“L A république n’a pas besoin de savants ni de chimistes.” With that curt dismissal a court in revolutionary France cut short the life of Antoine-Laurent de Lavoisier, argued by some to be the greatest chemist of all. Lavoisier’s sin was tax farming. He had been a member of the firm that collected the monarchy’s various imposts and then, having taken its cut, passed what remained on to the royal treasury. That he and many of his fellow farmers met their ends beneath a guillotine’s blade is no surprise. What had distinguished Lavoisier from his fellows, though, was what he chose to spend his income on. For much of it went to create the best-equipped chemistry laboratory in Europe.

Nothing comes of nothing. Where the story of the periodic table of the elements really starts is debatable. But Lavoisier’s laboratory is as good a place as any to begin, for it was Lavoisier who published the first putatively comprehensive list of chemical elements—substances incapable of being broken down by chemical reactions into other substances—and it was Lavoisier and his wife Marie-Anne who pioneered the technique of measuring quantitatively what went into and came out of a chemical reaction, as a way of getting to the heart of what such a reaction really is.

Lavoisier’s list of elements, published in 1789, five years before his execution, had 33 entries. Of those, 23—a fifth of the total now recognised—have stood the test of time. Some, like gold, iron and sulphur, had been known since ancient days. Others, like manganese, molybdenum and tungsten, were recent discoveries. What the list did not have was a structure. It was, avant la lettre, a stamp collection. But the album was missing.

Creating that album, filling it and understanding why it is the way it is took a century and a half. It is now, though, a familiar feature of every high-school science laboratory. Its rows and columns of rectangles, each containing a one- or two-letter abbreviation of the name of an element, together with its sequential atomic number, represent an order and underlying structure to the universe that would have astonished Lavoisier. It is little exaggeration to say that almost everything in modern science is connected, usually at only one or two removes, to the periodic table.

The mighty atom

The Lavoisiers’ careful measurements had discovered something now thought commonplace—the law of conservation of matter. Chemistry transforms the nature of substances, but not their total mass. That fact established, another Frenchman, Louis-Joseph Proust, extended the idea with the law of definite proportions. This law, published in 1794, the year of Antoine Lavoisier’s execution, states that the ratio by weight of the elements in a chemical compound is always the same. It does not depend on that compound’s method of preparation. From there, it might have been a short step for Proust to arrive at the idea of compounds being made of particles of different weights, each weight representing a specific element. But he did not take it. That insight had to wait for John Dalton, a man who was the polar opposite of the aristocratic bon vivant Lavoisier. Dalton’s parents were so poor that he had been put to work at the age of ten. The man himself was an ascetic, colour-blind Quaker. And he was English.

Dalton lived in Manchester, at a time when it was the world’s largest industrial city. He made a modest living tutoring, but spent most of his energy on scientific research, including into colour-blindness, a condition still sometimes referred to as Daltonism. That inquiry came to nothing. But during the first decade of the 19th century he took Proust’s concept and showed not only that elements reacted in fixed proportions by weight, but also that those proportions were ratios of small whole numbers. The simplest way to explain this—and indeed the way that Dalton lit upon—was to suppose each element to be composed of tiny, indivisible particles, all of the same weight. The Greek word for indivisible is “atomos”. Thus was the atom born.

Dalton based his system of relative atomic weights on hydrogen, the atoms of which he found to be the lightest. And it was quickly picked up by someone who, though less famous than Lavoisier, perhaps because of his grisly end, was arguably the greater man. Jacob Berzelius, a Swede, furnished chemistry with its language. It was he who came up with the idea of the abbreviations that now occupy the periodic table’s rectangles. It was he who combined those abbreviations with numbers, indicating the proportions involved, to make formulae for chemical compounds: H 2 O (water), H 2 SO 4 (sulphuric acid), NaCl (table salt). And it was he who used these formulae to describe reactions: H 2 SO 4 + Zn→ZnSO 4 + H 2 (sulphuric acid plus zinc becomes zinc sulphate plus hydrogen). Though Dalton invented atomic theory, it was Berzelius who embedded it at the heart of the subject.

