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ATOMIC ALGEBRA

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It was the work of the English chemist John Dalton at the beginning of the nineteenth century that provided the first real experimental justification for thinking of matter as made of indivisible atoms. His discovery that compounds seemed to be made up of substances that were combined in fixed whole-number ratios was the breakthrough, and it led to the scientific consensus that these substances really did come in discrete packages.

For example: ‘The elements of oxygen may combine with a certain portion of nitrous gas or with twice that portion, but with no intermediate quantity.’ It certainly didn’t constitute a proof that matter was discrete, and it was not strong enough to knock the belief of those who favoured a continuous model of matter. But it was highly suggestive. There had to be some explanation for the way these substances were combining.

The notation developed to express these reactions added to the atomistic view. The combination of nitrogen and oxygen could be expressed algebraically as N + O or N + 2O. There was nothing in between. It seemed that all compounds came in proportions that were whole-number ratios. For example, aluminium sulphide was given algebraically as 2Al + 3S = Al2S3, elements combining in a 2-to-3 ratio. Elements never combined in a non-whole-number relationship. It was like musical harmony at the heart of the chemical world. The music of tiny spheres.

The Russian scientist Dmitri Mendeleev is remembered for laying out this growing list of molecular ingredients in such a way that a pattern began to emerge, a pattern based on whole numbers and counting. It seemed that the Pythagorean belief in the power of number was making a comeback. Like several scientists before him, Mendeleev arranged them in increasing relative weight, but he realized that to get the patterns he could see emerging he needed to be flexible.

He’d written the known elements down on cards and was continually placing them on his desk in a game of chemical patience, trying to get them to yield their secrets. But nothing worked. It was driving him crazy. Eventually he collapsed in exhaustion and the secret emerged in a dream that, when he woke, gave him the pattern for laying out the cards. One of the important points that led to his successful arrangement was the realization that he needed to leave some gaps – that some of the cards from the pack were missing.

The key to his arrangement was something called the atomic number, which depended on the number of protons inside the nucleus rather than the combination of protons and neutrons that gave rise to the overall weight. But since no one had any clue yet about these smaller ingredients, Mendeleev was guessing somewhat at the underlying reason for his arrangement.

It was a bit like recognizing that a conventional pack of cards can be laid out in suits, but also that across those suits there are cards that are of equal value. A periodicity of eight seemed to underlie the elements, so that elements eight along seemed to share very similar properties. Eight on from lithium was sodium, followed after another eight by potassium. All soft shiny highly reactive metals. Similar patterns matched up gases with related properties.

This rule of eight had been picked up before Mendeleev’s breakthrough and was called the law of octaves. It was compared to the musical octave: if I play the eight notes of a major scale on my cello, the top and bottom notes sound very similar and are given the same letter names. When this law of atomic octaves was proposed by its originator John Newlands, it was laughed out of the Royal Society. ‘Next you’ll be trying to tell us that the elements can be understood by putting them in alphabetical order,’ joked one Fellow. Mendeleev’s arrangement confirmed to a certain extent the veracity of this law of octaves. It was this idea of repeating or periodic patterns that led to Mendeleev’s arrangement being called the periodic table.

Mendeleev’s genius was to realize that if sometimes the elements didn’t quite match up, it perhaps indicated a missing element. The gaps in his table were probably his most insightful contribution. The fact that there was a hole in the 31st place of his table, for example, led Mendeleev to predict in 1871 the existence and properties of a new substance that would later be called gallium. Four years later French chemist Lecoq de Boisbaudran isolated the first samples of this new atom, predicted thanks to the mathematical patterns discovered by Mendeleev.

What We Cannot Know

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