Atomic Radii exceptions

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Alright, so there are periodic trends, and there are exceptions to the periodic trends. I've been spending so much time trying to figure out just this one, little thing... WHY is it, that at the end (or a bit after) of the transition metals, the atomic radii of elements increase as opposed to decrease, like they're supposed to? Increasing effective nuclear charge should make them smaller; But no, their atomic radius INCREASES. One of the more drastic examples I can come up with is Polonium. Its radius is 30 picometers larger than bismuth, and it's right after it. Before it was discovered, theories and calculations said that Polonium should be smaller; But no, it's larger, and there are various other similar examples of this around that area. I've been researching for a good week now, and the closest there has been to a hint that those exceptions even EXIST is the disclaimer "generally" when I see "generally, from left to right in a period..." But no explanation. Not even my Chemistry teacher can offer up a reason why. I don't care how complicated it is, I just want to know a friggin' reason as to WHY its radius is bigger. Surely some scientist somewhere has discovered why. And I don't mean just for Polonium vs. Bismuth, but the other examples of this, too. On this topic, why are the Noble Gases also exceptionally large when compared to the rest on the periodic table, if their effective nuclear charge is supposed to be the greatest?

*sigh* It's been plaguing my mind so much...

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

You may want to track down the references on this web page to see how the calculations are done.

That doesn't help or explain anything; I became very, very familiar with that page during my search. There is no answer! Even just the briefest mention in that wikipedia page needs clarifications; Also, the calculated atomic radius chart in there is theoretical, made over forty years ago. Observed atomic radii are much different. Polonium is 190 picometers as opposed to bismuth being 160 picometers, breaking the trend severely. The closest to a guess I can get to is that the electrons begin to repel each other more violently due to there being more of them, thus increasing the overall radius; But that's just a guess, and I find it not too likely. There's a LOT of space in an atom for electrons to go where they wouldn't be repelled by others (as severely).

My chemistry teacher told me I needed to talk to someone with a Ph.D.

http://intro.chem.okstate.edu/1314f00/l ... 11300.html

The study of quantum mechanics is one approach to calculating the radii--I've never really studied it myself, but it seems that the current approaches involves probability or statistical calculations.

http://online.itp.ucsb.edu/plecture/girvin/
Here is a set of lectures that might be useful.

When I was student I had an experiment once where I tried to do a little extra by trying model the "screening" of the nuclear charge by the elections of the atom. When I got my write-up back the grad student had written a comment that doing that correctly is very complicated and very difficult.

Also, the QM orbitals for an atom can be really strangely shaped (they aren't all
spherical).

Read up on both the links you supplied, BDTD. All I got was a slightly more detailed version of what I already know. Heck, quantum mechanics interests me, but all I want to know for now is the reason as to why the empirical atomic radius of Polonium is much larger than the empirical atomic radius of Bismuth, despite what theories had supported before. Is there really no explanation as to why, other than "We can't measure these things properly enough to get a good reason why" or "It's shaped weirdly so we can't measure it right" or "It's just like that from what we've seen; Us chemists and physicists really have no clue."

Still no answer as to "Why are there exceptions to the atomic radii trend on the periodic table?" I have my answer for the Noble Gases, thankfully, but the Bismuth-Polonium example is one I am stuck on. Why is it so? Even as I'm writing this message, I'm searching... Alright, well, in one of the examples in that general area of exceptions, it seems as though the nuclear attraction is much, much (Think: Ten times) as high as the atom after it, and that compresses it so much that the atom becomes smaller than the atom after it. Still, the guy who says this (On Yahoo answers, mind you: Link to Post/Question) still doesn't know why. *rechecks* oh, dangit! He wasn't even talking about the area I was mentioning! That post has no relevance anymore, which means I'm back at square one... *sigh*

This is one of the downsides to being a really smart Aspie, you will discover lots of things that nobody has the time, smarts, or both, to figure out the answer to--I find that I often have to figure them out myself, or go without really knowing the answer!

Alright, now that I can see that there is no answer out there for me to find, I'm going to have to accept that and hunker down and study the subject until I make up my own theory about it. I'll be becoming an unofficial theoretical physicist soon enough, it means. I would have thought that someone would have paid more attention to this little detail. It's the freaking periodic table! Ah well. I'll become renowned for my smarts someday.

Noticing these issues is one thing--actually solving them is another. Our society spends very little on "pure" science and mathematics, which means there are few jobs for folks who want to answer these questions that don't involve teaching--it is the rare Aspie that can spend a busy day teaching students and grading papers--and still have lots of energy left over for solving difficult questions.

By "pure," I mean pursuits for the sake of doing them, as opposed to those with obvious economic benefit. If you are good in math and science, it is relatively easy for an Aspie to get an engineering degree--lots of good jobs because most NTs just can't handle the coursework.

Last edited by BTDT on 02 Dec 2011, 8:15 pm, edited 1 time in total.