And Berzelius did more. He used Alessandro Volta’s recently invented battery, which created electricity from a chemical reaction, to do the reverse. He employed electricity to drive chemical reactions in solutions (for example, releasing metallic copper from a solution of copper sulphate), a process called electrolysis.

Back in England, Humphry Davy, inventor of the miner’s safety lamp, picked up the idea of electrolysis and supercharged it. He employed a more powerful version of Volta’s battery to decompose molten materials, rather than solutions. In this way he discovered sodium and potassium in 1807 and magnesium, calcium, strontium, barium and boron in 1808. He also showed that chlorine, previously thought to be a compound of oxygen, was actually an element.

After Davy’s work new elements began to flow in thick and fast. Iodine (1811). Cadmium and selenium (1817). Lithium (1821). Silicon (1823). Aluminium and bromine (1825). By then there were enough of them for the next step on the journey to be taken.

It had been apparent from the time of their discovery that sodium and potassium were similar, as were calcium, strontium and barium. Lithium, when discovered, proved similar to sodium and potassium. Likewise, bromine and iodine proved similar to chlorine. In 1829 Johann Dobereiner, a German, noticed a curiosity about these trios (members of groups now known, respectively, as alkali metals, alkaline earths and halogens), and also another triplet that shared similar properties: sulphur, selenium and tellurium. In each case, if the members were arranged in order of atomic weight, the middle element (sodium, strontium, bromine, selenium) had a weight that was the average of the lightest and the heaviest of the three. Dobereiner called this the law of triads. It was the first hint of some underlying pattern.

The stamp collection continued to grow. Thorium was discovered in 1829 (by Berzelius, as it happened). Lanthanum followed in 1838, erbium in 1843 and ruthenium in 1844. Then, in 1860, Robert Bunsen, inventor of the burner that bears his name, showed how new elements could be recognised from brightly coloured lines in the spectra obtained when materials containing them were heated in a flame. This approach was an instant success. Bunsen and his colleague Gustav Kirchhoff added caesium (1860) and rubidium (1861) to the list. Others, copying them, added thallium (1861) and indium (1863). Spectroscopic analysis’s greatest triumph, though, was helium (1868). This was recognised not from a sample in the flame of a Bunsen burner but in the spectrum of the sun.

As more and more elements turned up, so the search for order intensified. In 1864 John Newlands, a Briton, almost got it. He published what he called the law of octaves. Arranging the known elements in order of atomic weight, he believed he had discerned that, like a musical scale, every eighth element “rhymed” in the ways that sodium rhymed with potassium, and chlorine with bromine.

The trouble with Newlands’ scheme was that an awful lot of the rhymes were forced. A glance at a modern periodic table shows why. For the tall, outer columns (and discounting hydrogen, which is a law unto itself) Newlands’ octaves work perfectly for the lightest elements then known. From the row beginning with potassium (K, from the Latin kalium, meaning potash), however, the tall outer columns are split asunder by the intrusion of ten other, shorter ones known as the transition metals. To deal with that intrusion using data then available required a mixture of luck and genius. And a few years after Newlands published, a lucky genius wrestled with the question in his study in St Petersburg.

Mendeleev

Albert Einstein, dapper in his youth, cultivated a waywardness of appearance in old age that has contributed to the trope of the mad professor. Dmitri Mendeleev (pictured) looked like that from the beginning—having his hair cut just once a year by a shepherd, using wool shears. He also behaved like a mad professor. He was prone to dancing rages that put one biographer in mind of the protagonist of “Rumplestiltskin”, a children’s fairy tale. Also like Rumplestiltskin he proved, metaphorically at least, able to spin straw into gold.

For a time, Mendeleev had worked in Germany with Bunsen and Kirchhoff, but he had fallen out with them and returned home. In 1869 he was professor of general chemistry at the University of St Petersburg and was writing a Russian-language textbook on the subject. On February 14th of the Julian calendar then in use in Russia (February 26th by the Gregorian calendar employed in most of the rest of Europe), having addressed halogens and alkali metals, he was racking his brains for an organising principle to act as a template for the rest. The 14th was a Friday, and the problem obsessed him more and more over the weekend. But on Monday 17th, while waiting for a sleigh to take him to the railway station for a trip to an estate he had bought in the countryside, he had a brainwave.

