What mercury being liquid at room temperature has to do with relativity | Hacker News Reader

What mercury being liquid at room temperature has to do with relativity

blogs.scientificamerican.com

140 pointshalostatue43 comments

The explanation, as described in the article, is lacking, since it does not really explain why no other elements are liquid. The suggestion is that it is that the 6s orbital is full. Why don't other large-Z elements with filled p- or d- or f- orbitals also become liquids?

TLDR is they do.

The medium form answer is look at the periodic table. There's block of s (which don't count because other than H/He they are buried deep in the atom) and a block of d where the full ones do have ridiculous low melting points compared to neighbors (like Zinc, Cadmium, Mercury...) and a block of p shell where the full p shells are the well known noble gases which are liquid at really low temps and the block of f weirdos who don't matter.

As for the f weirdos not mattering look at the electron configuration for something like Tb. Yes very nice that it has a peculiar collection of 4 level f shaped orbital electrons but I guess the more influential effect is the 5 level s and 5 level p and more importantly the 6 level s way out there in front of the mere 4 level f. Its kind of like D+D or pathfinder multiclass, oh, you have 2 levels of bard multiclassed into your level 10 sorcerer, well whatever, that bard isn't going to matter very much compared to the sorcerer level powers.

So back to your question, the filled p make great gasses at room temp not mere liquids you are totally correct here, the filled d have really low melting points for metals like Hg being a liquid as discussed, and the filled f are weirdos who fool around with electron configurations at mere level 4 when the real chemical action is at level 6 so they don't matter (sorta)

For a more correct, longer form answer someone else will have to step in.

Favorite analogy ever. Don't really know why the 4 level f shaped orbital electrons are a level 2 multiclassed bard and the two 5 level s/p and 6 level s are like a level 10 sorcerer, but that may be because I understand about 5 of the words at the beginning of this sentence. It's been a really long time since chemistry.

It has to do with the principal atomic number of those f orbitals. Some quick review (where ~ means "is related to in a monotonic, increasing fashion")

  n = Principle Atomic Number ~ energy,size of orbital
  l = Total Angular Momentum Number ~ abs(ang m.)^2

  n is 1,2,3,...
  l is 0,1,2,... (0=S 1=P 2=D 3=F ...)

Now you can tell that these two should be related by thinking about the classical "solar system" electron/nucleus model: if an electron has lots of angular momentum that means it must have lots of energy. Careful: if it has no angular momentum it could still have lots of energy if it's going straight at or away from the the nucleus (angular momentum cares about velocity perpendicular to the line between two objects; energy cares about the absolute velocity). This idea turns into an inequality we get by solving the Schrodinger equation for a H atom to find eigenstates which we parameterize on the quantum numbers:

  l < n

also we can figure out from the H-atom Schrodinger equation

  Increasing n only (going down a column) increases energy

The different "blocks" of the periodic table are named after the l quantum number because it is instrumental in determining the shape (as opposed to size) of the orbital. S is the 2 cols on the left, D is 10 cols in the middle, P is 6 on the right, and F is down below (it should actually be between S and D blocks but that wastes space on posters).

What does the inequality (and the intuition behind the inequality) tell us about these blocks? Let's go one by one

  S block. l=0. 0<n. n>=1. S orbitals have "size 1" or larger
  P block. l=1. 1<n. n>=2. P orbitals have "size 2" or larger
  D block. l=2. 2<n. n>=3. D orbitals have "size 3" or larger
  F block. l=3. 3<n. n>=4. F orbitals have "size 4" or larger

This sort of looks like larger l means larger orbitals, but not so fast! They fill in order of energy level, not momentum (low energy = tightly bound to nucleus, deep in its electrostatic well). If we fill orbitals one by one, we know the first P orbital will have size 1 but that doesn't tell us anything about the S orbitals that come before it, and indeed there is an S orbital of size 2 that comes before the first P orbital of size 1. Just read off the periodic table in order of increasing (proton count = electron count) to see what I mean.

