Daniel and Kelly’s Extraordinary UniverseDaniel and Kelly take a detour into the fascinating world of chemistry to explore why mercury is liquid at room temp. The answer is relatively surprising!
Even before we could pry open molecules and see the structure of atoms, we knew there was something fascinating going on. There had to be some kind of internal structure there. Why did we think so? How did we know? Well, because the periodic table is periodic. There are groups of atoms with similar behavior. As you march across column by column, atoms in those same columns have similar behaviors conductivity, reactivity. That can't just be random, and of course it isn't. It's because of the structure inside each atom, which was long invisible to us. The structure of the atom is of course dictated by quantum mechanics, which also reveals something about the basic laws of the universe. And now electron structure is the source of torture for high school chemistry students and physics podcast hosts, but it also completely and totally diff finds our world. It's why metals exist, why things are hard or soft, or liquid or solid. It's not magic, but changes to these properties can have dramatic effects on elements behavior, and the nature of our experience. And today we're going to dig deep into what might be the weirdest element on the periodic table. One that isn't just sensitive to quantum mechanics, but to our other great theory of physics relativity. Mercury, and here I mean the element, not the planet, whose orbit was famously predicted by relativity. Is very strange because it's liquid at room temperature. It's the only metal we know that is liquid at room temperature that you can pour without ever heating it up. It's even liquid if you put it on ice or snow. This is knowledge we share with the ancients. The name mercury comes from its Greek name, which I won't try to pronounce, but means watery silver. Why what is so special about mercury? What is going on inside that? Adam? Welcome to Daniel and Kelly's extraordinarily chemical universe.
Hello. I'm Kelly Wienersmith. I studied parasites and space, and because I was a child of the nineties and we got ourselves into all sorts of trouble, I had a necklace that was a vial of mercury. Oh no, And now I'm just glad it never got like smashed on me or something.
Are you sure it wasn't permeable in some way?
It would explain a lot.
Folks, Kelly would be so much smarter if it wasn't for that necklace. Oh oh ouch, I mean she's already super smart. I don't think we could handle it even smarter Kelly.
Oh good cover. I love it.
Well. I'm Daniel. I'm a particle physicist, and I'm not a big fan of chemistry, but I am in awe of its influence over our world.
Yeah. I was surprised to see that you picked a chemistry tim. Then you did this to us on purpose, and so let's try to focus on positives for chemistry for like half a second. What was your favorite moment in a chemistry class?
Ooh, I remember taking the final and being done with it.
Amazing.
No.
I was recently talking to the daughter of a friend of mine and asking her what she wanted to study in college, and she said chemistry and I said cool. Why? And she said, chemistry is very tactile. It relates to things that are right in front of us. It controls how things operate. It's almost like you can do magic. And she was right, you know, like, particle physics is very cool and reveals the fundamental nature of reality blah blah blah. But it talks about things you can't see really, and so like, how do you know the electrons are following those rules or the quirks are doing this or that, whereas like you can see stuff flow or boil or bond or reflect or whatever. It really does determine the nature of our experience.
Yeah, I agree, and I disagree. I agree on like a global level. So I did my senior honors research work in an organic chemistry lab because even though I talk about how much I disliked chemistry, I had a lot of chemistry friends and I was kind of into it for a while.
But didn't know that about you, Kelly. Hmmm, oh my god, recalibrating over here.
I made so many mistakes in the chem lab, though I'm so lucky I didn't die. But you know, I would mix things together and I'd be like, all right, clear liquid mixed with clear liquid, and it still looks like a clear liquid. Did I do the reaction I was trying to do? I don't know. And so I know there's a lot of stuff where it's like you can see stuff's happening, but there's also a lot of stuff where you have to just like expect the thing happening you thought was going to happen, and it's yeah, I don't know. I like fish. You can really see what's going on with fish.
You can see fish guts, but you can't see atomic guts. That's the issue, that's.
Right, that's what you can't see the backside attack happening in real time. I think that was a chemistry reaction that my friends and I maybe focus done a little bit too much. But anyway, we had some fun.
Yeah. Well, you know, underlying chemistry is physics, and there's a close relationship between chemistry and like quantum physics. It determines the nature of the atoms. And what we're going to discover today is that the answer to the question of the episode might not actually be chemistry, it might be physics.
After all all that, I think we just found our video uplip for this episode. You have the right voice for an evil scientist.
Left. Wow, I'll put that in my next grand proposal.
Okay, so today we're talking about why mercury is liquid at room temperature. And I didn't know the answer to this before reading the outline, and you know, to be honest, since it's a brief outline, I still don't think I know what the answer is, but I will by the end of the hour. And so let's see what our audience thinks about why mercury is liquid at room temperature.
So think about it for a moment yourself. Do you know the answer? Is it chemistry? Is it is it some weird combination? Is it physical chemistry. Here's what our audience had to.
Say, just characteristics of that particular.
Element based off of the chemistry of the items. So this sounds like a will make for a very interesting episode.
Mercury may not be very good at sharing its electrons and that's why it is a liquid at room temperature.
