Atomic physics became a major topic at the end of the 19th century, and Rutherford’s scattering experiment revealed the existence of the atomic nucleus. Classical physics, however, could not explain why electrons do not spiral into the nucleus. In 1913 Bohr adopted Planck’s quantum hypothesis and restricted electrons to discrete orbits. When an electron moves between these allowed orbits it emits or absorbs a photon whose energy exactly equals the orbit-energy difference. This produced a theoretical derivation of the Rydberg formula for hydrogen spectra that matched experiment. The model opened the road to quantum mechanics and underpins modern technologies such as semiconductors and lasers. It is also applied in astronomy to read chemical compositions of stars and distant galaxies from their spectra. Bohr’s achievements thus benefit both science and everyday life.

Bohr started from Rutherford’s nuclear atom and introduced the quantization condition L = nħ, where angular momentum is an integer multiple of ħ. This condition discretized the radius and energy of circular electron orbits, giving the nth orbit radius a₀n², with a₀ the Bohr radius. When an electron drops from n to m (< n) it releases a photon of energy En − Em, reproducing the Rydberg wavelength formula 1/λ = R(1/m² − 1/n²). The model, a hybrid of classical mechanics and the quantum hypothesis, avoided the radiation-collapse problem but could not be applied directly to multi-electron atoms. By adding relativistic corrections and the Landé g-factor it nevertheless explained fine-structure splitting and guided atomic-spectra analysis. Bohr also formulated the correspondence principle, insisting that any new quantum theory agree with classical predictions in the high-quantum-number limit. This principle influenced Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics. Although eventually replaced by full wave mechanics, the Bohr model retains pedagogical power and still appears in introductory texts. Concepts such as the Bohr radius and ionization energy serve as standards in atomic units for quantum-chemistry calculations. The 1922 Nobel Prize recognized not only Bohr’s contribution to atomic structure but also his decisive impact on the development of quantum theory.

In his 1913 trilogy Bohr derived stable electron orbits in a Coulomb potential via the Bohr–Sommerfeld condition mvr = nħ, exactly reproducing wavenumber formulae for the hydrogen Lyman series and others. He generalized the scheme to nuclear charge Z, introduced screening constants for multielectron systems, and used the correspondence principle to relate scattering cross sections to spectroscopic transition probabilities, laying foundations for Dirac’s radiation theory and selection rules. His theoretical evaluation of the Rydberg constant included reduced-mass corrections that later guided high-precision spectroscopy and QED tests. The notion of non-radiative (metastable) states evolved into lifetime theory and influenced laser-medium design. Scaling with the Bohr radius connected his work to the Thomas–Fermi statistical model, informing macroscopic estimates of nuclear screening. Subsequent WKB generalizations of the Bohr–Sommerfeld rule provided an analytic toolkit for multi-variable quantum systems. By highlighting outstanding issues such as relativistic corrections in high-Z atoms and the Lamb shift, Bohr motivated future precision atomic physics. His contributions thus propagated beyond spectroscopy into solid-state, plasma and nuclear physics, offering a unifying framework in the formative years of quantum theory.