Rutherford had shown in 1911 that a tiny nucleus sits at the centre of the atom; but this model led to an impasse. By classical physics an electron orbiting the nucleus should continuously radiate energy, rapidly slow, and spiral into the nucleus in an instant. That is, Rutherford's atom should collapse in less than a second — yet atoms were stable. Something was missing.

The young Danish physicist Niels Bohr (1885–1962), working alongside Rutherford, proposed a bold solution in 1913: suspend the rules of classical physics inside the atom. For Bohr, electrons orbit the nucleus not in any orbit but only in certain permitted "stable" orbits; while in these orbits they radiate no energy. An electron gains or loses energy only when it "jumps" from one orbit to another — and this energy comes not continuously but in discrete packets (quanta). The quantum idea that Planck and Einstein had introduced for light thus entered the structure of the atom.

The power of the model was that it made a prediction that was confirmed. When hydrogen gas is heated it emits light only at certain colours (wavelengths) — a kind of fingerprint. No one knew why this sharp pattern was as it was. Bohr's model calculated that the jumps of electrons between orbits would produce exactly these wavelengths; the numbers agreed strikingly with observation. The inside of the atom now had a mathematical order.

The Bohr model was not a complete theory but a transitional step; within a decade the full quantum mechanics of Heisenberg and Schrödinger replaced it, exchanging the idea of definite orbits for clouds of probability. But Bohr's leap opened the door to the quantum world of the atom; from the periodic order of chemistry to lasers and modern electronics, everything was built upon this insight.