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The Periodic Table: What Is It Showing?

The Periodic Table of the Chemical Elements is both a cultural icon and an extraordinary object in science space. This page explores what the periodic table is in terms of the philosophy of science.


The chemogenesis web book explores how chemical reactivity emerges from the periodic table of the elements using a root-trunk-branch chemistry-tree metaphor, with the periodic table situated at the base of the trunk:

The question is: What actually is the periodic table, and what it is showing? It transpires that matters are a little more involved than they may at first appear...

First, the long form 32 column periodic table (in this author's opinion, is the preferred formulation):

The 32 Column [Long Form] Periodic Table

But, the PT is usually reduced to the 'classic' 18 column medium form periodic table, as used by WebElements and most other web sites & textbooks:

The WebElements 18 Column [Medium Form] Periodic Table

There are many other possible formulation, as reviewed on the next page of this web book.

Philosophy | Chemistry | The Periodic Table

"[In 1913] when Henry Moseley experimentally determined and analysed the atomic inner shell X-ray spectra, and Niels Bohr invented his atomic model, the empirical and theoretical basis for the element number was found as the number of protons in the nucleus for the physicist, and as the number of electrons of the neutral atom for the chemist.

"This reflects a conceptual difference:

"A [physicist's] physical element is a nucleus and a [chemist's] chemical element contains atoms consisting of nuclei and electrons [able to] form stable molecules in their electronic ground states."

"[Atomic number] Z has proven useful as an ordinal number to order the nuclei on an isotopic [Segrè] chart, and also to obtain a chemically meaningful order of the chemical elements."

From: Physical Origin of Chemical Periodicities in the System of Elements, Pure and Applied Chemistry | Volume 91: Issue 12, 2019, Li & Schwarz et. al.

Philosophers of chemical science consider the elements in distinct ways:

  1. Firstly, there is the chemical element as the "basic substance", that is the abstract or transcendental element, the essence of the element, the element as "a bearer of properties" but not having any actual properties, except for atomic number Z. Chemical symbols, such as H and Cu, and names are assigned to the element as the basic substance.

  2. The isotopic composition of the nucleus is conserved, and the various nuclear properties move with the element as it undergoes chemical transformation and chemical reactions: average atomic mass, radioactivity, nuclear spin, electronegativity and because Z = n (the atomic number equals the principle quantum number in the neutral atom), the quantum numbers and electronegativity.

  3. Thirdly, there is the element as simple substance. A real physical 5.00g piece of copper metal has numerous, measurable, intrinsic properties such as: density, conductivity, colour, purity, etc. Crucially, these properties are NOT conserved when the copper undergoes chemical reactions, such as dissolving in concentrated nitric acid.

    [There is a language problem with this topic, and it concerns the use of the technical terms: 'basic' and 'simple'. These words are used in so many different contexts, that it can be very difficult to remember that here they have very specific meanings.]

Crucially, only the basic substance and the nuclear properties survive in a compound. These ideas can be illustrated with the statement:

"Sodium's metallic properties and chlorine, the green gas, do not exist in the colourless, crystalline ionic salt, sodium chloride."

In other words, the "silvery metal aspect of sodium" and the "green gas aspect of chlorine" do not exist in the binary compound sodium chloride.

These matters are discussed in a paper by Eric Scerri, HYLE--International Journal for Philosophy of Chemistry, Vol. 11, No.2 (2005), pp. 127-145: Some Aspects of the Metaphysics of Chemistry and the Nature of The Elements

Summarising Scerri's arguments:

Eric Scerri points out that the periodic table has, at times, been characterised as a:

This author agrees with Scerri that the periodic table is an ordered domain. But the periodic table is also a schema. Data, information & knowledge concerning the chemical elements can be mapped onto the periodic table.  

Periodic Tables on Walls and In Books: What are they showing? Why is there a problem?

Periodic tables use the design as an organising schema to list the chemical elements and to present physical data & material properties of the elements.