I think it's because the amount of energy that's required to break the bonds to turn into a liquid is really low, because it's just a bit quake. And yeah, like my son, I think it's because of dragons as.
Well, something to do with its electron orbitals.
I guess that the heavier the element, the more solid it should be. But mercury is a have metal, so this might not be an adequate explanation. Maybe this is related on how the molecules mercury utforms because of.
The way it's electrons behave Actually it has to do with the way that they are bonding or in this case not bonding, so it's a very weak chemical interaction.
Maybe it has something to do with how the electrons were arranged.
I thought mercury was a liquid at room temperature for a similar reason as to why water is as well, how the bonds between the atoms work and interact.
Mercury is liquid at room temperature because it's solid at a different temperature, a lower temperature.
I don't really know why metals are liquid at any temperature.
I don't know now I'm curious.
It's valence electrons are paired, which I guess makes it less necessary for it to form the kind of crystal structure that you get in most metals, because it's outermost electron shell loses electrons easily and does not form strong bonds.
Has to do with the specific heat of the substance.
I knew, aw forgot.
That at room temperature, the chemical bonding between the atoms are weaker than in cold, where they get stronger.
I love the answer that they would love to know this. There are so many amazing patterns in the periodic table. I love that curiosity about chemistry. You and I should maybe try to channel that a little bit more.
I totally agree with that answer. I think it is amazing the patterns in the periodic table, and I love how it reveals the structure of the universe, and it is very very cool. It's just also very complicated. Wow, it's not easy. So you know, my fear of chemistry is mostly in awe of the people who can do it, because I can't.
I found it very difficult. Mostly I was spilling the chemicals on myself or dropping the glassware. But my favorite moment in chemistry actually was the very first college chemistry class I took, where we got the melting point and some other features of some unknown substance, and by calculating these different features of the unknown substance, we were able to figure out what we had been given. And that felt like amazing, like forensic science CSI sort of stuff, and I just loved that. So I have a soft spot in my heart for calculating melting points, which is maybe not something I imagined i'd be saying when I was a kid, but I've never been cool, so I'm leaning in. So, Daniel, what determines melting points?
M hmmm, Yeah, this is very cool. You know that we even have melting points for stuff, that things have phases. I think phases are super fascinating. You can have like the same set of atoms and a slightly different temperature. They're dramatically different behavior, right. This is not like a smooth transition where it's like kand of mushy and then kind of gassy. It goes from like solid to flowy. You know, it's really incredible that phases even exist. And I just want to nerrod out about phases for another minute before we dive in, because phases are a much more general concept in science and in physics than just like the state of matter. We use phases to describe any time there are a set of equations that have limited applicability, Like you could talk about Newton's equations for the motion of stuff applied to a certain phase of matter when things are not very massive and not very fast. It's like the Newton phase of mechanics. So I think it's really a fascinating concept because it admits that all our laws are limited, the way that like the laws of fluid mechanics only apply to fluids and the laws of crystal lattices only apply to crystals and not to everything. So anyway, I think that's sort of deep and philosophical.
I think I'm not following all of the things that you just said. Still sound like you're talking about phases. So you said something about like how fast something's moving, and to me that makes me think about, you know, the transition from a liquid to a gas or something like, I'm missing the point.
No, you're right, and they're all linked to like the behavior of the stuff. But you know, think about like the very early universe. We think there was a time when things were so hot and so dense that even our laws of quantum field theory might not apply. So there's like a phase in the universe when quantum field theory applies, and there's a phase when it doesn't apply. Right, Because it's not like a fundamental theory of everything. It's an approximation that only works under some conditions. In the same way like the laws of the liquid phase of water only work when water is liquid, that don't work when water is solid or when water is a gas. All of our laws are approximate that way and only work in a certain phase.
Okay, Right, So when I was in my goth phase. The only thing that works for me was black clothing exactly, and I get it. Phase is a more general word. Yeah, okay, move it on.
So what's happening here? The listeners were right. Things melt when the bonds between them loosen. Right. So a solid often is a crystal you have, Like these pieces click together into a crystal lattice. Not everything ends up like a crystal, you know, glass for example, like a big disordered mess. But lots of things click together form a crystal. You can imagine, like the little lego pieces snap together and it's very solid. It acts like a big chunk, right. And that happens because there are bonds between them.
Right.
These things don't just click together physically. They're just physically sharing the space. They are connected to each other. They are bound together because of what their electrons are doing. So if you have strong bonds between stuff and the stuff doesn't have a lot of energy, you can't wiggle around a lot, then it clicks together to form a solid. Now, heat that stuff up, give it energy. Make those atoms wiggle and jiggle and zoom. If they have enough energy to overcome the power of those bonds, then they will break open. That crystal lattice and they will slide around, and that's how they become a liquid. That's what melting is. It's breaking down the crystal lattice so that the atoms are more loosely bound to each other. There's still connected, there's still some bonds there. It's not totally a gas. Gas is when you give up all connection to each other and they're all just a bunch of independent molecules or atoms, so liquid. When you break those strongest bonds and now you have very weak bonds, so the atoms can flow over each other.
