Niels Bohr, the Danish physicist who applied the nascent quantum theory to the structure of the hydrogen atom, was born In 1911, scattering experiments by Ernest Rutherford and collaborators had disproven the “plum pudding” model of the atom. Rather than a blob-like structure with + and - charge spread throughout, their experiments suggested that atoms have a tiny positive nucleus.
The negative electrons would have to orbit this positive nucleus. But classically this kind of configuration shouldn’t be stable! The accelerating electrons would radiate energy and spiral into the nucleus. Rutherford’s atom was at odds with classical physics.
But classical physics was already having problems with atomic phenomena. Atoms were known to emit and absorb light preferentially at certain wavelengths. The "spectral lines" fit simple patterns, but had no known explanation.
Bohr addressed both issues at once by positing the existence of "stationary orbits" around the nucleus. Electrons could exist in these stationary orbits without (as predicted by classical electrodynamics) radiating energy.
Transitions between these orbits emitted energy in discrete amounts (related to Planck's quanta) dictated by the initial and final level. This reproduced the empirical formulas obtained by Balmer and Rydberg for the wavelengths of the spectral lines.
Bohr's model was phenomenological; a hodgepodge of early quantum ideas that fit the data without offering deeper explanation. It preceded de Broglie's hypothesis, which would've allowed Bohr to explain orbits as integer multiples of an electron's wavelength.
But it seemed to explain (or at least relate) two outstanding puzzles that had baffled scientists. So, while many physicists were rightly concerned by the radical implications of Bohr's model, he was clearly onto something.
Bohr’s model is a central result of the "old quantum theory," the transitional body work straddling classical physics and modern quantum mechanics. These early results, which flew in the face of accepted theories, set physicists on the road to our present understanding of Nature.
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