In their simplest form, the periodic tables show elements with only the atomic number Z and the element symbol. Strictly, this is showing the elements as the basic [transcendental, abstract] substance.

However, they may go on to state:

Oxygen, O, atomic number, Z= 8, has a boiling point of oxygen is -182.9 °C.

But, this is the boiling point of O2, a diatomic diatomic, molecular substance called "dioxygen" !

In this author's opinion, there has been a logical sleight-of-hand.

The metaphysical periodic table of abstract, basic substances is being passed off as a periodic table of the material properties of simple substances, which is not the same thing at all.

This causes confusion as to what exactly it is that a particular periodic table is, and what it is showing.

Morphing Multiple Periodic Tables

At least three periodic tables can be easily identified (but as we will see there are actually many more):

When moving across these three periodic tables, the system complexity and the number of properties dramatically increases.

And there are yet more periodic tables:

Periodic tables may show the phase (solid, liquid or gas) state of the elemental materials at the standard temperature of 25°C and at other temperatures, for example 2025°C (from pTable):


All of these many & various periodic tables morph into each other to give the compound object that is commonly known as [and presented as] The Periodic Table.

Periodic Table of The Elements as Basic Substances

The long form periodic table of basic, abstract, transcendental substances showing the only property, atomic number Z, behaving as an ordinal number:

Periodic Table of Basic Substances (Atomic Number Z)

Element symbols and names are assigned to the atomic number Z:

Periodic Table of Basic Substances (Atomic Symbol)

In the basic substance formulation, oxygen atomic number 8 is "O" and not the common molecule "O2". Likewise, sulfur (Z = 16) is S and not the yellow solid S8.

The usual periodic table schema simply shows the element symbols in their respective periods, groups & blocks.

This, or an equivalent formulation, is the periodic table as Mendeleev would have intended it: a schema showing the elements as basic substances with their positions in the schema emphasising the periodic law:

"The periodic law is the principle that certain properties of elements occur periodically when arranged by atomic number. These similarities can be reflected best by a table, so that commonalties between elements appear both in rows and in columns of the table." Wikipedia

Periodic Table of Conserved [Nuclear] Properties

Conserved nuclear properties are a consequence of the isotopic composition of the element which directly account for the relative atomic mass (defined as the ratio of the average mass of the atoms of a chemical element in a given sample compared to 1/12 of the mass of an atom of carbon–12.)

Relative atomic mass is conserved in chemical reactions:

Na (mass = 22.99)    + Cl (mass = 35.45)    →    NaCl (mass = 22.99 + 34.45 = 58.44)

Likewise, radioactivity is transferred with the atoms. Radio-labelled sodium will react with chlorine to give radio-labelled sodium chloride.

There is a minor (but important) kinetic isotope effect or KIE. Heavier isotopes are very slightly less reactive than lighter isotopes, simply because they are less mobile. The KIE effect is most notable with hydrogen, where deuterium, 2H, has double the mass of protium, 1H. However, as a first approximation, KIE can be ignored.

In the element as the basic (abstract) substance, the atomic number Z is simply an ordinal (ordering) number. In the periodic table of conserved [nuclear] properties, Z is the charge on the atomic nucleus, in the neutral atom it is also the number of electrons, and hence, it directly determines the principle quantum number n.

The quantum numbers, n, , m & ms, lead to the corresponding electronic (orbital) configurations:

Neutral atoms: n = Z                  Ions: n = (Z – charge)

symbol Z n = (Z - charge) n electronic structure
Na 11 11 – 0 11       1s2, 2s2, 2p6, 3s1
Na+  11 11- 1 10       1s2, 2s2, 2p6
Cl 17 17 – 0 17       1s2, 2s2, 2p6, 3s2, 3p5
Cl  17 17 – –1 = 17 + 1 18       1s2, 2s2, 2p6, 3s2, 3p6

Note that not all atomic electronic structures can be so easily deduced: the simplistic man-made rules, such as Bohr's aufbau principle & Madelung's rule, are fine for the lighter main group elements but they do not always give the correct results with heavier d-block elements.

