Before attempting to answer the title question, we should be clear about what the term ‘periodicity’ actually means—and where better to turn for an explanation than the matchless OED. The entry under ‘chemistry’ is the most relevant, viz. ‘The complex periodic variation of the properties of the chemical elements with increasing atomic number’, the term’s use in this context dating from the nineteenth century. This was, of course, the time of the so-called chemical revolution and is, therefore, a good place to begin.
In fact, the chemical revolution started a little before the nineteenth century with the work of Antoine Lavoisier. Of his many contributions during the 1780s, one of the most important was to define a chemical element as a substance which cannot be further decomposed by chemical means. Soon after came John Dalton’s atomic theory (in the early 1800s) in which he proposed not only that all matter is made of atoms but that atoms have weight and, furthermore, that atoms of different elements (he accepted Lavoisier’s definition) have different weights. Accurate atomic weights (strictly, relative atomic weights) were not that easy to determine but following the Karlsruhe Congress organised by Stanislao Cannizzaro in 1860, a list of atomic weights for most of the sixty-odd elements then known became widely accepted. Such a list was important for many reasons but not least for the subsequent development of the periodic table which orders the elements according to their atomic weight (later by atomic number) but also in a manner that reflects their observed chemical similarities.
With regard to these similarities, it was Johann Döbereiner who, in the 1820s, drew attention to certain resemblances within particular groups of three elements (Döbereiner’s triads)—lithium, sodium, potassium and chlorine, bromine, iodine, for example. Additional groupings, some with more than three members, were later highlighted by others but by the 1860s several chemists had also begun to notice underlying regularities. Among them was John Newlands, who recognised that for the first fifteen elements known at that time (hydrogen to chlorine; helium and neon had not yet been discovered), chemical similarities were observed to repeat every eight elements, which he codified as the Law of Octaves. In just a few years, tables depicting further regularities were constructed with many more elements, most notably by the Russian chemist Dmitri Mendeleev, who published his first periodic table in 1869. (For an excellent history of the periodic table, see: The Periodic Table: Its Story and its Significance, 2nd edition, E. Scerri, Oxford University Press, 2020.)
It should not be forgotten that in these early periodic tables, the regular arrangement of elements according to their chemical similarities was entirely based upon empirical observations. But why should there be any such similarities and, moreover, why should these similarities occur in a regular or periodic manner? Something at a fundamental level must repeat, albeit imperfectly, but in the nineteenth century, it was entirely unclear what the nature or origin of this repeat might be.
By the end of the nineteenth century most chemists accepted that matter was indeed made of atoms, but it would soon be determined that atoms were not indivisible: they had structure. A model of the atom in which most of its mass, along with its positive charge, was concentrated in a tiny nucleus around which were distributed the much lighter, negatively charged electrons (discovered by J. J. Thomson in 1897) was proposed by Ernest Rutherford in 1911. Not long after, it was established that elements were better ordered according to the number of units of positive charge in the nucleus (later identified with the number of protons present), the so-called atomic number, rather than according to atomic weight (the number of protons plus neutrons).
At around this time, it was also revealed, principally by the Danish physicist Niels Bohr, that electrons in atoms occupied discrete shells, the reasons for which would emerge from the nascent quantum theory. As this theory developed it was established that these shells could accommodate up to a certain number of electrons but no more, initially two with a maximum of eight allowed in the next shell. Accordingly, we can represent the electronic structure of, for example, lithium (which has three electrons) as Li (2,1) whereas sodium (which has eleven electrons) would be denoted as Na (2,8,1). Thus, each has one outermost electron which accounts for why their chemistry is similar, albeit not identical; the chemistry of an element is determined in large part by the number of outer electrons.
Of course, it’s a bit more complicated than this (actually quite a lot more complicated) but at a fundamental level quantum theory allows us to understand the origins of chemical periodicity according to the electronic structure of atoms—ultimately providing the answer to the title question: why does the chemistry of some elements resemble the chemistry of others?
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