Mendeleev was an inveterate player of patience. His brainwave was to recognise that, just as games of patience require the player to organise the pack as a grid of suits in order of the value of the cards, so the elements might be arranged by their atomic weights in “suits” that shared chemical and physical properties. By making his own pack, with each card representing one of the 63 then-known elements, he was able to embark on what was arguably the most important game of patience ever played.

He claimed subsequently that the answer had come to him in a dream. Perhaps. But after having worked for four days on the problem without much rest, the boundary between sleep and wakefulness must have been pretty blurred. Whatever the details, the result was a grid of cards that arranged the elements in a pattern (see picture). He published it two weeks later.

Mendeleev’s dream

His grid was not perfect. Indeed, it was full of holes. But those holes (some of them, anyway) turned out to be keystones. Though there was no reason, in the 1860s, to believe that all the elements had been discovered, Newlands had behaved as though they had been. Mendeleev had enough confidence to leave gaps in order to make the pattern work. At the time, some took this as a sign of weakness. In fact, it was a sign of strength—the more so because, for several of the gaps, he described in detail the properties of the elements he predicted would fill them, and these predictions were, by and large, fulfilled.

Similarly, there are places in Mendeleev’s original table where it works only by cheating—that is, by swapping two adjacent elements between the places to which their atomic weights assign them. Here, Mendeleev argued that the accepted weights were incorrect, and needed re-measuring. Sometimes, he turned out to be correct about this, too. But not always. A few such pairs, cobalt and nickel for example (which actually share a slot in the published table), remained stubbornly out of kilter, providing evidence that atomic weight was really a proxy for some deeper structural principle

Crucially, Mendeleev was not constrained, as Newlands had been, by preconceptions about how things ought to be. At points where the octave rule did not work, he let the grid burst out of its corset. This can be seen at both the top and the bottom of the published table.

The upper-right-hand extension contains the transition metals. Here, subsequent discoveries have proved Mendeleev more or less correct in his insights. The lower-left-hand one is more problematic. Its contents are a grab bag, though it does contain all of the then-known members of the set of elements called lanthanides. Arguably, Mendeleev was lucky that by 1869 only three lanthanides had been discovered. In a modern table there are 15 and, together with the actinides below them, they form an awkward interpolation that is often relegated to the bottom as an asterisked footnote. Whether Mendeleev’s game of chemical patience would have been helped or hindered by having more lanthanides in the pack is an intriguing question.

There was also an invisible gap, the filling of which was one of the table’s greatest triumphs. Helium, which Mendeleev ignored because its atomic weight could not be established, turned out to be the lightest member of a whole, new row (or column, in a modern table). These are the noble gases, undiscovered previously because they are chemically inert. The others are neon, argon, krypton, xenon and radon.

Like Davy’s discoveries, the noble gases came all of a tumble. All but radon were the work of William Ramsay, a Briton. With various collaborators, Ramsay isolated argon in 1894, helium in 1895 and neon, krypton and xenon in 1898. Instead of chemistry, he used physical processes. All except helium were products of the newly developed technology of cryogenics, which he used to liquefy air and then separate it into its components, according to their boiling points. Helium, he found by heating a mineral called cleveite.

The transmutation of the elements

The 1890s also saw the first inklings that atoms themselves might not, despite the meaning of their name, be truly indivisible. The initial evidence that atoms could spin off parts of themselves, and must therefore have smaller components, came in 1896. That was when Henri Becquerel, who was investigating the nature of phosphorescence, wrapped some uranium salts in photographic paper and found that the paper got fogged. Thus did Becquerel discover radioactivity.

