Figure 1: Hydrogen’s Position in the Periodic Table [svg] [eps]
The main purpose of any periodic table of the elements is to help us understand the relationships among the various elements. We want to construct a “periodic table” that is a reasonably faithful representation of the observed relationships.
We shall see that there are many advantages to thinking of the periodic table as a three-dimensional object (rather than as a flat, two-dimensional object). The idea of a 3D periodic table is not new: in 1862 Alexandre Beguyer de Chancourtois published a description of his method for arranging the elements in a helix, on the surface of a cylinder. Note that this is many years before Mendeleev got into the game. For a good discussion of the history, see reference 1.
Devising such a table is akin to cartography. If we take something non-flat, such as the surface of the earth, and try to portray it on a flat piece of paper, there will be distortions. The cartographer’s task is to minimize the impact of these distortions, to prevent the distortions from causing too many misconceptions.
I will explain my three-dimensional periodic table in four steps, using four figures. Figure 1 logically comes first, but for pedagogical reasons let’s skip it for now, and deal with in in section 1.5.
Figure 2 contains the “main” part of the periodic table. If you cut out the figure, you can easily roll it into a cylinder. I arranged for each row of the table to run slightly diagonally, so as to exhibit the periodicity more clearly. In particular, sodium is connected to the right of neon just as clearly as fluorine is connected to the left of neon. This part of the table is periodic, with a period of eight.
To a fair approximation you could say that the actual elements exhibit the symmetry of a cylinder, but an even better approximation would be to say that they exhibit the symmetry of a helix that winds around the cylinder.
For some discussion of the strengths and weaknesses of this table, see section 3. A straw-man alternative is discussed in section 7, and a better alternative is discussed in section 8.
There is a conspicuous gap under aluminum in figure 2. The elements that fill this gap are the transition metals, shown in figure 3. You can cut out this figure and paste it onto the previous figure, forming a big bulge on the side of the cylinder. Note that both scandium and gallium have an equal claim to sit “directly” under aluminum. The name “transition metals” applies to the 11 elements (scandium through gallium inclusive) and to the elements directly below them. It does not apply to the elements shown in gray in figure 3; those are just there for context.
Loosely speaking, we can envision the 11 transition metals from 21Sc to 31Ga inclusive as being eka-aluminum plus some number of d-electrons, where the number runs from 0 to 10 inclusive. (This way of envisioning things is partly consistent with the data and partly not, as discussed in section 3.4.)
There is a conspicuous gap under yttrium in figure 3. The elements that fill this gap are the lanthanoids, as shown in figure 4. You can cut out this figure and paste it onto the previous structure, forming a bulge on the side of the previous bulge. Note that both lanthanum and lutetium have an equal claim to sit “directly” under yttrium. The name “lanthanoids” applies to the 15 elements (lanthanum through lutetium inclusive). It does not apply to the elements shown in gray in figure 4; those are just there for context.
To say the same thing another way, we can envision the lanthanoids as being eka-yttrium plus some number of f-electrons, where the number ranges from 0 to 14 inclusive. See section 3.4 for more on this.
So we have a bulge on the side of a bulge. That is, the lanthanoids are a bulge on the side of the transition metals, just as the transition metals are a bulge on the side of the “main” part of the periodic table. The transition metals are associated with the belated filling of a d-electron subshell, while the lanthanoids are associated with the belated filling of an f-electron subshell.
As promised, we now return to discussing figure 1.
In figure 1, the symbol n stands for neutron. (Note that uppercase N represents nitrogen, while lowercase n represents neutron. Similarly e represents electron and p represents proton.)
A neutron has atomic number Z=0 (no protons), just as hydrogen has atomic number Z=1 (one proton), and helium has atomic number Z=2 (two protons). The periodic table arranges things in order of atomic number, so the sequence n, H, He is perfectly consistent with the overall pattern.
On the other hand, it is true that n isn’t an element, so one could argue that it doesn’t belong anywhere on a periodic table of the elements. Still, it’s harmless where it is, and it serves the practical purpose of giving the model a good place to attach the left side of the hydrogen box.
The chemistry of hydrogen is exceptional. There’s no getting around that. Any attempt to fit hydrogen in to one of the 8 columns in the main part of the periodic table would be sheer lunacy.
Whereas the main part of the periodic table has a period of 8, as shown in figure 2, the hydrogen row has a period of only 2, and cannot be fitted into figure 2 satisfactorily. So logically what we should do is cut out figure 1 and roll it into a tall thin cylinder, with a periodicity of 2. Hydrogen is the only non-noble-gas element in this tall thin periodic table.
