Chemists faced a flood of new elements in the nineteenth century and needed a way to organise them. The story of the periodic table is really a story of pattern-hunting — spotting that certain elements behave like each other and refusing to treat that as a coincidence.
Early attempts
Döbereiner's Triads (1829): Johann Döbereiner grouped elements in threes where the atomic mass of the middle element was nearly the arithmetic mean of the other two. For the triad Li (7), Na (23), K (39), the mean of Li and K is $(7+39)/2 = 23$, exactly Na. The idea only worked for a handful of triads, so it was abandoned.
Newlands' Law of Octaves (1865): John Newlands arranged the known elements in order of increasing atomic mass and noticed that every eighth element resembled the first, like the octaves in music. It held up to calcium but collapsed beyond it, and the Chemical Society of London refused to publish his work.
Mendeleev's Periodic Table (1869): Dmitri Mendeleev ordered elements by increasing atomic mass and stated his Periodic Law: the properties of the elements are a periodic function of their atomic masses. His genius lay in two bold moves — he left gaps for undiscovered elements and even predicted their properties. He named them eka-aluminium, eka-boron and eka-silicon; these turned out to be gallium, scandium and germanium. He also reversed a few mass-based positions (e.g. Te before I) to keep chemically similar elements together, hinting that mass was not the deepest cause.
The Modern Periodic Law
Henry Moseley (1913), studying X-ray spectra, showed that the atomic number $Z$ — not atomic mass — is the fundamental property of an element. This resolved Mendeleev's anomalies (Te, $Z=52$, genuinely comes before I, $Z=53$). The Modern Periodic Law states: the physical and chemical properties of the elements are a periodic function of their atomic numbers. Periodicity arises because similar outer (valence) electronic configurations recur at regular intervals as $Z$ increases.
Long form of the periodic table
The modern long form has 7 horizontal periods and 18 vertical groups. A period number equals the principal quantum number $n$ of the outermost shell being filled. Down a group, elements share the same valence-shell configuration, which is why they show similar chemistry. The number of elements in each period (2, 8, 8, 18, 18, 32, 32) follows directly from the order in which orbitals are filled.
s-, p-, d- and f-blocks
The table is divided into four blocks by the subshell that receives the last electron:
s-block (Groups 1 and 2): outer configuration $ns^{1-2}$ — reactive metals. p-block (Groups 13–18): $ns^2np^{1-6}$ — includes metals, metalloids, non-metals and the noble gases ($ns^2np^6$). d-block (Groups 3–12, the transition elements): $(n-1)d^{1-10}\,ns^{0-2}$. f-block (lanthanoids and actinoids): $(n-2)f^{1-14}$ — the inner-transition elements, shown separately at the foot of the table.
IUPAC nomenclature for $Z>100$
To name newly discovered super-heavy elements provisionally, IUPAC uses numerical roots for each digit of $Z$: nil(0), un(1), bi(2), tri(3), quad(4), pent(5), hex(6), sept(7), oct(8), enn(9). The roots are joined in order, followed by the suffix -ium. For example $Z=104$ is un-nil-quad-ium = unnilquadium (Unq), later named rutherfordium. This system gives every element a name even before a permanent one is agreed.