Classification of Elements and Periodicity in Properties

By the middle of the nineteenth century, more than 60 elements were known, and chemists needed a systematic way to study and remember their properties. Early attempts included Dobereiner's Triads (groups of three elements where the middle element's atomic mass is roughly the average of the other two) and Newlands' Law of Octaves (every eighth element resembled the first, like musical notes), but both worked only for lighter elements and failed as more elements were discovered.

Dmitri Mendeleev (1869) proposed that the physical and chemical properties of elements are a periodic function of their atomic masses. He arranged the known elements in horizontal rows (periods) and vertical columns (groups) in order of increasing atomic mass, such that elements with similar properties fell into the same group.

Mendeleev's table had eight groups (I to VIII), each split into sub-groups A and B, with Group VIII accommodating triads of elements such as Fe, Co, Ni. A major strength of the table was that Mendeleev left gaps for elements not yet discovered and boldly predicted their properties by interpolating from neighbouring elements, calling them eka-boron, eka-aluminium, and eka-silicon.

Worked example: Mendeleev predicted eka-silicon with an atomic mass close to 72 and density about 5.5 g cm^-3. When germanium was discovered in 1886, its atomic mass (72.6) and density (5.36 g cm^-3) matched Mendeleev's predictions very closely, strongly validating the periodic law.

Despite its success, Mendeleev's table had important limitations: the position of hydrogen was uncertain since it resembles both alkali metals and halogens; isotopes of the same element (different atomic masses) could not be given separate positions even though the law was based on atomic mass; increase in atomic mass did not always match the increase in atomic number on moving to the next element; and at some places an element of higher atomic mass had to be placed before one of lower atomic mass to preserve similarity of properties (anomalous pairs), for example argon (39.9) before potassium (39.1), and cobalt (58.9) before nickel (58.7).

In 1913, Henry Moseley showed that the atomic number (number of protons) of an element is a more fundamental property than its atomic mass. This led to the Modern Periodic Law: the physical and chemical properties of elements are a periodic function of their atomic number. This single change resolved almost all the anomalies of Mendeleev's table, because arranging by atomic number automatically places Ar before K and Co before Ni in their correct groups.

The present (long) form of the periodic table, based on electronic configuration, has 18 vertical groups and 7 horizontal periods. The period number of an element equals the highest value of the principal quantum number (n) occupied by its electrons, so period 1 has only 2 elements (filling 1s), periods 2 and 3 have 8 elements each (filling ns and np), and periods 4 and 5 have 18 elements each (filling ns, (n-1)d, and np). Period 6 has 32 elements because the 4f orbitals (lanthanoids) are also filled, and period 7 is likewise expanded by the 5f orbitals (actinoids).

As elements beyond atomic number 100 were synthesised in laboratories, disputes often arose over naming rights. IUPAC therefore recommends a temporary systematic nomenclature based directly on the atomic number, used until a permanent name is officially approved. Each digit of the atomic number is represented by a numerical root: 0 = nil (n), 1 = un (u), 2 = bi (b), 3 = tri (t), 4 = quad (q), 5 = pent (p), 6 = hex (h), 7 = sept (s), 8 = oct (o), 9 = enn (e). The roots are joined in the order of the digits and the ending "-ium" is added; the symbol is formed from the first letter of each root.

Worked example: Name the element with atomic number 114 systematically. The digits are 1, 1, 4, corresponding to the roots un, un, quad. Joining them and adding "-ium" gives Ununquadium, symbol Uuq (its approved permanent name is now Flerovium, Fl, but the systematic name illustrates the IUPAC rule).

The modern periodic table can be divided into four blocks based on the subshell into which the last (differentiating) electron enters, following the Aufbau principle.

The s-block (Groups 1 and 2) has the general valence configuration ns^1-2; these are soft, highly reactive metals (alkali and alkaline earth metals) with low ionisation enthalpies. The p-block (Groups 13 to 18) has configuration ns²np^1-6 and contains metals, metalloids, non-metals, and the noble gases, showing the widest variation in properties of any block. A notable exception is helium: although its electronic configuration (1s²) matches the s-block pattern, it is placed in Group 18 with the noble gases because its valence shell (a complete duplet) is already full and its chemically inert behaviour matches theirs, not the reactive alkaline earth metals. The d-block (Groups 3 to 12), or transition elements, has the general configuration (n-1)d^1-10ns^0-2, where electrons fill an inner d-subshell; these are typically hard, high-melting metals with variable valence. The f-block (inner transition elements) comprises the lanthanoids (Z = 58 to 71) and actinoids (Z = 90 to 103), with configuration (n-2)f^1-14(n-1)d^0-1ns²; they are placed separately at the bottom of the table for compactness.

A useful rule is that for s- and p-block elements the group number is directly linked to the number of valence electrons, while for d-block elements the group number equals the sum of (n-1)d and ns electrons.

Worked example: Write the electronic configuration of the element with Z = 26 (iron) and identify its block, period, and group. Filling orbitals in order of increasing energy: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s², which accounts for all 26 electrons. Since the last electron enters a 3d orbital, iron is a d-block element. The highest principal quantum number occupied is n = 4, so it lies in Period 4; with 8 electrons in (3d + 4s), it belongs to Group 8.

Chromium (Z = 24, [Ar]3d⁵4s¹) and copper (Z = 29, [Ar]3d¹⁰4s¹) are well-known exceptions to the simple filling order: a half-filled or completely filled d-subshell provides extra stability through symmetrical charge distribution and exchange energy, so one 4s electron shifts into the 3d subshell.