Is it just that like some percent of the bonds have broken, or that bonds of a certain type have broken, like all the hydrogen to oxygen bonds have broken, but the carbon hydrogen bonds haven't broken yet. Or does it depend on the molecule that you're talking about.
It depends on the molecule, but it also depends on the type. And so for example, after the bonds are broken, there are still some bonds there, but they're weird, very soft intermolecular bonds. You know, you can have like a bond between this water molecule and that water molecule because of its polarity, like maybe they're overall neutral, but it's got a little bit more negative on this side and a little bit more positive on that side, and that can attract the neighboring atom, or they can organize themselves that way. It's sort of a loose bond, whereas when they're tightly bound, then they use a different kind of bonds. You know. The electrons can like literally be shared among them in some kind of lattices, like in metals, the electrons just flow freely, right, You can't even really say which atom they're connected to, They just like flow all around the whole thinking you have really complex energy level structures for those electrons because they're really just shared. It's that one really big atom or one super molecule.
You know, you and I might both know more chemistry than we've been letting on secrets coming out today.
That's solid state physics.
Oh no, all right, I was getting worried there. Okay, So it.
Really is about the strength of the bonds. If atoms are capable of making very strong bonds, then it requires more energy to break them, higher temperatures to break them, So stronger bonds between the atoms mean a higher melting point. If there are already very very loose bonds between the atoms, like the atoms don't like the bond at all, or they use none of the very strong categories of bonds, then the melting point is going to be lower because it doesn't take a lot of energy to release the atoms. So we're going to take several steps towards the understanding. The first one is melting point is determined by the strength of the bond. Stronger bonds higher melting point, weaker bonds lower melting point.
Okay, I've got that general concept. Can you get give me a little bit more information about what makes for a strong bond.
Yeah. So you basically you're asking like, well, what makes the bond stronger, what makes the bonds weaker? Why does it depend on the element? What determines that? And the answer there is the electron structure. The electrons are the things that do the bonding, and so the electron structure is what determines whether the bonds are strong or whether the bonds are weak. For example, one of the most important thing is have the electrons filled up their shells, Like the electrons form these shells around the atom, you know, there's the first energy level, the second energy level. If that outermost energy level is filled, then the electrons in the atom are pretty happy and they don't want to go anywhere. If, however, they're not filled, you have like four out of eight or seven out of eight, then that atom is happy to take another electron, or to share another electron with its friend. So together they have filled shells. So for example, if you have hydrogen, hydrogen can have two electrons in its outer shell, but it's only got one, so it likes to find another hydrogen. So together they have two. They can share those two in a bond. So those two electrons are shared between the two protons, and that thing is really bound together into H two. I know, it's very coozy. Actually, where do they hate each other? What if they're like, oh my god, this guy never does the dishes.
Oh I get that. I get that. But they can't get away from each other. Well, you got to turn up the heat so that they can escape.
Oh, melting is like chemical divorce. Wow, fascinating. We are liberating these abs. You've heard of women's liberation. Now we're doing proton liberation.
I thought it was electron liberation.
There you go, yeah, electronic hand proton Yeah.
Oh okay, got it.
Yeah. So there's a few things that affect whether these bonds are strong or not. One is are the shells filled, right, So do you have a complete outer shell it's like a set of armor, it's hard to penetrate. Or do you have an incomplete outer shell, in which case the atom likes to bond. And we're going to go through some examples later on. You'll see that these patterns emerge in the periodic table. The other is how closely is it holding on to those electrons, because the electrons can be like really far out and sort of a distant outer shell very weakly held, or they could be like really tightly held. If the atom is very very powerful, if it has like a lot of protons in it, it can really hold those electrons close. So that also determines it. So we sort of like two dimensions here to determine whether the bonds are strong or whether the bonds are weak, or is it filled shells is it not filled shells. So filled shells means harder to form bonds, not fieled means easier to form bonds. If the electrons are close, it's harder to form bonds with them because they're held tightly by their nucleus and the electrons are not close, it's easier to form bonds.
This is reminding me of the fun conversation that we had in response to a listener question about why life tends to be carbon based instead of silicon based. Yeah, silicon not silicone. I always mix those two up in.
Orange County, it's silicone mostly.
Actually, Yeah, well I live in Virginia where anyway, we don't need to go there. And the answer ended up depending on a lot of these questions.
Yeah, but you're putting your finger on a really important trend, which is that as you go across the periodic table, elements in the same column tend to have the same electron structure. Right, they have like one extra electron or two, or it's totally filled, or it's not right. So the rows in the periodic table reflect the energy levels, and then as you march along the columns, you have the same pattern of the electrons filling up. So you go from left to right in the periodic table, you're filling up that outer shell. And so, for example, the last column in the periodic table all have their last one all filled up because it's the last one, and so that whole column are folks with very filled shells. That's why they're called the noble gases. They don't like to interact with anybody, and that's why they're all on the same column because at the same electron structure, which is why they have the same kind of behavior. And like the first column, all are noble gases plus one, so they all have one extra electron, one only electron in its own last shell really dying to do something with its friends. And so that's why those are all very active. For example, they like to react and they interact. So the electron structure really determines all these properties and the periodicity of the table.