Nuclear spin is an isotopic property that is exploited in NMR spectroscopy, particularly with the 1H and 13C isotopes. Nuclear spin is conserved and transferred with an atom, from the elemental substance into its compounds.

For electronegativity, this author uses the definition:

"Electronegativity is a measure, integrated over numerous physical parameters, of the power of a gas phase or bonded atom to attract electrons to itself."

Sodium is a large atom that is easily ionised. In reactions, sodium generally reacts to give the sodium ion, Na+. These features lead to the conclusion that sodium is an electropositive element.

Chlorine is a small atom with a high electron affinity and a propensity to form chloride ions, Cl. These features lead to the conclusion that chlorine is an electronegative element.

Electronegativity is not a "simple" elemental substance property, like the metallic lustre of sodium or chlorine presenting as a green gas, but is intrinsic to every aspect of an element's chemistry and it travels with an atom. Electronegativity is a conserved property that is a consequence of Z.

Periodic Table of Gas Phase Atoms

The chemical elements as real, simple elemental substances can be physically normalised into a similar set by examining ground-state, monoatomic gas phase atoms of the material substance.

The periodic table of ground state gas phase atoms is known, and it represents the periodic table of the very simplest simple substances:

Periodic Table of Gas Phase Atoms

Apart from the title, the graphic is exactly the same as the periodic table of basic substances, but this periodic table represents real chemical entities with actual, measurable, physical properties, including:

Many modern technologies utilise gas phase atoms, including:

Crucially, when we consider the electronic structure of an atom [or the orbital structure of a molecule, for that matter], we are considering the atom to be an isolated entity, exactly as it would be in the gas phase. For example, when we say "sodium has a 1s2, 2s2, 2p6, 3s1 electronic structure", we are referring to the sodium the gas phase atom, Na(g), not sodium in its solid, metallic state, Na(s).

Periodic Table Chemical of Substances Under Standard Conditions

Under standard conditions, 298K and 100kPa (25°C & 1.0 atm), the chemical elements as simple substances – real chemicals, chemical reagents, chemicals in bottles – present as:


The chemical elements as material substances have many properties, including [from WebElements, copper]:

Abundance of elements (Earth's crust)
Abundance of elements (oceans)
Abundance of elements (meteorites)
Abundance of elements (stream)
Abundance of elements (sun)
Abundance of elements (Universe)
Abundances in humans
Biological role
Boiling point
Bond enthalpy (diatomics)
Bulk modulus
Covalent radius
Critical temperature
Crystal structure
Electrical resistivity
Element bond length
Enthalpy of atomization
Enthalpy of fusion
Enthalpy of vaporization
Examples of compounds
Hardness - Brinell

Hardness - Vickers
Health hazards
History of the element
Ionic radii (Shannon)
Ionic radius (Pauling)
Ionic radius (Pauling) of monocation
Isotope abundances
Isotope nuclear spins
Isotope nominal mass
Isotope nuclear magnetic moment
Lattice energies
Linear expansion coefficient
Meaning of name
Melting point
Mineralogical hardness
Molar volume
Names and symbols
NMR frequency
NMR isotopes
NMR magnetogyric ratio
NMR quadrupole moment
NMR receptivity

NMR relative sensitivity
Poisson's ratio
Properties of some compounds
Radius metallic
Radioactive isotopes
Reactions of elements
Reduction potential
Refractive index
Registry number
Rigidity modulus
Standard atomic weights
Standard state
Superconductivity temperature
Term symbol
Thermal conductivity
Thermodynamic properties
Valence orbital
Van der Waals radius
Velocity of sound
X-ray crystal structure
Young's modulus

Quantum Mechanics, Emission Spectra & The Axiomatic Periodic Table

In the first half of twentieth century, much effort was expended trying to make the periodic table of the elements axiomatic ("self-evident" or "unquestionable"), ie. trying to fully understand the Mendeleev system in terms of quantum mechanics.

