The periodic table

Everything around you is built from about a hundred kinds of atom. We call them the elements. Hydrogen, oxygen, iron, gold: each one is a different kind of atom, and each atom has its own fixed number of protons in its middle.

The periodic table is just a clever way of laying all those elements out in a grid. You put them in order by how many protons each atom has, one, two, three, and so on. But here is the neat part. When you lay them out that way and start a new row at the right moments, elements that behave alike end up stacked in the same column. Soft, reactive metals in one column. Gases that barely react in another.

That is what "periodic" means: the behaviour keeps coming back around, like the days of the week repeating. A man called Dmitri Mendeleev spotted this in 1869. He was so sure of the pattern that he left blank gaps in his table and said, there should be an element here that no one has found yet, and it should behave like this. Years later people found those elements, and he was right.

So the table is not just a list. It is a map. Tell me where an element sits, and I can tell you a lot about how it will act.

The elements are ordered by their atomic number \(Z\), the number of protons in the nucleus. Hydrogen is \(Z=1\), helium \(Z=2\), and so on up the line. The horizontal rows are called periods; the vertical columns are called groups.

Why do the columns matter so much? Because elements in the same group have the same number of electrons in their outer shell, and it is those outer electrons (the valence electrons) that do the chemistry. Same outer arrangement, same chemical habits. Group 1, the alkali metals, all have a single outer electron they give up eagerly, so they are violently reactive. Group 18, the noble gases, have a full outer shell, so they sit there and do almost nothing.

Three trends are worth knowing, and you can see all three in the table above. Atomic radius: atoms get bigger going down a group (more shells) and smaller going across a period (a stronger pull from more protons). Ionisation energy, the energy to tear off an outer electron, does the opposite: it rises across a period and falls down a group. Electronegativity, how hard an atom pulls on shared electrons in a bond, follows ionisation energy closely, peaking near fluorine in the top right.

Mendeleev actually ordered his table by chemical properties and atomic weight, and left gaps where the pattern demanded a missing element. A few pairs looked out of order by weight. The fix came from Henry Moseley in 1913, who showed the true ordering is by \(Z\), the proton count, not by weight. Order by \(Z\) and the anomalies vanish. The table also splits into metals on the left, non-metals on the top right, and a staircase of metalloids in between.

The real cause is quantum. The table is not an empirical accident that Moseley tidied up; it is a direct read-out of atomic structure. Electrons occupy orbitals grouped into shells and subshells (s, p, d, f), and they fill those states from the lowest energy upward, roughly in the order set by the Madelung rule. Each subshell holds a fixed number of electrons: s holds 2, p holds 6, d holds 10, f holds 14. The lengths of the periods, 2, 8, 8, 18, 18, 32, come straight out of these capacities, which trace back to the \(2n^2\) counting of states in a shell.

Valence configuration writes the chemistry. An element sits in a group because of its outer-electron configuration. The alkali metals are all \(ns^1\); the halogens are all \(ns^2np^5\), one electron short of a closed shell; the noble gases close the p subshell at \(ns^2np^6\). The s-block and p-block make up the main groups, the d-block gives the transition metals, and the f-block is peeled off below as the lanthanides and actinides so the table stays a sensible width.

The trends come from effective nuclear charge. An outer electron does not feel the full nuclear charge \(Z\); inner electrons screen it, so it feels an effective charge \(Z_{\text{eff}}\). Across a period \(Z_{\text{eff}}\) climbs while the shell stays the same, so atoms contract and hold their electrons more tightly (radius down, ionisation energy up). Down a group a new shell is added and shielding grows, so the outer electron sits farther out and leaves more easily. The trend lines are just \(Z_{\text{eff}}\) and shell number competing.

The awkward details are physics, not exceptions. Gold is yellow and mercury is a liquid because their inner electrons move fast enough for special relativity to matter, contracting the s orbitals and shifting energy levels. Chromium and copper break the tidy filling order because a half-filled or filled d subshell is slightly more stable. None of this is bolted on. The whole table is an emergent consequence of the Pauli exclusion principle stacking electrons into the solutions of the Schrödinger equation for atoms. Mendeleev drew the map decades before anyone knew why it worked; the answer turned out to live in quantum mechanics.