Now, I remember sitting in chemistry in high school and being like, all right, I think maybe I have finally memorized how many electrons are supposed to be in each one of these shells, But why are their shells in the first place? Yeah, And I never got a satisfactory answer, And maybe that's why I never could love chemistry until this moment, Daniel, because I'm gonna ask you, can you tell me why are there even shells?
And do they sell? Them by the seashore. Right. Yeah, So the answer is, of course, the underlying physics quantum mechanics. Like, let's start with a simple atom like hydrogen. Hydrogen has a proton and it has an electron. Where could that electron be. Well, quantum mechanics says, use the Shorting equation, And Shorting equation says, well, there's a bunch of solutions for where the electron can be, a bunch of places where everything is copasetic and the wave function is happy. But there's a ladder of solutions. It's not a continuous state of solutions. Like let's zoom out and take a classical example where we have intuition the orbit of a planet. Where can a planet orbit the Sun? Well, classical mechanics says, if you have a certain radius, you need to be moving at a certain velocity in order to have a stable orbit. Cool, But every radius has a velocity, Like you could orbit the Sun at literally any place. There's an infinite number of available radii. Once you pick a radius, you have to have the right velocity. You'll fall out of orbit or you'll zoom out of the Solar system. But you could pick any radius, any solution works around hydrogen that we like to think of these as like planetary orbits, and there's lots of misleading pop side diagrams that convince you. So these are not orbits, right, These are solutions to the shortening equation, and there's a ladder of solutions. There's a finite number that's like number one, number two, number three. The quantum mechanics dictates that. And an intuitive way to think about why there are a discrete number of solution is to think about how the wave function fits around the atom. It goes around the atom, it has to reinforce itself, so when you go around, you have to come back and basically be in the same part of the wave and so you can fit like one wave or two waves or three waves, but you have like three point seven waves, then it's going to interfere with itself and it's not going to be a stable solution. So you want a stable solution of the electron around the atom, you have to fit a certain number of wavelengths of the wave function around the atom. So that's why you have a discrete number. That's what causes the shells. And then it gets much more complicated if you have more protons and multiple electrons. I mean, you get all the way up to like mercury. It's a mess.
So does it have to be waves because electrons aren't point particles, they're actually waves, and that's where the wave thing comes in.
Yeah, exactly. You have the wave function, which is a complex value thing, and it is really the thing that tells you where the electron can be. And so when the electron is in its lowest state, you shouldn't think of it like, oh, it's orbiting at a certain radius. It's got a probability distribution and that's the minimal stable configuration for that state.
Okay, all right, got it. Chemistry is awful. That's what I think.
The other crucial piece of physics is that electrons have this weird behavior where you can't have two of them having the same state. They just will not share. You know. They're like grumpy siblings. You cannot put two of them in the same bed. You need to have different rooms or they need to have something different. So the first state, you can have two electrons because one can be spin up and one can be spinned down. The second layer has more energy, so they can wiggle in different ways. There's different patterns to have their energy is distributed, so there's more options there. But quantum mechanics tells us that we can only have one electron per unique energy level, and as the shells get bigger, there's more options for the electrons for ways to differentiate themselves, so you can have two in the first one, and then I don't even remember the numbers, and I'm not going to guess, but yeah, it gets very complicated. But there are quantum mechanical answers for why there are a certain number of electors allowed in each shell, as to do with the polyexclusion principle and the number of ways you can distribute the angular momentum solutions in each energy level.
In my head, at some point the number of electrons in the shells as you added shells started being the same. But I took chemistry when I was gosh, that was over thirty years ago, now, so that's just a bad memory, right. It's the number of electrons in each shell gets progressively higher the farther you get from the center.
Yeah, okay, all right, but the shells then start overlapping, and you know sometimes like the highest energy subshell from level four is actually higher energy than the lowest energy subshell from level five. So level five fills up before the last level four fills up, and the ordering starts to get really, really nasty, which is why electron configurations are hard.
I'm feeling angry. Why is it like that? All right? All right, let's give ourselves a chance to release the anger, and when we get back from this commercial break, we'll take up another peek at the periodic table and look for patterns and melting points and we're back. Okay. So at the beginning of the show, we talked about where you find electrons, how they fill up the shells, and how that impacts bonds between atoms. Now we're going to take a look at the periodic table because we're really interested in melting points to try to figure out why mercury is weird. So let's look for patterns in the periodic table to see what we should expect mercury to be doing in terms of melting points.
Yeah, and there's a lot of really interesting stuff to dig into here, and a lot of it can be explained by chemistry. But mercury sticks out like a sore thumb, and so we're going to walk you through a couple of the trends that explain what's happening in the periodic table, but they can't completely describe mercury, and they're not actually enough to make mercury liquid at room temperature. So there's a little bit of physics we're going to need at the end to give you that complete explanation.
Chemistry is never enough.
