« The shores of the island | Main | Kittens »

March 27, 2007

Comments

Feed You can follow this conversation by subscribing to the comment feed for this post.

Bernard Guerrero

This dovetails nicely into Carlos' topic du jour, of course. The Anderson was "Mirkheim", IIRC.

Will Baird

All hail, Victor Ninov!

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

Big black eye for us at the Lab. :S

Carlos

Picky correction: it's unlikely that the superheavy elements will have odd chemical properties by virtue of being superheavy elements, since chemistry is determined almost wholly by an atom's electron configuration. Funky g orbital chemistry, sure, but that would be derived from the electrons balancing the high positive charge on the nucleus, not from nuclear weight.

If you want an example of a heavy radioactive element which has benefited by being near an island of stability, there's bismuth, which was determined to have a half-life of ca. 10 ^ 19 years in 2003. It's right next to super-stable lead in the periodic table.

Bismuth is kinda dull.

Doug M.

"Relativistic effects in transactinides are crucial and show up in several ways. Most importantly, s and p1/2 atomic orbitals contract relativistically. The shrinking of the inner shells results in an increased screening of the nuclear charge, and this gives rise to an expansion of the p3/2 and of higher angular momentum orbitals.

"Another relativistic effect is a change in the spin-orbit coupling. Both can produce drastic rearrangements of orbital levels. That is what is predicted to happen for element 112. Recent calculations indicate that the 7s orbital should be shifted below the 6d5/2 orbital due to relativistic effects. It is the large relativistic stabilization of its valence 7s orbital, combined with its closed shell electron configuration, that has led to the prediction that element 112 is chemically inert."

That's from this article, but brief googling will turn up plenty more.

Some of the odd chemical effects have been tested experimentally -- which is quite an achievement, given that we're talking about handfuls of atoms and half-lives of minutes or less.

Note that these effects mean the superheavies will diverge from their homologues lower on the periodic table. And the bigger the mass, the greater the divergence. "Chemistry of the superheavy elements with Z > 118 is believed to show relativistic effects that are so large that comparison with lighter elements or nonrelativistic results is meaningless."

Of course, it's possible they might be boring anyway.


Doug M.

Carlos

Doug, you've misread the article. Those aren't nuclear shell effects, but relativistic corrections to electron energy levels. Gold has them, mercury has them. They contribute to the lanthanide contraction. The effects are interesting, but not new, and they're only dependent on Z, the positive charge on the nucleus. If you had the same positive charge with half the mass, or twice the mass, you'd get exactly the same electronic configuration. It has nothing to do with superheavy stability per se.

[snip discussion on isotope effects -- too tangential.]

Carlos

Throw in an 'almost' before the exactly -- might be a small correction for the change in the Compton wavelength of the nucleus, which would be about the fifth decimal place. (It's been a while.)

Doug M.

Um, what? Where did I say they were shell effects?

"Their nuclei are so massive that relativistic effects become important. So, instead of just being a heavier version of platinum or whatever, they may have very odd chemical and magnetic properties. "

I guess that was sloppy, since the relativistic effects depend on Z and not mass. But since Z increases pretty steadily with mass, I think it's a reasonable shorthand. "Their nuclei have so many protons that relativistic effects become important," 'kay?

And since the effects increase roughly proportionately to Z^2, by Z>110 they're strong enough to make the superheavies drastically different from their homologues. Eka-mercury is expected to be a gas, while eka-radon may be a semiconductor. (Though also a gas.)

"Misread the article..." Did you really think I thought the nuclear arrangements would directly affect the chemistry?


Doug M.

Carlos

"Their nuclei are so massive that relativistic effects become important. So, instead of just being a heavier version of platinum or whatever, they may have very odd chemical and magnetic properties."

I guess that was sloppy, since the relativistic effects depend on Z and not mass.

It's very sloppy shorthand, because it makes it sound like a relativistic mass-dependent effect, i.e. gravity. But it's because the "naive" velocity of the electrons of an atom become comparable to the speed of light, because of the increased positive charge of the nucleus.

(Checking the derivation, the relativistic factor v/c is roughly Z times the unitless fine structure constant alpha ~= 1 / 137. So just as you'd expect significant time-dilation effects at around half the speed of light in space travel, you'd see significant relativistic effects starting about Z ~ 137 / 2 = atomic number 69, which is in fact the case.)

Anyway. The article you quote is hyping it up. People have been speculating about relativistic effects since the Bohr model. While it's obscure, it's something I studied as an undergraduate (though granted, most undergraduates avoided quantum chemistry like the plague). It's not something exclusive to the island of stability, but something already known to affect well-known elements.

Some examples: Why is mercury a liquid? Because its 6s2 electron shell has been pulled in due to relativistic contraction, causing mercury atoms to resemble helium's very inert 1s2 configuration. Why is gold yellow and silver white? Because relativistic effects have lowered the energy difference between analogous orbitals in gold versus silver, so the transition which in silver absorbs in the ultraviolet, in gold absorbs in the blue. And so on.

The exact effects are almost impossible to predict in advance, because the calculations for the energy levels are almost impossible to perform. So the properties will be new. But they won't be unexplainably new.

"Misread the article..." Did you really think I thought the nuclear arrangements would directly affect the chemistry?

Honestly, it wasn't clear if you did or didn't. Nuclear shell terminology is fairly similar to electron orbital terminology (which in turn derives from spectroscopy). It looked like the type of mistake an informed layperson might make.

Carlos

Looking at the math, you know where there's a really interesting point? As I mentioned, the relativistic correction is analogous to time dilation, sqrt(1 - (v/c) ^ 2). The comparable term in the Dirac equation is sqrt(1 - (Z * alpha) ^ 2), where alpha is the fine structure constant, nearly exactly 1/137.

