The light quantum was one strand of the revolution. The other ran through the atom. In 1900 nobody knew what an atom looked like inside, or whether atoms were real at all, a question some respected physicists still doubted. Within two decades the atom had a nucleus, electrons and a set of rules that broke with classical physics outright.

Electrons and a nucleus

J. J. Thomson discovered the electron in Cambridge in 1897. He pictured atoms as a spread of positive charge with electrons scattered through it, the so-called plum pudding model. Then Ernest Rutherford's group at Manchester tested it. In 1909 Hans Geiger and Ernest Marsden, the second still an undergraduate, fired alpha particles at a thin gold foil. A few bounced almost straight back, which the plum pudding could not allow. In 1911 Rutherford proposed that an atom has a tiny, dense, positive nucleus with electrons around it.

Rutherford's atom raised a new problem. According to Maxwell's theory, any charge moving in a circle gives off light and loses energy. An orbiting electron, therefore, should radiate its energy and spiral into the nucleus, within a tiny fraction of a second. Yet atoms are stable, and when heated they emit light only at sharp, particular colors, called spectral lines, not a smear.

Those lines had been measured with great precision. In 1885 Johann Balmer, a Swiss schoolteacher, found a simple formula fitting hydrogen's visible lines, built from whole numbers. Nobody knew why it worked.

Bohr's bold postulates

Niels Bohr, a Danish physicist, came to Manchester in 1912 after an uneasy stay with Thomson in Cambridge. In 1913, aged 27, he published a three-part paper, "On the Constitution of Atoms and Molecules." He did not try to rescue classical physics. He simply laid down new rules. Electrons could occupy only certain stationary states, in which they did not radiate. Light came out only when an electron jumped from one state to another, and the energy difference between the two states set the frequency of the light. This was the deepest break: in classical physics the light's frequency would match the electron's orbital motion, while in Bohr's theory the two had nothing to do with each other.

From these rules, combined with Planck's constant, Bohr derived Balmer's formula and the numerical constant in it. He also made a prediction. Certain lines seen in starlight and in the laboratory had been assigned to hydrogen, but Bohr argued that those lines came from ionized helium, not hydrogen. Laboratory work by Evan Evans soon supported him, and the success impressed many skeptics.

Rutherford, reading a draft, raised a sharp objection: how could an electron, when it began a jump, already know which state it would land in? Nobody had an answer, and the question would come back.

Evidence for fixed energy steps

In 1914 James Franck and Gustav Hertz in Berlin sent electrons through mercury vapor. They found that electrons lost energy to the atoms only in fixed amounts, and that the mercury then glowed at the matching color. Franck and Hertz did not at first read their result as support for Bohr, but it soon became one of the clearest confirmations that atoms have separate energy states.

The old quantum theory

Others extended Bohr's model. In Munich, Arnold Sommerfeld added elliptical orbits and extra quantum numbers from 1916, explaining the fine splitting of spectral lines. Bohr himself relied on a guiding rule he called the correspondence principle: at large quantum numbers, the new theory's results must match classical physics, since classical physics works well for big systems. The principle let physicists borrow classical results and translate them into quantum ones.

By the early 1920s this old quantum theory was a patchwork: classical mechanics, with quantum conditions bolted on by hand. It worked for hydrogen and failed for helium, the next simplest atom. It could not explain the so-called anomalous Zeeman effect, the strange splitting of lines in a magnetic field. Still, it gave physics a home base. In 1921 Bohr's new institute opened in Copenhagen, and in 1922 he received the Nobel Prize. The institute became the place where young theorists came to work on what was wrong.

Worked example: reading a red line

Heat hydrogen gas in a tube and pass its glow through a prism. Among the lines you see is a bright red one at a very precise color. In classical physics, that color should reflect how fast something in the atom is circling, and a spiraling electron should change its rate steadily, giving a smear. Bohr's account explains the sharpness instead. The red line marks one particular jump, from the third stationary state down to the second. Every hydrogen atom has the same states, so every such jump gives exactly the same color.

The helium episode shows how a theory earns trust. Bohr's rules, applied to an atom with a doubled nuclear charge, predicted where its lines should fall, and the measurements agreed. A theory that only fits what it was built to fit proves little. One that predicts something unexpected, and is right, earns attention, even when its own author admits he cannot explain why its rules work.