Chemistry is never enough. So let's keep in mind that we're thinking about the electron structure of these elements, whether or not for example, they have a filled shell. And so let's like walk across the middle of the periodic table. So you have sc which is scandium, right, and then the next one is titanium, and it goes all the way across the copper and then to zinc. And if you look at the melting points here, they start pretty high, like scandium melts at fifteen hundred celsius, and then they go down to zinc, which melts at only four hundred celsius. Now that's pretty hot. You don't want to get into like a hot tub of zinc. But it's a big difference. It's like more than a thousand degrees difference. Why does scandium melt at a really high temperature, and zinc melts at a really low temperature. Because zinc is the end of this chunk of the periodic table, it's completed as shell. So zinc has a complete shell, which means it's not as likely to bond. It's not as easy for it to bond, which is why it has a lower melting point than all of its friends next to it, Like copper right next door to zinc, has a melting point of more than one thousand degrees C, where zinc again is just four hundred. And you see the same behavior in the next row, silver, which is right next to cadmium. Cadmium is just under zinc. Silver has a melting point of about one thousand C and cadmium of about three hundred. So just this one step over you add one proton and one electron, melting point drops precipitously, and the reason is that you filled up this shell. Now, these atoms can form the same kind of strong bonds where they're sharing electrons with each other, and so it's much easier to break them apart. So that's why zinc and cadmium and mercury, which is also in this column have much lower melting points than their friends copper, silver, and gold, which are right next to them in the periodic table.
They're more stable, and because they're more stable, it's easier to make them liquid.
It's easier to make them liquid because their bonds are weaker. It's not about the stability. These aren't like radioactive elements. It's just like do they like to click together? And zinc and cadmium and mercury all have a completed last shell. It's the S two, the four S two, the five S two, or the six S two. They've completed that little subshell, and so it's harder for them to form bonds like copper and silver and gold. The ones next door to them are missing one electron relative to our friends zinc, cadmium, and mercury. So they'd like to fill in that last shell. And if they meet another atom of their type, like two silver come together, they can complete that last shell together, and so they can form this kind of strong bond by sharing electrons. It's harder to break them apart. Mercury can't do that, cadmium can't do that, Zinc can't do that, so they can form the same kind of strong bond between the atoms, and so it's easier to break them apart, which means means a lower melting point.
Got it, okay, thank you.
So now we're comparing these two columns, right, Column eleven has a higher melting point than column twelve zinc, cadmium, and mercury. But still, mercury looks weird. Like zinc and cadmium melt at three hundred four hundred seeds, it seems like a very respectable temperature for a metal. Mercury melts at negative thirty nine c like, mercury has a crazy low melting point. Right. To make mercury solid, you have to get it to negative thirty nine celsius. That's very very cold, right, and it's a huge jump. And if you're saying, all right, well, this column is all colder than the other one. Still within the column, zinc and cadmium have a higher melting point than mercury. So what makes mercury so much lower than zinc and cadmium. Well, there is a trend there that we would expect. As you go from top to bottom in the column, you're getting heavier and heavier nuclei, right, Like, mercury has more protons than cadmium, which is more protons than zinc. And that's the other effect we talked about. Mercury holds on to its electrons more tightly than cadmium or zinc because it has more protons. Say you're an electron floating around the atom, there are more protons pulling you in, binding you tightly to that atom if you're mercury than if your cadmium or if you're zinc. Does that make sense kind of?
So if your mercury, though, you also have more electron shells, and so your outer shell, which would do the bonding, is farther away from your heavy nucleus. They're farther away. What does that do?
Yes, exactly. And this is my frustration with chemistry is that you can often tell your cells these intuitive stories and then somebody can come along with another intuitive sounding story that also makes sense, and you're like, huh hmmm, I don't know which one it is is right, you know, And the answer is that it's complicated. But overall the fact that they have more protons wins, and so it pulls these things in and you know, the way to think about it is like, yeah, these things can all be neutral. You have an equal number of protons and electrons, and the electrons don't like to be on top of each other. But still, these protons are very powerful and pulling them in, and each electron is having basically just a relationship with the protons, not with the other electrons. It's not like the power those protons is shielded by the other electrons. Instead it's now pulled in by eighty protons. Right, So it's a very powerful force. I think that one wins. But hey, chemistry experts out there right in and tell me if we got that wrong.
Okay, so mercury really wants to be a liquid, and we know that because it has a full shell and it's really big. But even knowing those two things, mercury wants to be a liquid at temperatures way lower than what we would have expected. So where do we go next to try to understand that.
Yes, so we're at the limits of chemistry here. Chemistry tells us yes, mercury should be lower than gold, for example, in the same way zinc should be lower than copper, and it is, and chemistry tells yes, mercury should have a lower melting point than cadmium or zinc because there's a bigger atom and it holds these things in and that's all cool. But if you run the calculations and you take all that into account, chemistry predicts that mercury's melting point should be eighty two C, but the measured value is negative thirty nine. See more than one hundred differents. So like, yes, there are these trends that suggest mercury should have a low melting point, but they suggest it should still be solid at room temperature. To get mercury even lower, To get that melting point down below room temp and even down below zero C, you need to do something else. Chemistry is not enough to make mercury liquid.
On chemistry, get better with your predictions. This isn't physics.
