In 1922 Otto Stern and Walther Gerlach sent a beam of silver atoms through a specially shaped magnet in Frankfurt. Classical physics predicted that the atoms, acting like tiny compass needles pointing every which way, would smear out into a continuous band on the detector plate. Instead, the beam split cleanly into two spots. Stern later told a story that the faint deposit became visible only after a colleague breathed on the plate, his breath full of sulfur from cheap cigars, which blackened the silver. Those two spots revealed a property that, together with one simple rule, explains the structure of every atom.

Spin

In 1925 two young Dutch physicists, George Uhlenbeck and Samuel Goudsmit, proposed that the electron carries a built in amount of angular momentum, as if it were spinning, and a tiny magnetism that goes with it. The name stuck, but the picture is only an analogy: the electron is not a little ball turning on an axis. Spin is an intrinsic property, like charge, that a particle always has and can never lose or speed up.

Spin is quantized in the extreme. Measure an electron's spin along any direction you choose, up and down, left and right, and you always get one of only two results, called spin up and spin down. A silver atom's magnetism comes from a single unpaired electron, which is why Stern and Gerlach saw exactly two spots.

Spin and measurement

Spin shows the strangeness of the earlier levels in its plainest form. Send atoms through a vertical magnet and keep only the spin up ones. Send them through another vertical magnet and they all come out up. But send them through a horizontal magnet, and half go left and half right. Now pass the "left" ones through a vertical magnet once more: after the horizontal measurement, half come out up and half come out down. Measuring horizontal spin erased the earlier vertical result, just as the middle polarizing filter did. An electron cannot have a definite spin along two different directions at once.

Two families of particles

Particles come in two great families. Electrons, protons and neutrons belong to the family called fermions, after the Italian physicist Enrico Fermi. Photons belong to the family called bosons, after the Indian physicist Satyendra Nath Bose. The families behave very differently in groups. Bosons are happy to crowd into the same state; a laser beam is many photons doing exactly that. Fermions refuse.

The exclusion principle

Wolfgang Pauli stated the rule in 1925: no two electrons in an atom can occupy the same quantum state. An electron's state in an atom is described by its energy level, the shape of its wave pattern, the pattern's orientation and its spin. Since spin offers only two choices, each wave pattern, called an orbital, can hold at most two electrons, one spin up and one spin down.

This sounds like a small technical rule. It is one of the most important facts in nature. Without it, every electron in every atom would drop into the lowest level, all atoms would behave much alike, and there would be no chemistry and no life. The rule also explains why matter takes up space: electrons cannot all be squeezed into the same region, so solid objects resist being pushed together. In collapsed stars called white dwarfs, it is this resistance, not heat, that holds the star up against its own gravity.

Orbitals are standing waves

An orbital is not a path the electron follows. It is a standing wave pattern, like the patterns on a vibrating drum skin, that gives the probability of finding the electron in each region. Only certain wave patterns fit around a nucleus, which is why energy levels are fixed. The simplest is a fuzzy sphere; others have lobes and rings, with nodes, places where the electron is never found.

Worked example: building the periodic table

Fill the orbitals of an atom one electron at a time, lowest energy first, two per orbital. The first level has room for only one orbital, so two electrons. Hydrogen has one; helium fills it with two. The next level has four orbitals, room for eight electrons, which is why the second row of the periodic table, from lithium to neon, has eight elements. Higher levels add new orbital shapes with more patterns, and the rows of the table run 2, 8, 8, 18, 18, 32 and 32 elements long. These counts, which chemists first found by sorting elements by their behavior, fall out of the wave patterns and Pauli's rule.

The outermost electrons decide how an element bonds. Quantum mechanics explains why those outer electrons are arranged as they are. Sodium has a single electron alone in a new level, far from the nucleus and easily given away; chlorine is one short of filling its level and grabs an electron readily. Put them together and you get table salt. Carbon, with four places to fill in its outer level, can link to four neighbors at once, which is why it can build the long chains and rings of living matter. The whole of chemistry, from rusting iron to the folding of proteins, rests on electrons obeying the rule that no two may share a state.