Logically, the next step is to paste figure 2 onto the aforementioned tall thin cylinder, so as to cover up the gap below hydrogen. This is logical ... but it is awkward, because the bulge is so much bigger than the cylinder it is attached to. On the other hand, this way of looking at things emphasizes the noble-gas column as the anchor and backbone of the whole periodic table, which it is.
So, given a periodic table with a gap beneath hydrogen, we then plug in figure 2 to fill in the gap.
Some people claim lithium should be placed directly below hydrogen. This makes a certain amount of sense, because hydrogen commonly exhibits a valence of +1. At the other extreme, some peope claim that fluorine should be placed directly below hydrogen. Again this makes a certain amount of sense, because hydrogen commonly exhibits a valene of -1 ... to the extent that valence means anything. Meanwhile, some people claim carbon should sit directly below hydrogen, since it has a similar electronegativity.
Arranging the periodic table as a cylinder with bulges allows you to satisfy all three claims simultaneously, if you want to. That is, you could say that lithium and fluorine and carbon are all claimants to the eka-hydrogen role.
The problem is, none of those claims fit the facts very well. This is not even remotely similar to the lanthanoids, which can be rather well described as competing for the eka-yttrium slot.
We need to look at the physics, rather than guessing, or wishing, or playing numerological games. The fact is that the H+ ion is very small. It’s just a bare proton. It’s about five orders of magnitude smaller than the Li+ ion. So if you describe LiF as a Li+ ion next to an F+ ion, you ought not describe HF in the same terms. It would be better to describe HF as a H+ ion deep inside the F+ ion.
From this point of view, it seems quite pointless to argue about the valence of hydrogen or the electronegativity of hydrogen. The hydrogen atom is going to do what it does ... and many of the things it does are not analgous to what any other atom does.
So, when we paste figure 2 into the gap in figure 1, the question arises of which elements “line up” below hydrogen. The question, alas, is not really answerable. The closest I can come to an answer is to say, very informally, that hydrogen is about 10% lithium-like, 10% carbon-like, 10% fluorine-like, 10% all of the above, and 60% none of the above.
Practical hint: By way of strain relief, you should trim the connection between He and Ne. Cut the left 1/3rd of the width and keep the right 2/3rds of the width. This allows the left 1/3rd to participate in the high curvature of the N=1 period. Similarly you should cut the right 1/3rd of the connection between n and He. In both cases, the cut is on the side nearest H, and the purpose is to lessen the workload on the H box. If you don’t do this, the N=1 “cylinder” will be squashed flat.
Some people are fond of drawing what they call a “full” periodic table (also known as an “extended” periodic table). Here is one good way of doing it:
Let me point out some features of this table. We can continue to think of it as a cylinder. It has periodic boundary conditions; for example the neon on the in the rightmost column is the same in every way as the neon in the leftmost column.
A cylinder without bulges could be slit and unrolled to make a smooth, flat chart. In contrast, if there are bulges, bad things happen when you try to flatten it. The elements directly above the bulge will get ripped in half. In figure 5 you can see that boron and aluminum have been ripped in half to “make room” for the transition metals, while scandium and yttrium have been ripped in half to “make room” for the lanthanoids and actinoids.
When there are two equally-good places to put an element, I put it in both places. Take yttrium for example: it makes equally good sense to line it up with the first of the lanthanoids (La) and/or to line it up with the last of the lanthanoids (Lu) … so I do it both ways.
You can compare and contrast this with the corresponding table featured in reference 2.
We start by pointing out some nice features of the “main” part of the periodic table, as shown in figure 2 and preserved in figure 5:
On the other hand, putting tin and lead in the same column as carbon and silicon is an example of letting the naively theoretical tail wag the factual dog – although I haven’t seen any good way of improving this. My point is that finding an element in a particular column of the periodic table sometimes predicts its properties, and sometimes doesn’t. As we go around the cylinder in either direction, columns near noble-gas column are more well-behaved than columns farther away.
A more subtle problem is that based on the observed chemical behavior, we might want to treat Zn the same way as Ca, and treat Ga the same way as Sc ... but the color code in these tables does not attempt to represent the chemistry. Instead, the color-code just indicates what column the element is in. The color-code depends on the atomic number Z, and not much else. That is, the color changes monotonically as a function of Z as we go across each row. It is not meant to encode any particular chemical property.