So you might think, well, it is quantum mechanics wrong, because chemistry is determined by quantum mechanics. We just told you about all the shells and the shortening their equation and all this stuff, right, So is quantum mechanics wrong. Well, quantum mechanics by itself is not wrong, but it's not the whole story. Right. We know that quantum mechanics doesn't describe the entire universe. Because quant mechanics, for example, can describe gravity, or black holes or the beginning of the universe. We have another theory in physics that helps us explain what happens when things get really really fast or when things get really really massive. That's relativity. All the calculations we've been doing, all the explanations we've been giving are chemistry based on quantum mechanics that assumes that relativity is not a thing. If, for example, assumes that there's no limit to how fast things can go, or that there are no black holes, we're essentially ignoring relativity and doing pure quantum mechanical calculations. And most of the time that's fine. Relativity is not really relevant. We're not doing chemistry around a black hole. We're not doing chemistry near the speed of light. So it works. But you know, sometimes it doesn't. And that's what's happening here, is that we've been ignoring the relativistic effects on the electrons of mercury.
And that's because everywhere there's mercury, there's actually a tiny black hole next to it. Is that right? No?
No, okay, though, but you know where you can get your mercury at.
The flea markets.
No in HG. Wells grown.
No that was great.
No it was not great, but thank you anyway. Yeah, So, what's happening here is not that there's a black hole next to every bit of mercury, although I love the theory and if you heard it that maybe every electron actually is a black hole and could we tell anyway. I love to talk about that on the podcast another time. You know, what's happening here is that electrons are actually relativistic around mercury. Mercury is so powerful with this nucleus, those eighty protons have such a strong hold on the electron that the electron velocities start to approach the speed of light. They're not going at like ninety nine percent the speed of light, but whereas electrons around hydrogen go about one percent of the speed of light, electrons near mercury move almost sixty percent of the speed of light, which is close enough for these relativistic effects to start to matter.
So that suggest to me then that everything with eighty protons are more should also have these relativistic effects. Is that true? From there on out, we need relativity to understand the melting points of atoms.
Yes, absolutely. And there's another guy under mercury in the periodic table, copronicsium, which is a crazy synthetic chemical element, which means we need to make it. It's not like found naturally in the wild, and people suspect that the relativistic effects for copronicsium are even stronger than from mercury. Mercury is something that's all over the place, so it's well studied and easy to play with. But turns out doing these calculations, including the relativity in our calculations, is very hard, which is one reason why only a couple of years ago were people able to do this calculation and predict the relativistic corrections to the original quantum mechanical calculations.
Say that again, this time in English.
So you can go out and measure the melting point of mercury, right, you put it on the table, you heat it up, you see it melt, you cool it down, you see it solidify. That's the measure value. Then you can go and say, I'm going to predict what it should be based on my understanding of what's happening. And they can do calculations, and they do these calculations like we referenced earlier on number of eighty two c that comes from using quantum mechanics to predict the strength of these bonds and understanding like at what temperature those bonds would break. So you're using quantum mechanics to predict the bonds and from that you can get the temperature. So that's the predicted value of mercury. Now, if you go in you say, well, I'm going to tweak quantum mechanics because I'm going to do quantum mechanics not by itself. I'm going to include relativistic effects in my quantum mechanics. Then you're changing what's going on in your predicted mercury, which changes the prediction of the bonds, which changes your prediction for the melting point. And so when we see a difference between our prediction and our observation, we know something is wrong. So we go back and tweak our predictions to make it right. And you know, in principle we should always be using relativity to get everything right. But most of the time it's irrelevant. You want to calculate when the train is going to go from Cleveland to New York. Relativity doesn't have any impact, right, so you can ignore it. Also, relativity is a huge pain, like, it's non linear, it's complicated, it's not easy to do. So most of the time, if you can't ignore it, you should. But when you discover that your non relativistic calculations are not up to the task, when they're getting me answer wrong, that's when you've got to go back and do your homework and include the physics in your calculation, because it turns out it's necessary beautiful.
Okay, all right, So now we've got electrons moving super fast and now we're incorporating relativity. What is the jump from there to understanding why melting point is affected?
Yeah, so first we should clarify which part of relativity we're including, because folks, everythinking Daniel's been telling us that quantum mechanics and relativity can't play nice together, like that's the whole goal of modern physics has come up with quantum gravity and understanding the early universe and blah blah blah and string theory.
That's right, Daniel has been telling us that.
And that was not a load of baloney. That's all true. That refers to our fail to unify quantum mechanics with general relativity, the theory of gravity and curvature and all sorts of crazy stuff, which we have not been able to do. But we have, and it's been decades and decades since we've done this. Unified quantum mechanics and special relativity, the theory of what happens when things go near the speed of light and incorporates the fact that light is always the same for all observers and that nothing can go faster than light. Special relativity, which is just like flat space, but includes things like time dilation and length contraction and maximum speeds and weird velocities and stuff. That's special relativity that we have been able to merge with quantum mechanics. We have relativistic quantum mechanics that allows us to do these calculations, or quantum field theory also has special relativity built in. So special relativity and quantum mechanics do play very nicely together.
Aw that's great, okay. And so when they're playing together, why does them playing together change?