That's why I'm going to study and make my own amateur theory without being in a lab. Even if it's wrong, I need to satisfy myself with a plausible answer...

This is how it was explained to me by my chemistry professor, who does have a Ph.D. He said the atomic radii is the result of two forces, the attraction between protons and electrons and the repulsion between electrons. If the proton/electron attraction is greater than the electron/electron repulsion, then the radii is smaller. If the electron/electron repulsion is greater than the proton/electron attraction, then the radii is bigger. Part of this also involves the energy levels of each shell/subshell/orbital of the electrons. As the shells/subshells/orbitals start filling up with electrons, the repulsion force increases. As the repulsion force increases so does the radii as you move across a period. Since the atoms of noble gases have their outermost available orbitals filled with electrons, they have the greatest radii for the given period. When you move to the next period down, the proton/electron attraction overcomes the electron/electron repulsion, resulting in a smaller atomic radii.

At least if I'm understanding it correctly.

The key is the Pauli Exclusion Principle.

ruveyn

For the Noble Gases, what I had discovered is that on graphs/charts, they are shown with much higher atomic radii (Except for Radon, as the data for its radius seems to be theoretical so far) because of what this says: "You have to ignore the noble gas at the end of each period. Because neon and argon don't form bonds, you can only measure their van der Waals radius - a case where the atom is pretty well "unsquashed". All the other atoms are being measured where their atomic radius is being lessened by strong attractions. You aren't comparing like with like if you include the noble gases." This quote is studying only two periods, but it explains the others, as well.

But otherwise, do I actually have an answer as to why? Does electron/electron repulsion make a huge enough difference between Bismuth and Polonium that Polonium becomes 18-20% larger, just because of one electron addition? I guess it does... Thank you, Darryl.

Hello,

I've been stuck on the very same matter as well. I'm following a course of quantum mechanical chemistry at University and we've been studying atomic radii as a part of it. On certain graphs I noticed how Polonium (Po) has a way bigger atomic radius than Bismuth (Bi), just like Tellurium's (Tl) radius is slightly bigger than Antimony's (Sb) radius. Both of these contradict the general rule that the radii in groups 13 to 17 decrease from left to right in one period of the Periodic Table. I haven't been able to find any explanation anywhere online or amongst students. So I've come up with two possible reasons for these particular phenomena, which are related.

The first reason is basically the same as ArtemisHolmes' reason: the addition of one electron could cause a greater repulsion between electrons, which in turn could cause the electron cloud surrounding the atom to extend with a certain amount. As to why this only happens in the periods 5 and 6, I think the fact that the filled 4f-, respectively 5f-subshells in those periods might have something to do with it. The filling of those deep f-subshells results in far more complicated electron interactions and thus it might lead to "strange" behaviour (like strong repulsions) when other subshells are filled later on, like in the Polonium atom. Only calculations with the quantum wave function of Polonium can resolve that particular question, but those are highly complex and can only be done with very specific programs and computers. This information might therefor not be accessible (to everyone) on the internet. Besides, no one is able to understand that information except for the people who work with it.

The second reason is related to the first and to what Ruveyn wrote:

The Pauli Exclusion Principle states that two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously. Or in other words: two electrons can occupy the same orbital, but they need to have a different spin quantum number, which is either +1/2 or -1/2. This comes down to saying that no electron can have the same set of 4 quantum numbers (an electron's state is defined by 4 quantum numbers, which allows it to be tracked down in time and space to a certain degree). So, one orbital, two possible electrons.

Now, assume we're filling a subshell of an atom. This subshell has 3 orbitals. So the subshell can hold 3*2 = 6 electrons. There's two ways of doing this: fill in the first orbital with two electrons, then the seconds one with two electrons and finally the third one with two electrons. Or you could fill in one electron per orbital at first and repeat that a second time to fill them completely. Hund's Rule states that the second option is more desirable than the first, as spreading the electrons throughout all the orbitals rather than filling each orbital up seperately costs less energy to perform. Which basically means it's easier to do. This can be easily seen by the following: if two electrons are orbiting in one orbital, they are taking up the same space and will repel one another. If two electrons are orbiting in two different orbitals, they don't repel one another, so it takes less effort for them to stay in the same space they're orbiting in.

How could this lead to bigger radii? If two electrons repel each other, they are less attracted to the core of the atom. Less attraction could mean their orbit grows (or distorts?) which in turn could increase the atom's radius. It happens to be that the Sb and Bi atom have all of their orbitals filled with one electron in the p-subshell which is being filled (according to Hund's rule). Thus the atoms Po and Te both have to add an electron to an orbital which already has an electron in it. This is the exact same situation as described above in which these electrons will repel each other and might cause a greater atomic radius.


This is what I came up with as a possible explanation, but I doubt it would be correct. I'd really like to know the real, full explanation as well.