Any attempt to construct a periodic table is beset by a dilemma:
The problem is, the physical properties of the elements do not vary monotonically as a function of atomic number. So we satisfy the requirements as best we can, making compromises where necessary.
In other versions of the periodic table, one often sees a big gap between beryllium and boron, and between magnesium and aluminum. This gap exists solely to make room for the transition metals, and is completely misleading as to the Be/B relationship and the Mg/Al relationship.
To say the same thing in more positive terms, the nine conventional transition metals as a group fit nicely directly beneath aluminum. This is particularly true of the end members, scandium and gallium, both of which have an equally good claim to sit directly below aluminum.
Note the contrast:
| Calcium oxide is always CaO. Aluminum oxide is always Al2O3. At the ends of the transition-metal series, scandium oxide is always Sc2O3, and galium oxide is almost always Ga2O3. This can be used to assign calcium to column 2 in the table, and aluminum, scandium, and gallium to column 3. | In the interior of the transition-metal series, there are four possible chromium oxides, including CrO3, CrO2, Cr2O3, and Cr3O4. There are five possible oxides for manganese, and five for molybdenum. This makes such elements useful in redox reactions, but it makes it hard to assign them to columns based on simple notions of “the” valence or “the” way they react. |
Identifying the lanthanoids as a series with 15 members is very well supported by the observed chemical properties. As a rule (with minor exceptions) the lanthanoids all act like each other, and all act like yttrium, so it makes sense to place all 15 lanthanoids in the periodic table directly under yttrium.
The rule is particularly clear when applied to the end-members of the series: Lanthanum is chemically much more like the other lanthanoids than it is like barium. At the other end, lutetium is much more like the other lanthanoids than it is like hafnium.
More generally, all the lanthanoids tend to form halides as LCl3 and oxides as L2O3 (where L stands for any lanthanoid). This is in analogy to YCl3 and Y2O3, and in contrast to BaCl2, BaO, HfCl4, and HfO2. You should check the data for yourself; see for example reference 3.
Virtually all our observations about lanthanoids apply equally well to actinoids. There are 15 of them, from Ac to Lr inclusive.
The similarity of the transition metals to each other is not quite so pronounced ... so figure 3 is more approximate and more arbitrary than figure 4. Still, scandium is at least as similar to aluminum as gallium is, so the widespread practice of putting gallium directly under aluminum, while not unreasonable, is by no means required by the data. Of course none of the predicted periodicities are exact; the details of atomic structure are fantastically complicated, and cannot possibly be summarized in at two- or three-dimensional chart.
If you look up1 the ground-state electron configuration (“GSeC”) of each transition metal (21Sc to 31Ga inclusive), you will find that the GSeC is not well described by the pattern tentatively suggested in section 1, namely “eka-aluminum plus some number of d-electrons”.
That’s a small problem for us, but not a huge problem. For present purposes we care more about the element’s ordinary chemistry than its GSeC. Ordinary chemistry rarely deals with isolated atoms in their ground state. The actual, practical chemistry of scandium is about what you would expect for eka-aluminum, which fits nicely with our model. If we were fixated on the ground state of the isolated atoms, we might be worried that the Al valence shell is s2 p1 whereas the Sc valence shell is s2 d1 (for the ground state of the isolated atom). But we are not fixated, so we are not going to worry about that. We’re not going to lie about it, but we’re not going to overemphasize it, either.
It is a mistake to think of the GSeC as “the” electron configuration. The fact that the GSeC is commonly tabulated on periodic tables may be part of the reason why some peope overestimate its importance. This is quite a common mistake, but it is still a mistake.
When we come the lanthanoids and actinoids, the small problem is even smaller. To a good approximation, for each of these elements, its chemistry agrees with its GSeC. The lanthanoids collectively can be reasonably described as eka-yttrium plus some number of f-electrons.
Consider the assertion that the chemistry of Zn is similar to the chemistry of Ca.
Reference 3 is a convenient source of data that you can use to check such assertions. On each element’s main page, over on the right side, there is a box entitled “compounds”. On the calcium page we learn that its fluoride is CaF2 and its oxides include both CaO and CaO2. Similarly on the zinc page we learn that its fluoride is ZnF2 and its oxides include both ZnO and ZnO2. And that’s not all; for each element, there are about 10 compounds listed; you can check for yourself.
Good science does not depend on taking somebody’s word for something.
You are not required to check every assertion that you encounter, but every assertion should be sufficiently well documented that you could check it if you wanted to.