Yeah? Great question. And since this paper came out, been a lot of coverage of this result in popular media, and I read all of them, and they're all wrong. What they all get the physics wrong.
Let's take a break, and when we come back, you're gonna tell us how we get it right. Before the break, Daniel was telling us that he's been reading a bunch of popsye articles that attempt to merge quantum mechanics and special relativity and that all of their explanations are wrong. So let's talk about the wrong explanations first.
Yeah, and these are not just popsye articles in like, you know, science News, dot buzz or something.
I hate science.
People are constantly boarding me articles from sites with names like that and being like is this true? And I'm like, man, why are you gonna read in that site? You know? But there's some pretty venerable places that have put out press releases and articles about this that get it wrong, and they all repeat the same nonsense. They all repeat this business about how electrons, when they approach the speed of light, gain mass become more massive. That's the heart of their explanation. And number one, that's not true. Things do not gain mass as they approach the speed of light. This concept of relativistic mass is outdated, it's not appropriate. It was Einstein's mistake. We talked about it recently on the podcast. We can dig in it again in a moment. Also, it doesn't really explain why mercury has a lower melting point, you know, electrons having more mass doesn't answer this question. I actually reached out to a chemist here at UCI to ask him about this, and he said, quote, most chemists know little about relativity, and I suspect that makes them more likely to swallow the pop side buzzwords.
Oh, I'm surprised any chemist was willing to talk to e given our reputations.
Well, maybe he's not a listener to the podcast. So let's unpack that for a minute. Why do I say that it's not true that electrons increase their mass because you hear that everywhere, right, And it's a very popular thing to say because it sounds weird. It's one of these things that people say a lot because that has an impact on your mind. But it doesn't really actually make sense. It just sounds cool. And we talked about on the podcast why that doesn't really make sense and why relativistic mass isn't even a useful concept. It doesn't make sense because if mass depends on velocity. Velocity is three directions, right, it's a vector. You can velocity in one direction, another direction, a third direction. There's three dimensions of space. If three dimensions of velocity. If mass depends on velocity, then mass also has three dimensions. Then you would have like a different mass in each direction. It's weird, it doesn't make any sense. It's not what we think about as mass, and mostly it's misleading people think that something weird and mystical is happening, like as the electron is a approaching the speed of light, it's growing and mass like it's getting more stuffed to it in some weird way. That's not what's happening at all. What's happening instead is that as electrons approach the speed of light relative to an object, our intuition about the relationship between energy and velocity fails down here at very low velocity is the surface of the Earth. When we're running around at low speeds and driving, and what we think our high speeds were really pretty slow compared to the speed of light. We think that as you add energy, velocity goes up to and they go up together, right, But what happens as you approach the speed of light is energy can keep going up. There's no limit to energy, but a velocity is limited to the speed of light, and so as you add energy to something, it's velocity doesn't go up by as much, and so that sounds sort of like, oh, it's getting more massive because it's harder to get it to go faster. Right, It's really just a relationship between velocity and energy that gets more complicated near the speed of light. So it's not like a useful things we can use energy. Energy contains all the same information as relativistic mass, and energy is not as misleading. It doesn't give people the impression that, like the electrons getting more stuff to it somehow, So it's not a useful concept and it's misleading. And in this case, it doesn't explain why mercury would have a lower melting point. You know, having more mass would mean it would take more energy to get you to higher velocities. But these things are moving at very very high velocities, so that would imply that they have even more energy, which would push them out from the center and would be easier for them to nab by other atoms. And so it sort of goes in the wrong direction as far as I understand.
It, all right, so I am definitely not going to be reading science dot buzz or what was it, science News dot bus because they clearly got this wrong. And you know, you mentioned that everybody was talking about it, and you know when my daughter came home from school and was like, electrons increase their mass as they approached the speed of light, I was like, I'm so disappointed in you, Ada, But so what is the right explanation?
So there is an explanation. It's not like as simple and as compact a story. As the electron gets weirdly massive. The answer is that to figure out where the electrons go, you have to solve the equations, and the equations depend on a lot of stuff, and the solutions to those equations, you know, the energies that the electrons are happy to be at are different if you include relativity than if you don't. And if you include relativity, you get electrons with smaller orbits. Right, they're still moving at very very high speeds, but they have tighter orbits. They're closer to mercury. Essentially, they have lower energy than without relativity, and so they have tighter orbits at these very high velocities, and because they have tighter orbits, mercury is able to hold on to these electrons even more tightly than its friends in the same column zinc and cadmium, for example. And so if you turn off relativity, then it relaxes a little bit and these electron get larger. If you turn on relativity, then the electron orbitals shrink a little bit. And I went back to that chemist and I asked him, hey, do you have an intuitive explanation for what's going on here? Is there a nice little story in the same vein as like, hey, electrons get more mass, but actually correct? And he said, look, chemistry is complicated. The answer is no, there isn't a nice simple explanation. It's just that when you include these effects, the first order relativistic correction if you're doing perturbation theory, is to reduce the energy of this shell. And it turns out to be a really hard calculation, which is why people only recently were able to do it. You have to model a bunch of atoms altogether to figure out the bonds between them and all of the electrons around those atoms, and this is a really hard thing to do you need really powerful computers? And then adding the relativistic pieces means every time you want to move your system forward in time, you have to do a bunch more complicated calculations. Like relativity makes everything harder, Like not only is it harder to think about it, but it's also harder to get our computers to predict. There's like more steps in each calculation, more multiplications and divisions and square roots and all sorts of really weird stuff. But it's these relativistic effects which push the prediction from chemistry down below room temperature. So there's a recent paper and they predict that the melting point of mercury should be negative twenty three C. So without relativity they predict eighty two c. With relativity, they predict negative twenty three c. Now the real value is negative thirty nine CE. So they're still not getting it right. There's still more to understand there, probably second third order relativistic corrections, more detailed, accurate predictions, but they have gotten it down below room temperature. And so this we're convinced is the explanation for why mercury is a liquid or room temperature. It's relativity.
