Understanding Nuclear Power, #2: THE PERIODICITY OF THE ELEMENTS

Larry Hecht April 21, 2006

[Figures for this pedagogical can be accessed at: www.wlym.com/~bruce/periodic.zip]

Dmitri Mendeleyev discovered the concept of the periodicity of the elements in 1869 while he was in the midst of writing a textbook on inorganic chemistry. The crucial new idea, as he describes it, was that when the elements are arranged in ascending order of their atomic weights, rather than simply increasing in some power or quality, he found periodically recurring properties. Mendeleyev noted explicitly that this discovery led to a conception of mass quite different from that in the physics of Galileo and Newton, where mass is considered merely a scalar property (such as F = ma). Mendeleyev believed that a new understanding of physics would come out of his chemical discovery. It did, in part, in the developments that led into the mastery of nuclear processes, even if the flawed foundations of the anti-Leibnizian conceptions injected by British imperial hegemony were never fully remedied. The development of the sort of conception connected with Dr. Robert Moon’s nuclear model will help to fulfill Mendeleyev’s insight on this account.

There are just 92 naturally occurring elements in the universe. Their existence and organization in the periodic table discovered by Mendeleyev is the most fundamental fact of modern physical science. We will soon see how the discovery of radioactivity and nuclear power, among so many other things, would not have been possible without the prior achievement of Mendeleyev. Let us first get a general idea of what the periodic table is, and then examine some of the considerations which led Mendeleyev to his formulation.

The periodic table systematizes the 92 elements in several ways (Figure 1). The horizontal rows are known as {periods} or {series}), and the vertical columns as {groups}. The simplest of the organizing principles is that the properties of the elements in a group are similar. Among the many properties which elements in a group share: Their crystals, and the crystals of the compounds which they form with like substances, usually have similar shapes. Elements in the same group tend to combine with similar substances, and do so in the same proportions. Their compounds then often have similar properties. Thus sodium chloride (NaCl) which is table salt and potassium chloride (KCl) combine in the same 1:1 proportion, and show similar chemical and physical properties. Partly because they tend to make the same chemical combinations, the members of a group and sometimes adjacent groups, are often found together in ore deposits in the Earth. For example, copper usualy occurs in ores with zinc and lead, or with nickel and traces of platinum. If you look at a periodic table, you will see these elements in nearby adjacent columns. Or for another example, when lead is smelted, trace amounts of copper, silver, and gold (which occupy a nearby column to the left), and arsenic (in the adjacent column to the right) are found. We will look at more of these sorts of relationships shortly.

(To prevent confusion, we should interject this note of warning. When the periodic table is taught in the schools today, it is usually presented as an ordering principle for the electron shells which are thought to surround the nuclei of atoms. The modern explanation of chemical reactions invokes the interaction of the outer electrons in these shells. It is important to understand that at the time of Mendeleyev’s discovery, no chemist had any idea of the existence of an atomic nucleus nor electrons. The electron was considered as a theoretical entity in the electrodynamic work of Wilhelm Weber (1804-1891), but this had little to do with chemical thinking at the time. The first approximate measure of the mass of the electron came in the first decade of the 20th century, and the validation of its wave properties came in 1926. In the prevailing view of the atom at the opening of the 20th century, there was no central nucleus, but rather a homogeneous spread of charges. Thus, to understand how Mendeleyev came to his discovery of the periodic table in 1869, we must discard most of what we might have learned of the subject from modern textbooks. If we feel a slight pang of remorse in giving up what little we think we know of the subject, we shall soon find that we are rewarded by a far greater pleasure in discovering how these discoveries really came about. We shall then also be at the great advantage of knowing where the assumptions lie which will surely need correcting to meet the challenges of Earth’s next 50 years.)

By arranging the elements in increasing order of their atomic weights, Mendeleyev found that they fell into periods which repeated themselves in such a way that elements possessing analogous properties would fall into columns one below the other. Within the periods, many properties, including the valences (defining the small whole number proportions in which the elements combine with each other), the melting and boiling points, and the atomic volumes (which we shall discuss further on) showed a progessive increase and decrease which was analogous for each period.