We can deepen our understanding of the periodic table by using some simple ideas from atomic physics. One essential idea is that a completely full shell is almost as nonreactive as a completely empty shell. (This is a well-known rule, sometimes listed as one of Hund’s rules; see reference 4.)
We have to be slightly cagey about what we consider a “shell”. There is a difference between mathematics and physics. Mathematics will tell you the symmetry of the Ylm spherical harmonics, but will not tell you the energy of the atomic energy levels.
Yes, closing out the N=1 shell gives us helium, which is the first noble gas. And yes, closing out the N=2 shell gives us neon, which is the second noble gas. However, the third noble gas, argon, does not (in the mathematical sense) close out the N=3 shell, because the 3d orbitals remain empty. So we see that chemical idea of closed third shell does not correspond to the mathematical idea of filling up all the N=3 orbitals. The distinction depends on the energy; the neon 3d orbitals are more-or-less inaccessible because they are too high in energy.
Another essential idea is that chemical properties are determined by the valence electrons, while the non-valence electrons don’t matter very much. This is an approximation, but it is often a good approximation. For example, potassium and sodium have the same valence-electron configuration, and differ only by a closed shell of non-valence electrons. This leads us to expect them to be chemically very similar, as indeed they are. To a fair approximation, potassium is just heavier.
If potassium didn’t already have a name, we could perfectly well call it eka-sodium (following a naming convention that goes back to Mendeleev).
Caveat: Although talking about “the” valence of a given element makes sense at certain locations in the periodic table (notably the noble gases and the alkali metals), at other locations (notably the transition metals) we need to be more careful. For instance, we know that copper can form both cupric chloride (CuCl2) and cuprous chloride (CuCl).It is traditional for periodic tables to display “the” electronic configuration for each element. If you read the fine print, it says this is the electronic configuration for the ground state of the isolated atom. As discussed in section 3.4, the GSeC is sometimes not useful, and sometimes very misleading. You are very unlikely to encounter isolated ground-state copper atoms in the chemistry laboratory. The copper atoms you do encounter will be ionized and/or bonded to other atoms. The ionic and molecular electronic configuration is determined by many factors, not solely by the atomic ground state.
The f-electrons almost never participate directly in covalent bonds. They don’t stick out far enough, not nearly as far as the s and p electrons do.
I don’t know any simple atomic-physics explanation of why the lanthanoids sit exactly where they do in the periodic table. They have to sit somewhere of course, but it would be a tour de force to prove from first principles why they act like eka-yttrium as opposed to (say) eka-strontium.
One thing is for sure: There are very strong theoretical and observational reasons why La and Lu should belong in the same column of the periodic table. There is no logical basis for putting one of them – and not the other – under Y.
A more-common but less-satisfactory version of the periodic table is shown in figure 6, using the “medium width” format.
The same idea is shown in figure 7, using the “full width” style.
The problem with both these figures is that a particular type of “block structure” has been imposed, as reflected in the labels and in the color-coding in the figures. This sort of block-structuring has some superficial advantages and some fundamental problems.
Let’s consider the following pros and cons. The pros are remarkably weak, and can be considered “damning with faint praise”.
| The blocks make the table appear to have a simple, precise, systematic structure. | The problem is that this table-on-paper does not reflect the actual properties of the chemical elements. A lesser claim of precision would fit the facts better, for the same reason that it is far better to say “π = 3.1±0.1” than to say “π = 3.1 exactly”. |
| The blocks are superficially attractive. They look nice from a distance. It is understandable that people find rectangular regularity more esthetically pleasing. | We must not let the esthetic tail wag the scientific dog. Esthetics is not science. |
| I suppose a regular rectangular pattern is easy to remember. | It is unhelpful to have an easy way of remembering “facts” that are not true. The raison d’être of the periodic table is to reflect the properties of the real chemical elements ... which the “f-block, d-block, etc.” presentation does not. |
| The numbers that specify the width of the blocks (2, 6, 10, and 14) are the same numbers we encounter in atomic physics. | Numerology is not science. See the discussion of fencepost errors, below. |
| The block-structured periodic table appears in many textbooks. | Dogma is not science. |
At the next level of detail, we should consider the following points:
All in all, it does not appear that calcium’s claim on the eka-magnesium slot is particularly stronger than zinc’s claim.
Similar words apply to strontium versus cadmium.
Similar words apply to yttrium versus indium, and to thallium versus the lanthanoids.
Similar words apply to actinium versus lawrencium.