OK, now we jump to the F block. We know the first f orbital we see has size 4 -- it is the outermost orbital of Lanthanum. But what is the preceding orbital, the one with slightly less energy (slightly more tightly bound to the nucleus)? It's the outermost orbital of Barium, and it's an S orbital of size 6.

S orbital of size 6 is bigger than a P orbital of size 4 :-)

This is counterintuitive because it breaks the "bigger orbitals have more energy / are less tightly bound" rule. The solution to the paradox is that the part of the orbital (probability density function) that contributes most to the energy is the part near the nucleus where the electron is far down the rabbit hole, so to speak. While the outermost part of 4f is smaller than that of 6s, the inner part of the 4f has pulled away from the nucleus while the 6s still sits squarely on top of it. 6s gets out to play with other atoms more than 4f but in terms of energy it more than balances that out by spending time really close to the nucleus.

Hope this helps!

EDIT: fixed an off by one bug on the inequalities

Firstly, I'll offer that the article doesn't claim to explain why other elements aren't liquid, and simply observe that it does explain why mercury is: the math works out.

But interestingly there is one other element which is liquid at STP: Bromine. Every element has a melting point, and some element has to have the lowest[1]. If Earth was just a few dozen degrees cooler, we'd have no liquid elements at "STP", a few dozen degrees warmer, and we'd have several liquid elements. So there's nothing particularly special about mercury being the only liquid metal.

Check out this periodic table[2] annotated with melting temperatures. See a pattern? You might argue that the other elements in mercury's column have significantly lower melting points than the metals to the left; indeed Zinc and Cadmium have filled s orbitals as well.

But putting general pattern-ology aside, the macroscopic properties of an atom are essentially completely defined by the orbital structure. Observable properties such as melting point depend on these details in a highly nontrivial way.

[1] Actually many elements are gaseous at STP and have very low "melting" points. Most would actually sublimate at standard pressure.

[2] http://www.emsb.qc.ca/laurenhill/science/trends2/melting%20p...

It does seem unusual that there is exactly one metal that is liquid at STP (room temperature? been a long time since chemistry). On the other hand, it's always blown my mind, just a little, that the moon's orbital period and rotational period almost exactly match, so it's not like the universe isn't filled with these weird coincidences, based on relatively simple interactions exploded on macro scales.

STP is specifically 20 deg Celsius. It's in the room temperature range, but is more precise than that.

It's actually 'standard temperature and pressure'.

http://en.wikipedia.org/wiki/Standard_conditions_for_tempera...

The different organizations have different exact definitions.

Well, the notion that one metal is liquid at our arbitrary reference temperature is a coincidence. But it is no coincidence that the moon's orbital and rotational periods are the same; this is due to a mechanical phenomenon called Tidal Locking[1] and is actually quite common for natural satellites.

[1] https://en.wikipedia.org/wiki/Tidal_locking

(posting as alt because I left noprocrast on!)

An amazing actual coincidence is that the sun and moon appear almost the same size as each other from the surface. The opportunity for such perfect total solar eclipses (with naked-eye visible Baily's Beads) is not common in the universe.

There is at least one short story (the title escapes me) that suggests that our #1 tourist attraction for visiting aliens would be total solar eclipses.

edit: Found it, maybe. This does not sound like the one I read.

> Illegal Alien, by Robert J. Sawyer (1997). An alien visits Earth, supposedly for "research purposes", and observes a total solar eclipse. He then speculates that Earth may be the only planet in the entire Universe whose moon covers its sun perfectly (with only transits or occultations occurring on other planets).

Interesting point - but wouldn't Jupiter or Saturn with their many moons also experience solar eclipses in a similar way ? Maybe not as perfect as on Earth, but certainly some of their moons could obstruct the sun?

Those are called transits and occlusions. Very dull and quite frequent.

And gas giants don't have a fixed surface you can stand on. I guess you could find the optimal distance to hover in your space ship to see an eclipse, assuming it is above the cloud layer. But where is the novelty in that?

