What is an Element?

The question which forms the title of this blog has exercised the minds of thinkers for at least two and half millennia from early philosophical musings in classical times to more modern considerations, particularly following Lavoisier’s definition of a chemical element in the late eighteenth century. Fascinating though this history is, the purpose of this contribution is to focus very much on the present following some of the points raised in a recent (2026) article by Eric Scerri entitled “What is an Element, and How is it Defined in the IUPAC Gold Book?” [1,2]. In brief, Scerri argues that the standard definition of an element should make some reference to a nature that is, at least in part, abstract. However, it is argued here that whilst attributing certain abstract qualities to elements may be understandable from a historical perspective, there is no compelling case to be made for any such qualities in modern chemistry.

Let us start with precisely what the IUPAC “Gold Book” has to say on this matter [3]. Two points are noteworthy. The first is that the terms ‘element’ and ‘chemical element’, each of which has an entry in the “Gold Book”, are treated as synonyms and the second is that, as Scerri notes in his article, IUPAC actually provides two definitions, both of which are reproduced below [4].

1. A species of atoms; all atoms with the same number of protons in the atomic nucleus.

2. A pure chemical substance composed of atoms with the same number of protons in the atomic nucleus. Sometimes this concept is called the elementary substance as distinct from the chemical element as defined under (1), but mostly the term chemical element is used for both concepts.

Since the early twentieth century, a chemical element has indeed been characterised by the number of protons in the atomic nucleus (the so-called atomic number), a definition formalised by IUPAC in 1923. Gold, for example, has 79 protons in its nucleus which is one of the criteria used in assigning gold to its position in the periodic table. We should recognise that this definition makes no mention of the number of neutrons present in the nucleus and nor should it. Whilst properties such as chemical reaction rates and their associated rate constants do depend on atomic mass (i.e., the number of protons plus the number of neutrons) and hence differ for different isotopes (so-called kinetic isotope effects), these differences are generally small and more fundamental properties such as an element’s chemical valence(s) and its position in the periodic table (i.e., its chemistry) are not determined by the number of neutrons present [5]. What of IUPAC’s second definition? There is no doubt that the first sentence captures what many chemists usually mean when they’re talking about a chemical element although the second sentence offers a proviso or caveat related to ‘the elementary substance’, a term that is sometimes encountered in this context.

So much for the modern definitions but Scerri cites Dmitri Mendeleev’s contention, articulated in the latter part of the nineteenth century, that the concept of ‘element’ has a dual nature and that a distinction should be made between an element as a homogeneous substance (i.e., IUPAC’s second definition) and an element that exists in some abstract sense within a chemical compound (i.e., as an underlying principle or basic substance). Somewhat later in the 1930s, this apparent dichotomy was discussed at length by Friedrich Paneth who wrote about a ‘dual epistemological status of the concept of element’ [6]. To quote Paneth in more detail, he makes a clear distinction between simple and basic substances in the concluding two sentences in ref. [6] where he writes [in translation]:

As has been shown, this concept [i.e., element] must be taken in the naïve-realistic sense when meaning “simple substance”, but has to be understood as transcendental when meaning “basic substance”. We have also tried to emphasise the close relationship of the concept of basic substance to the “metaphysical” principles of the Aristotelians and the alchemists.

The assertion regarding some abstract or transcendental nature of an element expressed by Mendeleev and Paneth, and recounted by Scerri, may be illustrated with an oft-cited example. Thus, under ambient conditions, sodium is a silvery grey metal and chlorine is a pale green gas (often referred to as simple substances) but in combination they form sodium chloride which is a white solid. Clearly metallic sodium and gaseous chlorine are not present in that form within sodium chloride: it is a compound not a mixture. It is presumed, however, that some aspect (for Mendeleev it was atomic weight) of sodium and chlorine, i.e., an abstract or basic substance, persists within sodium chloride as evidenced by the fact that, under the right conditions, both elements can be recovered from sodium chloride in their simple substance form.