When I say two elements have “comparable claims”, that is based on solid theory (section 5) and on observation (section 4). It is easy to understand in terms of atomic physics why a completely filled shell should behave very similarly to a completely empty shell, as discussed in section 5. This is supported by innumerable observations, as discussed in section 4. Applying this idea to the present discussion, we find that La and Lu are the same, except that one has a completely empty 4f shell, while the other has a completely full 4f shell. Theory predicts that they should be chemically very similar, and this is in fact observed. It is hard to imagine why anyone would put them in different “blocks”.
One should never support a strong argument with a weak one, but it is amusing to note that about half of the schemes collected in reference 2 put La (not Lu) below Y, and about half do it the other way. This suggests that nobody has a very convincing reason why either way is better. In my opinion, both are equally wrong.
All lines of evidence suggest we should represent the periodic table as a cylinder with bulges. This has the advantage of giving La and Lu equal status as members of the bulge below Y.
I am comfortable talking about 15 lanthanoids and 15 actinoids, as illustrated in figure 4, because the concept is well supported by the data and the theory. In contrast, I have never willingly used the term “f-block elements" except in scare quotes, because the concept is not well supported by the data, nor by legitimate theory (where by ‘legitimate’ I mean to exclude numerology).
The existence of the lanthanoid series is related to the filling of
the atomic f-orbital.
– Yes, there are at most 14 f-electrons in any given atom.
– No, that does not mean there are at most 14 lanthanoids.
The square directly below yttrium in figure 3 can be called the eka-yttrium square. As discussed in more detail in section 5, the entire lanthanoid series can be fairly well decribed as eka-yttrium plus some number of f-electrons. The point is, when we say “some number” of f-electrons, the number runs from 0 to 14 inclusive, for a total of 15 possibilities, i.e. 15 lanthanoids.
Let’s be clear about the arithmetic: if you have items labelled 0 to 14 inclusive, that makes 15 items. This is not a chemistry issue. This is not a physics issue. This is just arithmetic. (If you get this wrong, it’s called a fencepost error. See reference 5.)
I emphasize this because many people who ought to know better believe there are only 14 lanthanoids. This is pretty astonishing, especially considering that to arrive at such a misconception you need to make at least two mistakes. That’s because the right answer is well supported by data as well as theory. So to get the wrong answer you have to ignore the data and then misunderstand the theory.
Some periodic tables, to their discredit, make this mistake quite explicit. Reference 3 labels La as an f-block element (color-coded green) and labels Lu as a d-block element (color-coded red).
In contrast, to its credit, IUPAC (reference 6) lists all 15 lanthanoids together, leaving a hole in the eka-yttrium square, as we have done in figure 3.
If you do the physics right, it tells you that there are 15 lanthanoids. They can be reasonably well described as eka-yttrium with some number of f-electrons, where the number runs from 0 to 14 inclusive.
Those who propose a 14-element “f-block" are free draw their periodic tables any way they like, and they are free to color-code their “f-block" elements any color they like. But they should not expect Mother Nature to pay any attention to what they have done.
It just cracks me up when people who don’t understand atomic physics try to claim that figure 7 is based on physics. Let’s be clear:
If you do the physics right, it agrees with the observed chemistry.
To get a feeling for the sort of engineering that goes into the design of a periodic table, consider the hypothetical alternative versions shown in figure 8 and figure 9. The transition elements start one element earlier and end one element earlier, compared to the “standard” version presented in section 1. Consider the comparison:
| Standard statement: 21Sc and 31Ga have an equally good claim to sit directly below aluminum. | Alternative statement: 20Ca and 30Zn have an equally good claim to sit directly below magnesium. |
Neither statement is significantly better or worse than the other.
We cannot continue this process another step in either direction. That is, nobody thinks 19K is closely analogous to 29Cu, and nobody thinks 22Ti is closely analogous to 32Ge (although it is possible to have TiF4 in analogy to GeF4).
Loosely speaking, the story that goes with figure 9 is that we can describe calcium through zinc as being eka-magnesium plus some number of d-electrons, where the number runs from 0 to 10 inclusive. This story is not nearly so precise as the corresponding story about the lanthanoids, because the transition-metal d-electrons are vastly more chemically active than the lanthanoid f-electrons. Also, this version of the story does not fit the data any better than the more conventional version based on eka-aluminum, as mentioned in connection with figure 3.
Actually, the hypothetical version is slightly disadvantageous for some purposes. For one thing, the color-coding of the lanthanoids in figure 10 wrongly suggests they are more akin to the divalent alkaline earths than they are to the often-trivalent transition metals. Partly this means that the hypothetical color coding is wrong, but it is also a hint that the hypothetical columns are not lined up optimally.
