Bohr model
In 1913 Niels Bohr proposed a model of the atom that boldly mixed classical orbits with quantum rules. He imagined the electron circling the nucleus like a planet, but allowed only certain special orbits, those in which the electron's angular momentum is a whole-number multiple of ħ. In these chosen orbits, he simply declared, the electron does not radiate and does not spiral inward — sidestepping the classical catastrophe that had doomed earlier atoms.
Each allowed orbit corresponds to a fixed, quantized energy level. An electron can leap from one level to another, and when it drops to a lower level it emits a photon carrying exactly the energy difference; absorbing such a photon lifts it back up. With this picture Bohr derived the Rydberg formula from scratch and even computed the Rydberg constant from fundamental quantities, an astonishing success that pinned the spectrum of hydrogen to the structure of the atom.
The Bohr model was a triumphant halfway house. It explained hydrogen beautifully yet failed for atoms with more than one electron and could not predict the brightness of lines. Its picture of electrons on tidy little tracks is now known to be wrong — electrons occupy fuzzy probability clouds, not orbits — but its central insight, that atomic energy is quantized and spectra come from jumps between levels, survived intact into the full theory.
Only special orbits are allowed; jumps between their fixed energies emit or absorb photons.
Do not take the orbiting-planet image literally. Modern quantum mechanics replaces sharp orbits with probability clouds called orbitals; the Bohr model gets hydrogen's energy levels right almost by lucky accident, not by a correct picture of where the electron is.