By examining these periodic properties, it was also possible to see that there were gaps in the table. Some viewed those gaps as a weakness in Mendeleyev’s hypothesis. But Mendeleyev was convinced the conception was right, and that the gaps represented elements still to be discovered. He worked out the probable properties of some of these unknown elements on the basis of their analogy to the surrounding elements. Within a few decades of Mendeleyev’s publication of his periodic concept, several of these missing elements were discovered.

For example, in the Fourth Group (the 14th in the enlarged numbering system adopted in 1984), below the column containing carbon and silicon, Mendeleyev saw that there must exist an element which was unknown at the time. He called it {eka-silicon,} the prefix {eka-} meaning {one} in Sanskrit. By looking at the properties of silicon above and of tin (Sn) below, and also of zinc and arsenic surrounding it, he could guess such properties as its atomic weight, the probable boiling point of some of its compounds, and its specific gravity. In 1886, C. Winkler from the famous mining center of Freiberg in Saxony found the new element in a mineral from the Himmelsfurt mine and called it Germanium. Its actual properties were found to correspond entirely with those forecast by Mendeleyev. There had also been a gap in the Third Group (the 13th in the new system) in the position just under the elements boron and aluminum. In 1871 Mendelyev had named this still unknown element {eka-aluminum.} In 1875, Lecoq de Boisbaudran, using techniques of spectrum analysis, discovered a new metal in a zinc blende ore from the Pyrenees. He named it Gallium. At first it semed to differ considerably from the density Mendeleyev had predicted it would have if it was indeed eka-aluminum. But as observations proceeded the new element was found to possess the density, atomic weight and chemical properties which Mendeleyev had forecast.

That is the essential concept of periodicity. In order for Mendeleyev to arrive at it a great deal of prior chemical investigation was required. Perhaps the most important prerequisite had been the discovery of new elements. The ancients knew 10 of the substances we call elements today, most of them metals. These were iron, copper, lead, tin, antimony, mercury, silver, gold, carbon, and sulfur.[fn 1] All but two of the rest were discovered in the modern era. Between 1735 and 1803, 13 new metals and four gaseous elements were discovered. In 1808 six new elements from the alkali and alkali metal groups (Group 1 and II) were discovered. [fn 2] And the discoveries continued through the 19th century, capped by Marie Curie’s isolation of radium in 1898. In 1869 when Mendeleyev conceived the idea of periodicity about two thirds of the 92 naturally occurring elements were known. Still a few more remained to be discovered in the 20th century. And then came the synthesis of the artificial elements beyond the 92 naturally occurring ones, beginning with neptunium and plutonium.

What do we mean by an element? Chemistry deals primarily with homogeneous substances, not differing in their parts. But the fact that a substance is the same in all its parts does not distinguish it as an element. Sulfur which we consider an element is a yellow powder or cake, but many compounds such as chromium salts can take on a similar appearance. Table salt is uniform and crystalline, but not an element. We consider hydrogen gas an element but carbon dioxide gas a compound. Sometimes elements are described as the elementary building blocks from which more complex substances are formed. But a better definition is the one Lavoisier gave, which describes an element as the result of an action, as that which cannot be further separated by chemical procedures:

“[I]f by the term {elements} we mean to express those simple and indivisible atoms of which matter is composed, it is extremely probable we know nothing at all about them; but, if we apply the term {elements,} or {principles of bodies,} to express our idea of the last point which analysis is capable of reaching, we must admit, as elements, all the substances into which we are capable, by any means to reduce bodies by decomposition. Not that we are entitled to affirm that these substances we consider as simple may not be compounded of two, or even of a greater number of principles; but, since these principles cannot be separated, or rather since we have not hitherto discovered th means of separating them, they act with regard to us as simple substances, and we ought never to suppose them compounded until experiment and observation has proved them to be so.” [fn 3] Lavoisier’s warning remains applicable today. By heeding it, we do not fall into the trap of supposing we are dealing with irreducible elementarities, for the history of scientific progress has shown that increasing mastery over nature always permits us to delve deeper into the microcosm. For chemical technology, the element was the irreducible substance. But later developments allowed us to reach down to the electron, the nucleus, and to subnuclear particles.

