are – they will hit their isotope and they’re stable forever?

    Dr. Pamela Gay: As near as we can tell. There are a few dozen atoms that are just stable. So, for instance, helium is gloriously stable. Certain isotopes. So there is a whole list of atoms that, depending on whether or not protons decay – and this is one of those great debates we’ve talked about in many different episodes – if protons don’t decay or, at least until the proton starts to decay, then yeah, those suckers are stable.

    Fraser Cain: And so you can imagine some future universe when everything in the universe is just made up of those stable atoms.

    Dr. Pamela Gay: Yes.

    Fraser Cain: Wow.

    Dr. Pamela Gay: And – yeah. And then, of course, there’s neutron stars and things like that, which are completely different but are looked at as stable. So, we have things like Carbon 12 and 13 are stable; Oxygen 16, 17, 18 is stable; Potassium 39, 41. There’s lots of different stable things out there.

    Fraser Cain: Right. Wow. That’s really interesting.

    Cool. Well, I think that’s great Pamela. Thank you very much.

    Dr. Pamela Gay: My pleasure.

    Male Speaker: Thanks for listening to Astronomy Cast, a non-profit resource provided by Astrophere New Media Association, Fraser Cain and Dr. Pamela Gay. You can find show notes and transcripts for every episode at astronomycast.com. You can email us at info@astronomycast.com. Tweet us @astronomycast. Like us on Facebook or circle us on Google Plus.

    We record our show live on Google Plus every Monday at 12:00 p.m. Pacific, 3:00 p.m. Eastern or 2000 GMT. If you missed the live event, you can always catch up over at cosmoquest.org. If you enjoy Astronomy Cast, why not give us a donation? It helps us pay for bandwidth, transcripts, and show notes. Just click the donate link on the website. All donations are tax deductible for US residents.

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    Duration: 32 minutes

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    4 Responses to Ep. 323: Isotopes

    1. Charlie December 3, 2013 at 10:07 pm #

      Thank you soo much for this pod cast I lesson to you guys every night and truly enjoy hearing everything you have to say,I’m a mechanic out in Illinois so im not really around many people that like to about about the universe, that is until i pop my headphones in and hangout with my friends Pamela and Fraser

      Thanks guys

      Charlie

    2. Robert McDowell December 4, 2013 at 12:50 pm #

      Dr. Gay:
      Nucleotidesre building blocks of nucleic acids. Please pronounce nuclides correctly!

    3. John Molineaux December 8, 2013 at 1:53 pm #

      Ay ay ay! Pamela, there are no nucleotides in a nucleus! Nucleotides are the submolecules of DNA that encode genetic information. I think you mean that protons and neutrons are nucleons. Plus, the singular of nuclei is nucleus.

    4. Bart December 19, 2013 at 5:02 pm #

      Hey guys, another great podcast as usual, though like the other pedants who posted before me, I too have a small correction. Pamela referred to the singular of atomic nuclei repeatedly as ‘nuclei’. The singular is ‘nucleus’, as in “the atomic nucleus of a carbon 14 atom contains 6 protons and 8 neutrons”. The plural of course, is ‘nuclei’.

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