Plus the sun is much less impressive way out there. Jupiter is 5 times further (Sun appears 0.04 the size). Saturn is 9.5 AU and so the Sun appears 0.011 the size.

Eclipses are still not likely just because you have a bunch of moons. Usually moons will orbit on the planet's plane of orbit. The Earth-Moon system (being more of a binary planet relationship) orbits on the solar plane instead of around the Earth's tilted equator, meaning the Sun/Moon/Earth is vastly more likely to be in alignment for an eclipse.

I think my favourite coincidence, are Saturn's moons Epimetheus and Janus.

One of them orbits just below the other and they happen to be in such a position, that as they approach each other, the lower one gains momentum from the mutual gravitational attraction, while the higher one loses momentum. So every four (earth) years, they swap orbits!

When I first heard about that, I just thought it was awesome :-D

Are you thinking of Iain Banks' Transition? (Not a short story though).

You're right that the article doesn't mention it explicitly, but it seems to me that the explanation is "large Z and filled 6s orbital yields a liquid at STP if you account for relativity". So I wanted to know why "large Z and filled 6p orbital yields a liquid at STP if you account for relativity" is false.

I think the true explanation is the one you give: STP is totally arbitrary and it's a coincidence that this is the standard we use. That is, my question was a silly one; I didn't notice that this is a coincidence.

However, I think there's a related, more well-formed question: Br, Hg, and Ga are liquids (or nearly so) at reasonable Earth temperatures (from your [2], Cs is also), but all other elements seem to be solid or gas at reasonable Earth temperatures at 1 atm.

Why is the range where you get a liquid so narrow? Why do melting temperatures vary so widely? What sets the scale, and how does it vary over 4 decades (or three decades, excluding H and He---I understand that quantum effects are dominant there at standard pressure)?

EDIT: Would copernicium be a liquid, if its nucleus lived long enough?

Well, my point is that the macroscopic properties of an atom are the result of a quite complicated dependency on the orbital configuration. It's not like the orbitals are legos which you just clunk together to form the atom -- "stick in 4s^2 and you get conductivity, and throw in a 2p^5 for that nice deep red color".

The detailed set of rules that give these results is called quantum mechanics. We have a pretty good idea of the general equation to describe an atomic system (although it's still just an approximation), but we actually don't have closed-form mathematical solutions for many-body systems. The best we can do (except for case of hydrogen, and maybe helium) is to make a numerical simulation, which is what the authors in the article did.

You see, if you throw in even one different electronic orbit, you're liable to radically change the results. If the ingredients are complicated (hundreds of relativistic+quantum-mechanical particles), you're going to get complicated results! By way of analogy, consider how genes encode lifeforms: flip a few CGAT bits and you get cancer; flip some other bits and maybe you'd get some disease resistance.

As to your point about the range of variation -- this is perhaps one of my favorite reasons to study physics! To paraphrase JD Jackson, "Coulomb's law is experimentally known to hold for over 25 orders of magnitude in length scale!" But consider this; the masses involved in the periodic table cover two decades; does this perturb you? The wavelengths of light emitted by a star cover many of orders of magnitude; is that a problem?

(posting as alt because I left noprocrast on)

Very cool, too bad they listed the melting point temperatures in Celsius instead of Kelvin.

It would be interesting to see it tipped over as a 3-D bar graph (in K). Some of the rows have little dips in them (not just mercury), not just a hump (with carbon at the peak)

[edit:]

Oh (via few seconds google) http://www.webelements.com/_media/periodicity/tables/cylinde...

Another metal that melts slightly above room temperature - and is liquid at human body temperature - is gallium. You can get a solid piece of gallium, put it in your hand, and watch it slowly melt [1]. Pretty neat.

[1] http://www.youtube.com/watch?v=QYioZFOhxow

There is another interesting Q/A on physics.stackexchange about why gold is... gold.

http://physics.stackexchange.com/questions/72368/why-are-mos...

And here's an interesting story on why gold was destined to be used as currency: http://www.npr.org/blogs/money/2011/02/15/131430755/a-chemis...

