Niels BohrSaid Nothing Clearly. Explained Everything.

The sticker says Said Nothing Clearly. Explained Everything. In 1913 he said one thing very clearly. It was wrong in its details and right in its numbers.

Rutherford had shown that an atom is a tiny, heavy nucleus with electrons far outside. Classically, a circling electron should radiate and spiral inward in a tiny fraction of a second. Atoms do not do that. In a trilogy of papers in the Philosophical Magazine in 1913, Niels Bohr simply declared that electrons can occupy only certain orbits, fixed by Planck's constant, and give off light only when they jump from one to a lower one.

The rules on this page are the payoff. The allowed energies of hydrogen are minus 13.6 electronvolts divided by n squared, and a jump from level i to level f releases a photon whose energy hν is the difference. From level 3 to level 2 that is about 1.89 electronvolts: red light near 656 nanometres, the brightest line in hydrogen's visible spectrum, measured decades before anyone knew why.

The orbits themselves did not survive. Quantum mechanics, built in the 1920s with Bohr's Copenhagen institute as one of its centres, replaced them with wavefunctions; the electron in hydrogen's ground state does not circle at all. But the energy levels, and the rule that light comes out in jumps between them, came through intact. So the formula stays.

His other legacy was harder to state clearly: complementarity, the idea that wave and particle descriptions are both necessary and cannot be used at the same time. He argued about the foundations with Einstein for decades, and neither fully convinced the other. He received the 1922 Nobel Prize and the 1938 Copley Medal.

Said nothing clearly? He said 13.6 electronvolts, and hydrogen agreed.