Recently I was reading Theodore Gray's colorful coffee-table book/ebook "The Elements", where he shows an illustration of each element and a few trivia bits about their physical and chemical properties. I was surprised to see a few passing references to the ease or difficulty of acquiring samples for "collectors". Are there really people who collect chemical elements as a hobby? A bit of quick web searching showed that this was no joke-- there is a noticeable element-collecting community out there, who take their hobby quite seriously. The goal of an element collector is to acquire samples of every element in the Periodic Table.
I know what you're probably thinking now. "Sounds interesting, but this is a math podcast, not a chemistry podcast!" True, but if you think about it, I believe this interest is a kind of mathematical obsession. After all, the beauty of the Periodic Table is the way that a simple mathematical pattern has be used to understand and predict the occurrence of the basic elements that make up our universe.
Let's review the basic concepts of the periodic table. As you may recall, each row of the table represents an electron shell, which you can think of as a layer of orbiting electrons around the nucleus of an atom. Each column represents a configuration of 'valence electrons', the outermost electrons that are most important in determining chemical reactions. Once a shell is full of electrons, the next row begins filling in a new shell with a similar pattern of electrons-- thus the pattern of valence electrons repeats in the next row, which is what makes the periodic table periodic. The electrons in each shell must fit into a finite set of known orbit patterns, but the inner shells have fewer orbits than outer ones, which is why there are the noticeable gaps in the upper rows, representing the inner shells. Once the basic pattern is established, the elements go in the table in order of increasing number of protons, or atomic number, and the families with similar sets of valence electrons fall neatly into the columns. There are a few other complications which you can read about in detail on the wikipedia page in the show notes, and modern quantum mechanics shows that the solar-system-like vision of simple orbiting particles isn't quite right. But for this podcast, the important point is the mathematical elegance of having a table filled in using simple patterns, and being able to connect this to reality by neatly checking off each box as you acquire samples of each of the elements.
But for people who actually want to take up element collecting, there are a few minor issues they have to deal with. An obvious one is simple chemical safety: numerous elements are poisonous in their pure form. It sure looks tempting to open that vial of mercury and actually feel the bizarre sensation of a liquid metal rolling around your hand-- but that is not medically advisable, to say the least, as mercury is extremely poisionous and can be absorbed through the skin. Many other elements are relatively safe in solid chunks but can be extemely dangerous in powdered form, which is unfortunately often the easiest to acquire. One Russian company used to sell cheap samples of many elements by mail order, including a glass vial of powered beryllium, which could be fatal if it broke during shipping and someone inhaled the scattered powder. Any element collector has to think carefully about the form and storage requirements for each element.
And then there are the radioactive elements. Aside from the obvious dangers of radiation poisoning and the need for careful storage, there is the question of how to acquire them in the first place. Some that have real-life applications are available in tiny amounts in commercial products: for example, in the 1990's, teenager David Hahn, nicknamed the "radioactive boy scout", ordered decommissioned smoke detectors by the dozens to extract the tiny clumps of americium. There are also some historical sources for some radioactive elements that were discovered before their dangers were known: in the early 20th century, radium paint was used to create glow-in-the-dark clocks and watches. Hahn got his nice radium sample when he found an old clock in an antique shop with a vial of spare paint to refresh the dials. Hahn's success in acquiring radioactive elements eventually led to a national security incident, and the need for a federal cleanup of his backyard. And if you look at the scary online photo of Hahn today, covered in open sores from the effects of radiation, your admiration for his element-collecting skills might be dampened somewhat.
Another issue is that such a collection can never be truly complete. As you get to the heaviest elements, they are not only highly radioactive, but decay almost instantaneously when formed. The highest-numbered element actually synthesized so far is number 118, ununoctium, but only four atoms of this element have ever been known to exist. All were synthesized in scientific labs and detected only indirectly. Good luck collecting that!
Anyway, if you're a fan of this podcast, you probably realize that you can appreciate the periodic table from a poster or chart with or without actually holding the elements. In the show notes you'll find a link to Theodore Gray's book and the beautiful associated poster, which I highly recommend. The existence of physical objects is just a minor corollary of this mathematically elegant table, and the underlying quantum mechanical laws that make it possible; why sully it by obsessively acquiring a bunch of rocks, liquids, and powders that could potentially kill you anyway?
And this has been your Math Mutation for today.