The following year, J.J. Thomson worked out that “cathode rays” emitted into a vacuum by a negative electrode were electrically charged particles that weighed far less than any atom. Then, in 1899, Ernest Rutherford, a former student of Thomson’s, showed that Becquerel’s radiation had two components, which he dubbed “alpha” (heavy, positively charged particles) and “beta” (light, negatively charged ones).

There’s antimony, arsenic, aluminum, selenium. And hydrogen and oxygen and...

Becquerel himself, in 1900, showed that beta particles were the same as Thomson’s cathode rays. Seven years later, Rutherford demonstrated that alpha particles were helium ions (thus incidentally explaining why cleveite, which is an ore of uranium, is also a source of helium). The stage was now set for some of the most important experiments in history: Rutherford’s attempts to find out what atoms looked like.

One previous guess had been that they were vortices in the luminiferous aether through which light and radio waves were thought to propagate. That hypothesis, however, died with the aether itself, when the latter’s existence was disproved experimentally in the 1890s. Rutherford’s experiments, conducted between 1908 and 1910, probed matter by firing alpha particles at gold foil. Most sailed through, to be recorded by a scintillation screen beyond the foil. But a few were deflected from their courses, to be recorded by other screens, including one behind the source. This screen’s recording of alpha particles returning whence they had come was described by Rutherford as being “almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you”. His explanation, now abundantly proved true, was that the atoms in the foil had tiny, positively charged nuclei, which were reflecting the positively charged alpha particles, and that these nuclei were surrounded by electrons.

Regardless of an atom’s exact nature, losing alpha and beta particles necessarily changes it. Such radioactive decay proved a source of yet more members of the periodic table. Polonium and radium—decay products of uranium—were found in 1898 by Pierre and Marie Curie. Actinium, the lightest actinide, followed in 1899. Radon was recognised in 1900. Protactinium in 1913.

Models of the atom also became more sophisticated. In 1913, Rutherford and a Danish colleague, Niels Bohr, suggested electrons orbit the nucleus as planets orbit the sun, with electrical attraction playing the role of gravity. In the same year Henry Moseley, another of Rutherford’s confrères, found a mathematical relationship between an element’s X -ray spectrum when bombarded with electrons and its atomic number in the table. In pairs like cobalt and nickel, where the table had been fudged, Moseley confirmed the fudges to be correct. He tidied up the lanthanides, predicting missing elements as Mendeleev had done. He also predicted two new transition metals, with atomic numbers 72 and 75, which duly turned up in 1923 (hafnium) and 1925 (rhenium).

Moseley’s X -ray spectra demonstrated that an element’s atomic number does not depend directly on its atomic weight. Rutherford soon showed that the atomic number is actually the number in a nucleus of a positively charged particle that came to be known as a proton. Even though protons weigh almost 2,000 times as much as electrons, the two have equal (though opposite) charges. An atom, which has equal numbers of both, is therefore electrically neutral. Protons are not, though, heavy enough to account for measured atomic weights. That requires a second, electrically neutral particle, the neutron. This was discovered in 1932. Neutrons are also the reason that an element can have atoms of different atomic weights, known as isotopes. These isotopes have different numbers of neutrons.

The Bohr-Rutherford model of the atom had a problem, though. Electrostatic forces should pull the electrons into the nucleus rather than keeping them in orbit. Here, the new science of quantum mechanics came to the rescue. Quantum theory requires objects to be both particles and waves. The wavelike aspect of electrons means that when they circle an atomic nucleus they settle into self-reinforcing three-dimensional standing waves, called orbitals. The stability of these standing waves stops the electrons being drawn into the nucleus. And here, at last, is the explanation for why the periodic table is the way that it is.

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For reasons deep in the heart of quantum mechanics, each orbital can have either one or two electrons in it, but not more. The orbitals themselves come in different types (see diagram) and these are arranged in shells around a nucleus. The first shell has one type “s” orbital, for a maximum of two electrons. The second, a type s and three type p, for a maximum of eight. The third has one s, three p and five d, for a maximum of 18. The fourth, one s, three p, five d and seven f, for a maximum of 32. Et cetera. The names are derived from the spectral lines seen by Bunsen and his followers. The colours of these lines represent energy released as light by electrons moving between orbitals.