So that is super cool. So mercury has an atomic number of eighty and it's got a really low melting point, But why doesn't everything past eighty also have a really low melting point. It still feels like mercury isn't all relative to everything else.
Yeah, well it sort of does, like if you keep going. You know, lead, for example, has a melting point of three hundred and twenty. That's not that high. It's a lot lower than silver and gold, and that's because it's really heavy and it has these relativistic effects. But also it doesn't have a complete shell, so it's much higher than mercury because it doesn't have a complete shell. If you get all the way over to the end of the periodic table, if like xenon, its melting point is like negative one hundred C and radon is like negative seventy. See, these things are gas at room temperature, so you see those effects. As you move down the periodic table, melting points are shrinking, and one of these reasons is relativity. But it's not the only thing that's.
Happening, right, Okay, So it's the combination of the shells being filled, how tightly those shells are held by the nucleus being heavy, and the fact that that heavy nucleus is causing the electrons to move faster. Now you have really sativistic effects, and all three of those things come together with mercury to impact a s melting point more than anything else. So like, for example, if you move to ten, ten, yes, still has that relativistic effect going on, but now you have one electron in the outer shell, and so it's wanting to react to stuff, and so now you're in a different world altogether, and that's why it doesn't have such a low melting point.
I think maybe you're thinking about thallium, which is the next one over for mercury, and it looks like ten but it's actually a TL. But otherwise, yes, exactly, yeah, And so that's why thallium is like three one hundred and fifty degrees higher melting point than mercury, because it's got this one extra electron which we're very happy to bond with other thallium atoms.
My annual eye appointment is next week, and so maybe in a few weeks I'll be able to read the periodic table.
But even if it was TI, that wouldn't be ten ten is s n right because it's got some weird Latin name.
Oh, how embarrassing. How embarrassing.
But you're right that there are relativistic effects all over at the bottom of the periodic table, for example gold. Why is gold beautiful and gold colored? Whereas silver, which has the same electron structure and is one above and in the same column, is basically colorless. It's you know, silver. The answer is relativity. The color of an element depends on the photons it will emit and absorb, which depend on the spacing between the energy levels, and relativity changes those energy levels in gold much more than they do in silver, which makes it gold colored. Without relativity, gold would look like silver.
Oh my gosh, I know so much cool stuff happening with relativity.
People always say relativity is beautiful. Now you know why it's gold.
People are always saying that, like it's common on T shirts and stuff like that.
People are saying that you're being ironic, but I'm not. Relativity really is beautiful.
I do think it's beautiful. I do, And this has been super cool. So how recent is this incorporation of special relativity into our understanding of what's happening in the periodic table. Is this something I think I'm remembering you said, we've kind of known about it for a while, but haven't been able to calculate it until recently, Like, how recently have we started incorporating this stuff in there?
So you know, we've known about quantum mechanics for about one hundred years and relativity for about one hundred years. They were merged together into relativistic quantum mechanics only a few decades after the birth of both of those theories, so that's been for a long time. But in order to do this calculation requires a lot of computing, So it's only about ten years ago the people were able to do this calculation and predict the melting point of mercury more accurately than eighty two c And so yeah, this is a pretty recent calculation.
It's a cool time to be alive.
It is a cool time to be alive. But while mercury is amazing and gorgeous and fascinating, please don't play with it, don't drink it, don't throw it at your sister.
You probably don't want to put a vial of it on your neck.
Though it turned out pretty well for you. Kelly.
That was probably one of the less dangerous things kids like me were doing in the nineties. We were sort of free ranging around our neighborhoods. All right, well, I'm going to get my special. Relativity is awesome t shirt M because you've convinced me and I look forward to talking to you next week.
That was good, and so for those few folks out there keeping track, relativity has now explained two totally different kinds of mercury, both the orbit of the planet mercury and the melting point of the element mercury. Relativity is all over it.
Ah. You know, actually, when I read your intro, I thought to myself, I don't know the story about how relativity predicted Mercury's orbit. Should that be another episode? Is there a thirty second version? Or should we do a future episode?
Future episode? Let's do it.
Future episode locked in? All right, Thanks for listening. If you want to get in touch, please send us an email at questions at Daniel and Kelly dot org. We can't wait to hear from you.
Thanks for staying with us for this Chemistry episode.
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