Relativity behind mercury's liquidity (2013) | Hacker News Reader

Relativity behind mercury's liquidity (2013)

chemistryworld.com

37 pointszeristor19 comments

It seems this Wikipedia article on why Gold is yellow was posted a while back:

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

>"In the 1960s, Pekka Pyykkö, now at University of Helsinki, Finland, discovered that gold’s colour was the result of relativistic effects. He showed that the lower energy levels of the 6s orbital of gold means that the energy required to excite an electron from the 5d band lies in the visible rather than UV range of light.

This means that gold absorbs blue light, while reflecting yellow and red light, and it is this that gives the metal its characteristic hue."

So are even heavier elements more interesting. I would expect more coloured elements, more liquid elements at room temperature for heavier elements.

Can the number of neutrons in an isotope make a big difference, there are a few elements which have a wide range of isotopic weights, if a property was quite delicate I’d expect such changes to be quite apparent, tricky for millisecond half lives.

One thing that comes to mind is https://en.wikipedia.org/wiki/Kinetic_isotope_effect , although this seems to mostly affect elements that only have a few protons, like hydrogen or oxygen. Still, it adds up enough so that replacing most of the water in your body with heavy water (D₂O) would be fatal.. But, you'd have to drink exclusively heavy water for a long time to actually reach a toxic dose.

Yes thanks for reminding me about Heavy Water ice, and how it sinks in a glass of water too.

Also I have subscript envy, and shall scour the Internet as to how to do subscripts in HN.

I used the subscript 2 unicode character (U+2082). As far as I know, HN's formatting doesn't include anything to do subscripts. (At least, https://news.ycombinator.com/formatdoc does not mention it.)

Most of the properties of materials are from the charged pieces that make them up -- the protons and electrons. Since adding neutrons wouldn't change the number of electrons or protons other isotopes would be almost identical for the purposes of chemistry, light, etc.

Some small differences might crop up in things that depend explicitly on the mass of the nucleus (e.g. sound propagation, density). But given adding a few neutrons in heavy nucleus is a change of order a percent or so in mass it isn't likely to be dramatic.

My main question was are the only examples in Mercury, and Gold?

AI, and Hg are next to each other on the periodic table, just on the metal / non-metal boundary, beneath them are the Rg, and Cn.

Rg Roentgenium has a short half life, but seems to be tricky to make, it is expected to show some Relativistic properties though:

https://en.m.wikipedia.org/wiki/Roentgenium

Cn Copernicum, according to Wikipedia seems to show RQM effects it acting like a noble gas, albeit one with a half-life of at most 28s: https://en.m.wikipedia.org/wiki/Copernicium

If so why only these too? I’d expect there to be several others with mysterious properties too.

I understand electrons are a probability cloud but suddenly

> The larger the nucleus gets the greater the electrostatic attraction and the faster the electrons have to move to avoid falling into it

and now they're moving (and in this case, faster). So how does a particle with no attributable position move faster? This doesn't make sense.

It's a probability cloud of different possible locations, but also it's a probability distribution of different permitted possible speeds, as well. This probability distribution has a peak (a mode). When he writes "the faster the electrons have to move", he means this mode for a heavier nucleus is larger than that of a lighter nucleus.

Please let me know if I'm not being clear enough.

Actually thanks, that's very clear at that level, however that leads to a further confusion (of mine) about what speed implies, that being that the electron is moving (obviously) from x to y, which apparently contradicts the probability cloud concept of probabilities of a position at instant x, and only for that instant.

That is, if it's moving from x to y (because it has speed) then it's more likely to appear on some vector between x and y.

Please feel free not to answer that question, as I may drag you down the rabbit hole - but if you can, I'd love to know.

On possible way to think about it, is to imagine a probability cloud of something else, but made of classical particles. For instance, all of the cell phones in Chicago. Someone like Google can probably compute an average position, such as maybe a center of mass, but also an average speed based on knowing the speeds of all the phones as they're carried about, driven in cars, etc.

Now what we might have done in quantum mechanics class, without thinking too hard about the implications, is to assign mathematical functions to the things that we want to know about the electron using rules of thumb for how to turn functions of classical systems into corresponding functions of quantum systems. Then we apply the "what is your average speed" operator, and out pops a number.

I didn't get very far past the basic quantum mechanics where we were able to compute stuff but were left on our own to speculate about the meaning of the philosophical implications. Then I joined an experimental research team where I was able to think my way through problems using electronics, vacuum pumps, and computer code. ;-)

Thank you. I kind of get it but perhaps some things are best not considered too deeply.

Its because the object that nature works with is not the probability distribution but the complex (as in real number plus imaginary number) wavefunction. The probability of being at a location is proportional to the wavefunction squared and the velocity is proportional to the derivative of the wavefunction times the wavefunction (? its been a while). take the function e^(i*x) the magnitude is a constant and so is the magnitude of the derivative.

Consider the simplified example a electron uniformly distributed around a single circular orbit. If we say that it has a speed of 90°/sec, then its position at t=0s is uniformly distributed, and its position at t=1s is uniformly distributed, but those positions are correlated such that, conditional on it being at 12 o'clock at t=0s, it's most likely to be at 3 o'clock at t=1s. If its speed is instead 180°/sec, then (conditioned on 12 o'clock), it would most likely be at 6 o'clock one second later.

But it's not more likely to appear between 12 o'clock and whereever, because that's only in the subset of cases where we assume it started at 12 o'clock; if we instead assume it started at 5 o'clock, it'll be moving to 8 or 11 instead. The starting positions are uniformly distibuted, so the later positions are also uniformly distibuted.

If you have a probability distribution of position.

Then increment time by one tick. If you have a second probability distribution (assuming some time dependence) then you have now a distribution of distance travelled and therefore a distribution of speeds.

The alarming thing about QM is that it is fundamentally probabilistic and yet a little classical at the same time.

I don't think that's right. If you increment the time by one tick, you have the same position probability distribution. That is, the wave function didn't change. Why should it?

But that position probability distribution has a very specific energy. And at each point of that position distribution, the electron has a specific electrical potential energy. So at each point, it also has to have a kinetic energy. It has a kinetic energy probability distribution to match the position probability distribution. And now we can talk about velocity.

https://phys.org/news/2014-10-function-electron.amp

This was on HN before - it's a fun illustration of QM influencing "position" in a non intuitive classical sense

Think of it less as an actual particle that has a speed and position at a certain time, and more that "speed", or "position" are just the results of measurements that are made.

The electron is a cloudy, blurry mess, yet if you measure its position, you'll find it is in a certain location, but that's all it means. It doesn't mean it "was there" before the measurement!

Likewise, if you measure its speed, you'll likewise get a precise speed measurement, but it doesn't mean it had that speed before the measurement! Or that it was actually speeding from any point x to a point y.

So, while the measurements work, what breaks down are the regular common sense implications that the measurements normally imply.

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