It is the shells that define the table’s rows. In the first row, which consists of hydrogen (one electron) and helium (two), the first shell is filled up. In the second row, from lithium to neon, the second shell is filled. The third row, from sodium to argon, fills the s and p orbitals of the third shell. The fourth, from potassium to krypton, fills the s and p orbitals of the fourth shell and the d of the third shell (which has ten electrons altogether, for the ten columns of transition metals).

Compounds are created either by unpaired electrons from different atoms forming joint orbitals called covalent bonds, or by the complete transfer of unpaired electrons between atoms, to create paired orbitals in the recipients. When this happens, the resulting positive and negative ions are held together by electrostatic forces—a process called ionic bonding. The repetitive order in which the shells are filled in each row means that elements in each column of the table have the same combination of unpaired electrons, and thus similar properties. For example, the noble gases are inert because they have no unpaired electrons. Further analysis showed, moreover, that the difference between metals and non-metals depends on how easy an atom’s outer electrons are to detach (if easily detached, they can flow as an electric current, reflect light in the way that makes metals shiny, and confer ductility on the solid form of the element). And that, essentially, is chemistry solved.

It is not quite, however, the end of the story. In the 1930s physicists discovered that radioactivity could, in essence, be reversed by bombarding atoms with subatomic particles to increase their atomic numbers. This way, new elements can be produced. Technetium, created in 1937, was the first such. Two years later francium, the last to be discovered in nature, was isolated as a decay product of actinium. From that moment the extension of the periodic table became work for physicists, not chemists.

Technetium is strange. Despite its low atomic number (43) it has no stable isotopes, and is thus found only transiently in nature. This is a quirk of the physics of protons and neutrons that it shares with promethium (61). But at the heavy end of the table, beyond lead (82), radioactivity is compulsory for all. And beyond uranium (92) it is so compulsory that “transuranics” were once thought not to occur in nature.

This part of the periodic table was the playground of Glenn Seaborg, an American physicist. In 1940 Seaborg was part of a group at the University of California, Berkeley, that made neptunium (93). When the group’s head left later that year, Seaborg took over. On his watch americium (95), curium (96), berkelium (97), californium (98), einsteinium (99), fermium (100), mendelevium (101) and nobelium (102) were all created. But his first discovery, plutonium (94, in 1941), was the most important. On July 16th 1945, the first atom bomb, a plutonium-implosion device, was tested at Alamogordo, New Mexico. On August 9th of that year another of the same design destroyed Nagasaki, in Japan.

Americium has its uses, too. Since it was a synthetic product, it was patentable, and Seaborg did, indeed, patent it. It was (and is) employed in smoke detectors, and he drew a tidy income from that fact for many years. Beyond 95, though, the practical point of extending the table became less and less obvious as elements became less and less stable.

Efforts to make new elements slowed down after 1955, though there was a pick up again in the mid 1990s. Neither chemistry nor the wider world, however, reverberated with excitement at the creation of darmstadtium (110), roentgenium (111), copernicum (112) and nihonium (113) in the way that they had with the discovery of potassium, or helium, or radium or plutonium. What started as stamp collecting has returned to its roots—except in one regard. This is that, thanks to Mendeleev’s brilliance, element-hunters now have an album in which to stick their discoveries.

The heaviest element of all, oganesson (118), was created in 2002, though named only in 2016. Oganesson completes the table’s seventh row. Chemically, it should be a noble gas. But, with only a few atoms of it to play with at a time, and with those atoms having lifetimes measured in milliseconds, it seems improbable anyone will ever know for sure.

Despite physicists’ best efforts, then, the eighth row has not been reached. But as Mendeleev himself said, “To conceive, understand and grasp the whole symmetry of the scientific edifice, including its unfinished portions, is equivalent to tasting that enjoyment only conveyed by the highest forms of beauty and truth.” For those who share this view, and see in the periodic table a supreme example of nature’s poetry, the row-completing, album-filling addition of oganesson may seem as good a place as any to stop.