Bohr model (source code)

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The Bohr model assumes circular electron orbits with quantized <orbital angular momentum> $N\hbar$. It reproduces the hydrogen energy levels, but <wavefunctions> in quantum mechanics describe spatial probability distributions rather than definite trajectories. In particular, spherically symmetric <Coulomb bound states> have zero <orbital angular momentum>.

The puzzle is the coexistence of reproducible <spectral lines> and stable <chemical atoms>. A classical circular <orbit> in a <Coulomb potential> can have any negative <energy>: <Coulomb's law> alone selects no special radius or emitted <frequency>. Moreover, its <electron> has <centripetal acceleration>. The <Larmor formula> then predicts positive radiated power, so <conservation of energy> makes the <orbit> shrink. Simply drawing concentric circles explains neither stability nor a discrete <spectrum>.

<Niels Bohr> postulated nonradiating <stationary states> and emission with $h\nu=E_i-E_f$. His circular-orbit condition is $L=n\hbar$. These assumptions override classical radiation; the emitted <frequency> need not equal an orbital <frequency>.<On the Constitution of Atoms and Molecules, Part I by Niels Bohr>[Part I, pp. 7–8, 15: postulates]{ref}