Atomic radius is measured in different ways depending on bonding type: covalent radius (half the internuclear distance between two like atoms singly bonded together), metallic radius (half the distance between adjacent nuclei in a metallic crystal), and van der Waals radius (half the distance between two adjacent atoms of neighbouring molecules held together only by weak van der Waals forces, as in noble gases).

Across a period, electrons are added to the same outermost shell while the nuclear charge (Z) also increases with each element; the increase in effective nuclear charge (Z_eff = Z minus shielding) pulls the electron cloud inward more strongly than the added electron can shield, so atomic radius decreases from left to right across a period. Down a group, a new principal shell is added at each step, so despite the increasing nuclear charge, atomic radius increases down a group because the outer electrons are farther from the nucleus and shielded by more inner shells.

Ionic radius follows related rules: a cation is always smaller than its parent atom because it has lost one or more electrons (often losing an entire shell) while the same nuclear charge now pulls on fewer electrons; an anion is always larger than its parent atom because added electrons increase inter-electronic repulsion for the same nuclear charge. For a set of isoelectronic species (same number of electrons), radius decreases steadily as nuclear charge (atomic number) increases, since a more positive nucleus pulls the same electron cloud in more tightly.

Worked example: Arrange N^3-, O^2-, F^-, Na⁺, and Mg²⁺ in increasing order of ionic radius. All five species have exactly 10 electrons (isoelectronic), so only nuclear charge decides size. Their atomic numbers are N = 7, O = 8, F = 9, Na = 11, Mg = 12; since radius falls as nuclear charge rises, the increasing order of radius is Mg²⁺ < Na⁺ < F^- < O^2- < N^3-.

Ionisation enthalpy is the minimum energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state, expressed in kJ mol^-1: M(g) → M⁺(g) + e^-. Removing a second electron from the resulting cation requires the second ionisation enthalpy, M⁺(g) → M²⁺(g) + e^-, which is always larger than the first because it is harder to remove an electron from a positively charged, smaller ion.

Ionisation enthalpy generally increases across a period (increasing Z_eff, decreasing radius) and decreases down a group (increasing radius and shielding, despite increasing nuclear charge). Two well-known exceptions occur within a period: Be (ns², fully-filled and stable) has a higher first ionisation enthalpy than B (ns²np¹, since removing the single, higher-energy p-electron is comparatively easy); similarly, N (2p³, extra stability from a half-filled subshell) has a higher first ionisation enthalpy than O (2p⁴, where pairing of electrons in one orbital adds repulsion that makes removal easier).

Electron gain enthalpy is the enthalpy change when a neutral gaseous atom gains an electron to form an anion: X(g) + e^- → X^-(g). Most atoms release energy on gaining an electron, so this value is usually negative; a more negative value means a greater tendency to gain electrons. It generally becomes more negative across a period (increasing Z_eff attracts the incoming electron more strongly) and less negative down a group (increasing atomic size). Noble gases have positive electron gain enthalpies since the added electron must enter a new, higher-energy shell. Fluorine is an important exception: its electron gain enthalpy (-328 kJ mol^-1) is less negative than that of chlorine (-349 kJ mol^-1), because fluorine's very small 2p orbital already has high electron density, so the incoming electron experiences strong inter-electronic repulsion that partly offsets the advantage of its small size. Nitrogen is another exception: its half-filled, extra-stable 2p³ configuration gives it an electron gain enthalpy that is actually slightly positive (about +7 kJ mol^-1), unlike the negative values of its neighbours.

Worked example: The successive ionisation enthalpies of magnesium (Z = 12, configuration [Ne]3s²) are IE1 = 738 kJ mol^-1, IE2 = 1451 kJ mol^-1, and IE3 = 7733 kJ mol^-1. The huge jump from the second to the third value shows that removing a third electron means breaking into the stable, completely filled [Ne] noble-gas core, which needs vastly more energy; this is why magnesium readily forms Mg²⁺ but never Mg³⁺ in ordinary chemistry.

Electronegativity is the tendency of an atom, when bonded in a molecule, to attract the shared pair of electrons toward itself. Unlike ionisation enthalpy or electron gain enthalpy, it is not a measurable, isolated-atom property but is defined only for an atom within a bond, and it has no fixed units (the most common scale, devised by Linus Pauling, assigns fluorine the highest value of about 4.0). Electronegativity increases across a period (smaller atoms with higher Z_eff hold shared electrons more tightly) and decreases down a group (larger atomic size moves the shared pair farther from the nucleus). Fluorine is the most electronegative element, and electronegativity broadly parallels non-metallic character.

Valence is the combining capacity of an element, and it too shows periodicity: it depends on the number of valence electrons (ve). For elements with up to 4 valence electrons, valence usually equals the number of valence electrons; for elements with more than 4 valence electrons, valence is usually 8 minus the number of valence electrons (following the octet rule for covalent combination). Valence thus rises from 1 to 4 and then falls back to 0 across a typical period, repeating in the next period; this periodic rise-and-fall is itself one of the clearest demonstrations of periodicity.

Worked example: Determine the valence of the elements of Period 3 (Na to Ar) using their valence electron counts. Na (ve = 1) gives valence 1; Mg (ve = 2) gives valence 2; Al (ve = 3) gives valence 3; Si (ve = 4) gives valence 4; P (ve = 5) gives valence 8 - 5 = 3 (though pentavalent compounds like PCl₅ also exist by using d-orbitals); S (ve = 6) gives valence 8 - 6 = 2 (also shows 4 and 6 in higher oxides); Cl (ve = 7) gives valence 8 - 7 = 1 (also shows 3, 5, 7); Ar (ve = 8) gives valence 0, since its octet is already complete. This confirms the classic periodic pattern of valence: 1, 2, 3, 4, 3, 2, 1, 0.