It was necessary to perform chemical operations on substances to know if they were elements or compounds. Many things that were once considered elementary were later found to be composite. Lavoisier’s study of the separation of water into hydrogen and oxygen gas, and their reconstitution as water is exemplary. Similarly, his demonstration that the atmospheric air consists primarily of oxygen and nitrogen gas. The metals that were discovered in the 18th century were mostly separated from their ores by processes of chemical reaction, distillation, and physical separation.

At the time Mendeleyev was writing his textbook experimenters had accumulated an enormous store of information concerning the properties of elements and their compounds. Especially of note were the many analogous properties among the elements and their respective compounds. For example, lithium and barium behaved in some respects to sodium and postassium, but in other respects to magnesium and calcium. Looking at such analogies as markers of an underlying ordering principle, Mendeleyev suspected that there must be a way to find quantitative, measurable properties by which to compare the elements. There were four different types of measurable properties of the elements and their compounds, which he took into consideration in formulating his concept of periodicity. He identifies these in Chapter 15 of his textbook as:

(a) isomorphism, or the analogy of crystalline forms; (b) the relations between the “atomic” volumes of analogous compounds of the elements; (c) the composition of their saline compounds; (d) the relations of the atomic weights of the elements.

Think of each of these types of properties as different means of “seeing” into the microcosm. Let us begin with the first, crystal isomorphism. When a compound is dissolved in water or some other solvent, and the water removed by evaporation or other means, it can usually be made to crystallize. All of the familiar gemstones and many rocks are crystals that have been formed under conditions present within or at the surface of the Earth. Table salt and sugar are familiar crystals. Most metals and alloys cool and harden in characteristic crystalline forms. Organic compounds, even living things like proteins, can be made to crystallize for purpose of analyzing their structure. With the development of chemistry following Lavoisier, the crystalline form began to receive more attention, and close study eventually showed that every compound crystallizes in a unique form. Many of these forms are quite similar, but careful measurement of the the facial angles and the proportional lengths of their principal axes will always show some slight difference. Crystallography thus became a means of chemical analysis, and by the 1890s there existed catalogues of the crystallographic properties of nearly 100,000 compounds. [fn 4]

Despite these very fine differences, the general forms of crystals fit into certain classifiable groups. Their shapes include the cube and octahedron, hexagonal and other prisms, and a great number of variations on the Archimedian solids, their duals, and many unusual combination forms. The German chemist Eilhard Mitscherlich first demonstrated in 1819 that many compounds which have similar chemical properties and the same number of atoms in their molecules also show a resemblance of crystalline forms. He called such substances isomorphous. He found that the salts formed from arsenic acid, (H3AsO4) and phosphoric acid (H3PO4), exhibited a close resemblance in their crystalline forms. When the two salts were mixed in solution, they could form crystals containing a mixture of the two compounds. Mitscherlich thus described the elements arsenic and phsophorous as isomorphous.

Following Mitscherlich a great number of other elements exhibiting crystal isomorphism were found. For example, the sulphates of potassium, rubidium and cesium (KSO4, RbSO4, CsSO4) were found to be isomorphic; the nitrates of the same elements were also isomorphic with each other. The compounds of the alkali metals (lithium, sodium, postassium, rubidium) with the halogens (fluorine, chlorine, bromine and iodine) all formed crystals which belonged to the cubic system, appearing as cubes or octahedra. The cubic form of sodium chloride (table salt) crystals is an example, as one can verify with a magnifying glass.