Scerri states the following: ‘It is easy for a modern chemist to dismiss any notion of an abstract understanding of the concept of an element...’, and advocates a modified definition of element following Paneth’s suggestion reproduced below [1]:

I suggest that we should use the term “basic substance” whenever we want to designate that which is indestructible in compounds ... and that we should speak of a “simple substance” when referring to the form in which such a basic substance, not combined with any other, is presented to our senses... .

Scerri concludes with the phrase, ‘...the precise wording of any modified definition of the word “element” remains to be formulated, and we believe, should make reference to their abstract sense...’ and ‘...the author welcomes suggestions from readers, including chemical educators, as to how this might be achieved.’ [1]. As a chemical educator, I hope the following suggestions may indeed be welcome.

To my mind, the discussion around any difference between simple substance and basic substance, and to what extent the latter embodies some abstract (or even transcendental or metaphysical) aspect or character, seems a rather contrived problem and represents a false dichotomy, perhaps not historically but certainly in the present day. The element gold, as stated above, is defined (according to IUPAC’s first definition) on the basis of having 79 protons in the nucleus of its atoms and, perhaps more importantly from a chemist’s perspective, a neutral gold atom also has 79 electrons, the arrangement of which determine its chemistry. In the gas phase, electrons can be removed to form cations or added to form anions (the Au^– anion is stable with respect to loss of an electron). These are gold ions but of more general significance is the fact that when gold atoms are brought into contact with other atoms, chemical bonds are formed by the sharing of electrons. When the other atoms are gold atoms, one forms what is commonly referred to or described as elemental gold (IUPAC’s second definition) having all the properties we associate with that substance, at least once a sufficient number of atoms are present [7]. If the atoms are of other elements, one forms compounds of gold. From a chemist’s perspective, there is, therefore, no meaningful or fundamental difference between elemental gold (i.e., the elementary or simple substance) and its compounds, nor is there for other elements many of which exist as a number of different allotropes, for example carbon (diamond, graphite, fullerenes, carbon nanotubes). All are aggregates of atoms of one or more chemical elements.

In whatever substance we are considering (simple or compound), the nuclei remain unaltered. Atoms can lose or gain electrons and in association share electrons to form materials with particular properties but why privilege or focus on one particular assemblage in which all the atoms happen to be the same? Moreover, one could argue that the pure elements referred to as simple substances that we perceive with ‘our senses’ (see above) are largely chimerical. Thus, for most metals (although, as it happens, not gold) the surface comprises an oxide layer, not the metal itself. Similarly, in polymeric allotropes, the ends, edges or faces (according to their dimensionality) are terminated by other elements, often hydrogen atoms or hydroxide groups. This is certainly the case with diamond and one might ask at what point between the hydrocarbon molecule adamantane (C₁₀H₁₆), in which the ten carbons are arranged as in diamond, and diamond itself (assuming all terminating groups are hydrogen) do we transition from a molecular hydrocarbon to a form we would be content to describe as an allotrope of carbon [8]. And what about impurities which are always present to some degree or other [9]? Simple substances, it turns out, are not so simple in the real world.

I contend that there is nothing to be gained from the dichotomy based around some abstract, transcendental or metaphysical nature of an element that is manifest in a simple substance but somehow hidden in the form of a basic substance within a chemical compound, nor indeed from continued use of the terms ‘simple substance’ and ‘basic substance’. Chemists are only rarely concerned with isolated atoms (or ions). In most cases, we deal with atoms in association with other atoms and the properties of the substances in which we are interested are a result of the sharing of electrons (bonding) and how the atoms are arranged in space (structure). Whether these substances contain only one type of atom or more than one type does not really matter. To address Scerri’s question posed in the title of his article, I’ll therefore offer a suggested definition of ‘chemical element’ (a term to be preferred over just ‘element’):

A chemical element is defined by the number of protons (or units of positive charge) in the nucleus of its atoms, i.e., its atomic number: hydrogen has one, helium has two etc. In common chemical parlance, bulk samples of a material consisting of only one type of atom are often referred to as the elemental form of that element, for example, elemental carbon or elemental gold, many of which (e.g., carbon) have more than one allotrope.