In 1929 Paul Dirac famously claimed this situation had been fully and completely achieved in principle:

"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble."
P.A.M. Dirac, Proc.R.Soc.Lond.Ser.A 123 (1929) 714

We certainly teach school and university students that "the periodic table is fully understood in terms of electronic theory", and this line of reasoning is advanced elsewhere in this web book, here and the HyperPhysics site, here.

The argument is put forward that:

Yes, there is an empirical (experimental) correspondence between gas phase atoms and their spectra, but is there a 1-to-1-to-1 correspondence between: the periodic table, atomic spectra & quantum mechanics?

Eric Scerri: Chemist | Philosopher | Theorist | Author

Eric Scerri:

Eric Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Read an interview with the author, here, and a review of the book here.

disputes the full and complete axiomatic mapping between theory and the periodic table:

"Electronic configurations are not [fully] reduced to quantum mechanics nor can they be derived from any other theoretical approach. They are obtained by a mixture of spectroscopic observations and semi-empirical methods like Bohr's aufbau scheme". Has The Periodic Table Been Fully Axiomatized? Erkenntnis, 47, 229-243, 1997

The reason for the discrepancy concerns difficulty of dealing with multi-electron atoms (ions and molecules).

Read more here: Physical Origin of Chemical Periodicities in the System of Elements, Pure and Applied Chemistry | Volume 91: Issue 12, 2019, Li & Schwarz et. al.

Furthermore, there is even an issue with the concept of the atomic orbital:

From: Philosophy of Chemistry by Martín Labarca:

"Orbitals cannot be observed since, strictly speaking, they do not exist."

The debate [about orbitals] is a manifestation of a problem that has profound consequences for the teaching of chemistry, since the teachers of the discipline cannot do without the concept of orbital in their teaching [including in this web book!].

Some authors have pointed out that this position collides with the assumption that quantum mechanics has the last word on the subject: only the concept of wave function is legitimate; the term 'orbital' has no real-world reference.

In particular, the realistic view of orbitals adopted by chemistry teachers turns out to be inconsistent with their own position when they introduce quantum mechanics as the underlying explanatory theory of chemical phenomena.

This problem is explicitly pointed out by Scerri when he posed the question: "Can orbitals be real in chemistry but not in physics?" It seems quite clear that this paradoxical situation has negative consequences for a deep understanding of the discipline for the following reasons:

a) Students face the alternative of living in a kind of "conceptual schizophrenia" or accepting that chemistry describes merely apparent phenomena or [is] "metaphorical".

b) If the "correct" definition of the concept of atomic orbital only lies in the field of physics, students who decide to study chemistry would find that textbooks from their own discipline provide a "wrong" definition of the concept. 

Basic & Simple Substance | Theoretical & Practical Chemistry: Does Any of This stuff Matter?

The reader may consider that the concept of element-as-basic-substance and element-as-simple-substance to be an arcane distraction. However, the analysis does actually have implications for how we understand and teach the subject of chemistry.

Beginning chemistry students always have access to a periodic table, but unfortunately this may not the PT they actually need. Students are expected to know and understand that all of the reaction equations involving chemical elements will likely involve the chemical substance, the chemical in the bottle, the reagent. Thus, reactions of hydrogen involve and should show molecular hydrogen, H2 and should therefore be written as:

2H2    +    O2    →    2H2O

and NOT:

2H + O     →     H2O

Likewise: nitrogen is N2, oxygen O2, fluorine F2, chlorine Cl2, bromine Br2 & iodine I2. Reactions involving these entities should always be written so as to show the dimeric species. However, somehow students are also expected to know that molecular sulfur, S8, and phosphorus, P4, are usually written as involving S and P.

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QNs to PTs INTERNET Database of Periodic Tables

© Mark R. Leach 1999-

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