This was the first of the clues which suggested the concept of periodicity. When Mendeleyev arranged the elements in order of increasing atomic weights, the isomorphic substances were found to form one above the next in a single column. Thus arsenic and phosphorous were part of Group V (15, in the modern nomenclature). The alkali metals fell under Group I; the halogens became Group VII (17 in the modern nomenclature). Not only this, but the elements of the same groups combined with one another in the same proportions. Thanks to the work of Gerhardt and Cannizzaro in establishing a uniform system of atomic weights, it had become a simple matter to determine the chemical formula for a great number of substances, once the proportion by weight of the component elements had been determined. It thus turned out that the elements of the first group (designated R) combined with the elements of the seventh group (designated X) in the proportion RX, as in NaCl. The elements of the second group combined with those of the seventh group in the proportion RX2, as in CaCl2, and so forth. If the combinations with oxygen were considered (the oxides being very prevalent), the first group produced RO2, the second group RO, the thrid group R2O3, and so forth. This is what Mendeleyev is describing in the periodic chart we show in Figure 2. We shall save the fascinating question of the investigation of the atomic volumes and many other properties of the elements which prove to be periodic for another time, and end this exercise for now.


1. Mining and metallurgy was clearly a part of ancient science, though the thinking and discovery process is mostly lost to us. Heinrich Schliemann, the discoverer of Troy, suggests that the word “metal” came from Greek roots (met’ alla) meaning to search for things, or research. Archaeological remains indicate an ordering of discovery of the metals and the ability to work them, with copper and its alloys preceding iron for example. Ironworking is associated with the Hittite and Etruscan seafaring cultures of Anatolia and north central Italy, who spoke a common language related to Punic or Phoenician.

2. The four gaseous elements were hydrogen (Henry Cavendish, 1766); nitrogen (Daniel Rutherford, 1772); oxygen (Carl Scheele, Joseph Priestley, 1772); chlorine (Scheeele, 1774). Among the metals discovered in the 18th century were:

Platinum (Antonio de Ulloa, 1735); Cobalt (Georg Brandt, 1735); Zinc (Andreas Marggraf, 1746); Nickel (Axel Cronstedt, 1751); Bismuth (Geoffroy, 1753) Molybdenum (Carl Scheele, 1778); Zirconium (Martin Klaproth, 1778); Tellurium (Muller, 1782); Tungsten (Juan and Fausto d’Elhuyar, 1788); Uranium (Klaproth, 1789), Titanium (William Gregor, 1791), Chromium (Louis Vauquelin, 1797); Beryllium (Vauquelin, 1798)

In 1803, William Hyde Wollaston and Smithson Tennant found the elements rhodium, palladium, osmium and irridium in platinum ore. In 1808, Humphry Davy isolated the alkali elements sodium, potassium, magnesium, calcium, strontium, and barium by electrolysis of their molten salts.

3. Antoine Laurent Lavoisier, {Elements of Chemistry,} translated by Robert Kerr, in {Great Books of the Western World,} (Chicago: Encyclopedia Briitannica, 1952) p. 3.

4. In the history of physical chemistry, the study of crystals provided one of the first means of access to the microcosm. It continues to be of importance today.This is great fun because Kepler’s playful work {The Six-cornered Snowflake,} is actually the founding document of modern crystallography. The student must take advantage of this, for the topic, as presented in the usual textbooks, is a confusion of mathematical formalisms and systems of classification. In Kepler, we see that the question is really very simple: why is the snowflake six-sided? why is the beehive made from cutoff rhombic dodecahedra? How shall we get an answer? It can only be by attempting to shape our imagination in conformity with the mind of the creator. If we do not get the complete answer, we see, nonetheless, that it is through the playful exercise of the mind in advancing and pursuing hypothesis that we come closer to it.

Among the many discoveries presented in that small work, Kepler introduces the concept that the study of the close-packing of spheres, which copy the space-filling property of rhombic dodecahedra, can help to explain the mineral crystals, all of which exhibit the characteristic hexagonal symmetries. Kepler thus suggested the existence of an atomic or molecular structure within the abiotic domain. Kepler’s insights were carried forward in the study of mineral crystals especially by the work of the Abbe Hauy (1743-1822) in France, who was followed by a great number of other investigators.