Interesting that it misses what I always thought was the most important property of gold in this regard which is that it is (for a pre-technological society at least) completely unadulterable. It's the densest material you can readily obtain, without the ability to smelt platinum (whose melting point issues were mentioned in the article as a disqualifier for functioning as money). That means that I can't make a coin that matches both the size and the weight of a real gold coin out of anything other than gold. If you'd picked iron as the precious metal, I could fake an iron coin by mixing tin and lead together so the alloy's density matches iron's. But to make a fake gold coin without using gold, I need to mix something lighter than it with something heavier - and my options looking for something heavier are either in the platinum group, or are heavy radioisotopes like Uranium. All of which are probably sufficiently rare in a pre-technological society that they're worth more than their weight in gold anyway, so not much use as raw materials in a forgery. Density is destiny...?

Ok. So what is interesting here, is that chemists have long suspected this (to the point that this explanation was dogma to me as a grad student) but new paper gives it a fairly rigorously demonstrations from first principles in a less-handwavey fashion.

Could somebody please make that lower-case "mercury"?

Every time there is an edit, no matter how small, the article shows up once per edit in my RSS feed. I think edits should be kept to a minimum or not published multiple times.

I de-dup based on both title and URL such that changing one won't cause me to see it again unless the other is changed at the same time; it seems to help.

What reader are you using that offers de-duping?

Interesting; does the id in the URL change?

A really cool idea would be a site where people can submit anything they want with any title they want, and users' votes will determine how the stories get sorted. That way, the community could easily express and realize their preference for titles by upvoting the ones they prefer.

The problem with a system with no moderation is that the abusers of the system have more time and incentive to abuse than the community does to moderate.

It seems quite bizarre that the introductory chemistry about elements is taught without the prerequisite knowledge of Schrödinger equation and special relativity in college.

Interestingly the actual melting point of Mercury (according to Wikipedia) is 234.3210K which is still a way off the 250K calculated by this study. I wonder how realistic is it to exactly calculate melting points of metals and other materials from first-principles?

Well, it's an order of magnitude closer than the 355K that was predicted without accounting for relativity, and I think the point was that a melting point of 355K (82C) means it would be solid at room temperature, while 250K (-23C) means it is liquid at room temperature, so they can conclude it's the relativistic effect that's responsible for its weirdness. tl;dr: close enough.

It's a miracle they did it anyway. I still remember calculating the hydrogen atom back in college. It's a trivial case compared to mercury, yet it takes a surprising amount of scribbling.

I assume they did all sorts of approximate models for mercury. An analytic, rigorous solution must be impossible.

Gallium melts not much higher than room temperature... Is that explained by orbitals as well?

> the electron approaches about 58% of the speed of light, and its mass increases to 1.23 times its rest mass

Does this mean that as mercury is cooled to absolute zero, the electron will slow down and mercury will become lighter?

No. You can't have an electron filling lower energy levels if they're already occupied.

Also, I'm guessing what they mean by "electron speed" is actually electron energy.

If it's just about the electrons being pulled closer to the nucleus, why doesn't the effect apply nearly as much to it's neighbors on the periodic table?

Because it's the one with full d orbitals as the outer electrons.

To extend on wiredfools remarks, the effect of non-full means lots of electron sharing going on. But if they're full, the (smaller) effects of relativity are the only effects so they're dominant. The neighbors are non-full so the sharing they do is way more important level than relativity level effects.

I wish I could understand this.

What I'm getting from this is that -

  > under relativity fast things are heavier
  > electrons are fast, they actually have about a 23% weight boost
  > heavier electrons 'orbit' closer to the nucleus
  > the atomic size is then smaller than anticipated
  > this has a bunch of interesting effects on melting points, reactivity, colour/reflectivity etc, (especially of transition metals?)
  > this stuff has not always been well understood.

It's been a long time since I studied chemistry, so I may be reading it wrong. It's pretty cool though :)

inter-disciplinary science of such effects

http://en.wikipedia.org/wiki/Relativistic_quantum_chemistry

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