When designing a periodic table, we cannot escape the fact that the potassium row is ten elements longer than the sodium row, so we need to stick the extra elements somewhere. We should choose somewhere that does not unduly disrupt the vertical correspondences in the table (alkali metals all in the same column, halogens all in the same column, et cetera). We also need to preserve the ordering of the elements, i.e. in order of atomic number. This last requirement is tricky. It cannot be based solely on simple chemical data, because many important chemical properties – notably the valence of the transition metals – are complicated non-monotonic functions of atomic number.
Let’s combine the ideas of section 7 with section 1. In particular let’s retain both the gap under Al from figure 2 and the gap under Mg from figure 8. The result is shown in figure 11.
That leaves us with 12 columns of elements to patch into this double-width gap, as shown in figure 12.
According to this arrangement, the 12 elements from 20Ca through 31Ga inclusive can be described as eka-magnesium or eka-aluminum plus some number of d-electrons, where the number runs from 0 through 10 inclusive.
This description has some strengths and some weaknesses. The strengths include the following: In the first row of figure 12, starting from the left of the row we have K–Ca–Sc whose observed behavior fits nicely under Na–Mg–Al, so the table is faithful to reality in this regard. Similarly at the right end of the top row, we have Zn–Ga–Ge whose observed behavior fits nicely under Mg–Al–Si, so this is another place where the table is faithful to reality.
The weaknesses are concentrated in the middle columns of figure 12. As an extreme example, the observed chemistry of chromium is not what you would expect from eka-magnesium or eka-aluminum. Forsooth chromium does not behave like eka-anything, so any attempt at a faithful periodic table is going to have problems. This is understandable, because the d-electrons are not chemically inert. In any case, though, figure 11 makes at least as much sense as figure 2, and more sense than figure 8.
The design principle here harks back to Hippocrates: “First, do no harm.” In this case that means that when there are two comparably-good claimants to a particular spot in the table, rather than arbitrarily choosing one and hanging the other out to dry, it is better to put a patch over the contested spot, so that the patch can show both contenders on an equal footing.
The diagrams in section 10 are available in Scalable Vector Graphics (.svg) format, and also in Encapsulated PostScript (.eps). Both are modern open standards. Using a scalable format means you can shrink or enlarge the diagram as much as you want without losing any detail.
To download the scalable files, click on the [svg] link or the [eps] link at the right side of the caption.
You should then be able to read your copy of the file into any image processing program worthy of the name, rescale it, and write it back out again. The .svg format is better for embedding in HTML documents; the firefox browser can render .svg natively. Meanwhile, the .eps format is more widely recognized by other applications.
In this section, the first three figures – namely figure 13, figure 14, and figure 15 – are periodic tables that display some basic data for each element, namely
The color coding in these three figures reflects the element’s position within the period.
Figure 16 is the same as figure 14 except that it doesn’t use color. This is useful if you have a printer that doesn’t reproduce color.
In figure 17, the bottom row in each cell shows the first ionization potential. Also, the color coding is based on the first ionization potential.
When closing the main group piece into a cylinder, it helps to have a mandrel that you can slip inside the model and push against. I have a chair that has an arm that works well for this. You can also build something suitable using a chem-lab clamp stand.
Closing the hydrogen group piece into a cylinder is even trickier, because it is so small. A pen, pencil, or paintbrush-handle might make a suitable mandrel, if you can find one that is round, not tapered, and not too big around. Another option is to buy a small dowel rod at the hardware store. You can hold it in place with a clamp-stand, or C-clamp it to a table. Some people use it freehand like a rolling pin, but this requires some deft technique.
Attaching to the mandrel some slightly sticky stuff such as the sticky part of a Post-It note is helpful. Don’t use anything too sticky, or you’ll have a hard time getting the model off the mandrel.
The term rare earth is also widely used. It is often used to refer to the lanthanoids and actinoids collectively, but historically it had a different meaning, namely the set consisting of scandium, yttrium, and the 15 lanthanoids (without the actinoids). See reference 7 for more about this.
As for the actinoids, uranium is more abundant than tin, and thorium is even more abundant than that. The other actinoids are have very little, if any, natural abundance.
For key data on any given element, click on that element. For example, the key data page for La is http://www.webelements.com/webelements/elements/text/La/key.html On that page, a list of typical compounds can be found in the far-right column.
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