This proposed definition is an amalgamation of the current two distinct IUPAC definitions in which the first sentence is unarguable and the second reflects a common usage of the term. We might wish to refine the wording but surely this is sufficient for most, if not all, practical and pedagogical purposes and we need not be concerned with anything of a purported abstract nature.

I should note in conclusion that following Scerri’s article in Chemistry International (ref. [1]), there is a follow-up response from Doug Templeton which addresses the points that Scerri raises [10]. In brief, Templeton argues against there being any abstract nature of an element but does support the need for two definitions, his proposals for which are broadly in line with the current two IUPAC definitions. I agree with Templeton on the first point but remain unconvinced about the requirement for two definitions as noted above: one would seem sufficient.

References

[1].       What is an Element, and How is it Defined in the IUPAC Gold Book? E. Scerri, Chemistry International, 2026, 48, no. 1, 36-38, https://doi.org/10.1515/ci-2026-0122 (accessed on 28 March 2026).

[2].       Scerri has considered this matter previously and in more depth in the article, The Many Questions Raised by the Dual Concept of “Element”, E. R. Scerri, 2002, Ch. 1, 5-31 in, What is a Chemical Element?, E. R. Scerri and E. Ghibaudi (Eds.), Oxford University Press, 2002. Many of the chapters by other authors in this book also address the topic discussed here (and refer to an extensive prior literature) but it is the points made by Scerri that are the principal focus of this contribution.

[3].       IUPAC. Compendium of Chemical Terminology, 2^nd Ed. (the “Gold Book”). A. D. McNaught and A. Wilkinson (Eds.), Blackwell Scientific Publications, 1997. The “Gold Book” is a compendium of, in part, authoritative chemical definitions and terminology approved by the International Union of Pure and Applied Chemistry (IUPAC) available in both printed form and online (https://goldbook.iupac.org).

[4].       The definitions of the term ‘element’ and ‘chemical element’ (which are the same) are available in the online version of the “Gold Book” at: https://goldbook.iupac.org/terms/view/C01022 (accessed on 28 March 2026).

[5].       Kinetic isotope effects are at their greatest when mass differences are at their largest. Thus, such effects are significant in the case of hydrogen (¹H) vs deuterium (²H) where the masses of the isotopes differ by a factor of two but very much less so, for example, with uranium where the mass difference between the two naturally occurring isotopes (²³⁵U and ²³⁸U) is only a little over 1% and even less in its compounds.

[6].       The Epistemological Status of the Chemical Concept of Element. F. A. Paneth, British Journal for the Philosophy of Science, 1962, 13, 1-14 (Part I) and 144-160 (Part II). Reprinted in Foundations of Chemistry, 2003, 5, 113-145.

[7].       The point made in this sentence about a sufficient number of gold atoms being present is important in terms of the properties of assemblages of gold atoms. Thus, individual gold atoms, the diatomic gold molecule (Au₂), small gold clusters (e.g., Au₂₀), gold nanoparticles of the order of 100nm, and macroscopic samples of gold (all of which have been studied) have quite different properties.

[8].       On this basis, the only true allotropes of carbon are the fullerenes, C₆₀, C₇₀ etc. All other forms, except perhaps under rather exceptional conditions (certainly not ambient), have edges or faces terminated with other elements such as hydrogen.

[9].       The point about impurities may seem pedantic but consider the following. Bulk samples of pure silver and pure gold can certainly be imagined and a few atoms of one in samples of the other might rightly be regarded merely as impurities. At what stage, however, is the concentration of an impurity deemed sufficient to classify the material as an alloy? In the case of these two elements, the precise points at which gold becomes electrum (a common name for a gold-silver alloy) and electrum becomes silver are entirely arbitrary.

[10].     Follow-up Response. D. Templeton, Chemistry International, 2026, 48, no. 1, 38-40, https://doi.org/10.1515/ci-2026-0123(accessed on 28 March 2026).

*Nick Norman is Professor of Inorganic Chemistry (Emeritus) at the University of Bristol, UK.