This means, when Z > 137, it's analogous to going faster than the speed of light.

I must look into this.

Robert P.

Carlos, your instincts are right: there is every reason to think that all hell will break loose somewhere around Z ~ 137. Among other things, consider the possibility of spontaneous production of real particle-antiparticle pairs by the electric field gradients in the vicinity of such a nucleus. Chemistry as we know it ceases to make much sense when one has to worry about electrons appearing out of nowhere. I have seen at least one speculative monograph on the topic - it will take me a while to track it down.

Do not forgot that the perturbation expansion that underlies QED is asymptotic, rather than convergent. (A property that it has in common with just about all perturbation expansions for real-world problems.) The entire apparatus of renormalization, diagrams, and all that relies upon \alpha being much smaller than one. By taking Z>137, you are effectively making the expansion parameter of order one. Very little is known, AFAIK, about the detailed properties of QED outside of the domain of perturbation theory.

Gareth Wilson

The relativistic effect that turns gold yellow came up in one of Baxter's _Manifold_ books - an child prodigy was able to deduce it just by looking at a gold ring.
As for the superheavy elements, one bit of speculation I've seen is that their critical mass for fission would be very low, so you could have nuclear bombs the size of bullets. But the cost of synthesis would probably make each bullet more expensive than an aircraft carrier.

Doug M.

"It looked like the type of mistake an informed layperson might make."

Ri-ight, because as I've often said, U-235 and U-238 have quite different chemical properties. Making it easy-peasy to separate them! Armenia has the Bomb!

Anyway. The business about Z=137 is v. interesting. Nobody has the faintest idea how we'd go about building nuclei that big, but there's supposedly another island of stability around Z=126; that falls under the category of "we might, just maybe, be able to do something with that in ten or twenty years". At over 90% of "light speed", the effects should be strong enough to keep things interesting.

Of course, it's also possible that (1) the laws of physics will allow certain superheavy nuclei to be long-term stable, but (2) there may be /no/ combination of nuclei and collision speeds that will let us build them. That would kinda suck, but the universe is under no obligation to put everything interesting within reach of our little monkey hands.


Doug M.

Carlos

"It looked like the type of mistake an informed layperson might make."

Ri-ight, because as I've often said, U-235 and U-238 have quite different chemical properties.

Dude. The type of error I thought you were making wasn't a simple "isotopes will have different chemical properties" error, but one more like "these new nuclei, because of their superheavy mass and novel structure, will interact with electrons through entirely new mechanisms, making comparison with lighter elements meaningless".

I'm re-reading the thread, and it's very hard not to take that impression away from the discussion. But since I've misinterpreted it, I apologize.

Robert, I've found Reinhardt and Greiner's review from 1977, "Quantum electrodynamics of strong fields", Rep. Prog. Phys. (1977) 40, 219-295. Some intense stuff. The finite size of the nucleus seems to extend the critical Z number to about 170 or so. Past that, a charged vacuum state with electron-positron pair production, positrons emitted, electrons ending up associated with the nucleus in a bound state -- it's not obvious to me how these differ from an electron shell.

Will Baird

Past that, a charged vacuum state with electron-positron pair production, positrons emitted, electrons ending up associated with the nucleus in a bound state -- it's not obvious to me how these differ from an electron shell.

Wow.

Do they say anything about the theoretical 'production' rates?

Doug M.

Brother, there is no need to apologize.

And isn't this wonderfully interesting stuff? Superrelativistic atoms: who knew?

Oganessian seems to be a widely liked and respected figure: when he turned 70 a few years ago, the SHE community turned out in force. He's one of the last survivors of the Golden Age of Soviet nuclear physics.

I find myself hoping that he lives to see the island reached.


Doug M.

Carlos

Will, I think the way it works is, if you try peeling off the electrons so the exposed charge is creater than about Z = 170, you get pair formation: the electron goes to the shell, and the positron goes bye-bye, so you can never actually 'see' the high-Z nucleus.

Doug, He's one of the last survivors of the Golden Age of Soviet nuclear physics.

Remind me to put up my Dyson lecture notes soon. (What a fascinating man!) Pneumonia, bronchitis, and now an ear infection: I feel like a human Petri dish. And allergy season is coming...

Will Baird

if you try peeling off the electrons so the exposed charge is creater than about Z = 170, you get pair formation: the electron goes to the shell, and the positron goes bye-bye, so you can never actually 'see' the high-Z nucleus.

ok.

*thinks aloud*

If you try to pull off an electron, you get a
positron and an electron that zips into the shell. I am assuming that the positron annihilates with the electron you tried to peel off, right?

hmmm. Must peel and keep them separate. hmmm.

Now how much of a fool do I look like?

Robert P.

Greiner ! Of course, that's where I read about this stuff - he covers it in the volume on Relativistic Q.M. in his series of textbooks on Theoretical physics. (Walter Greiner has been orchestrating on a sort of up-dated Landau and Lifshitz - a series of textbooks covering all of theoretical physics, written by a small group of authors. They have a reasonably high probability of showing up on the 40% off tables at University bookstore sales. )

BTW, the second paragraph in my previous comment is crap, I've decided, so don't try to make sense of it. (The stuff about perturbation theory being asymptotic rather than convergent is true - but the rest does not follow.)

There have been some major advances in incorporating relativistic effects, at a pretty sophisticated level (Breit-Pauli, and sometimes beyond) into quantum chemistry programs in the past five years or so. It's not quite at the point where a synthetic chemist can specify "Relativistic" as an option when running Gaussian on some favored molecule, but that day isn't far off.

The comments to this entry are closed.