Bohr's Atomic Model

Niels Bohr resolved the contradiction between Rutherford's mostly-correct nuclear picture and the classical prediction of atomic collapse by borrowing ideas from the newly emerging quantum physics of his time. His key insight was that Rutherford's model needed only ONE fundamental fix: some orbits must be inherently stable, with electrons in them simply not radiating, contrary to what classical electromagnetism demands. Bohr built his complete atomic model around three postulates.

First, electrons revolve around the nucleus in circular orbits, exactly as in Rutherford's model, with the necessary centripetal force supplied by the electrostatic force of attraction between the electron and the positively charged nucleus.

Second -- and this is the genuinely new, quantum ingredient -- the radius of an electron's orbit cannot take just any value. Only orbits in which the electron's angular momentum is an exact integer multiple of $h/2\pi$ (h being Planck's constant) are allowed: $m_ev_nr_n=\frac{nh}{2\pi}$, where n = 1, 2, 3, ... is called the principal quantum number. Electrons in these special, quantized 'stable' or 'stationary' orbits do not radiate energy, in flat contradiction of classical electromagnetism -- Bohr simply postulated this as a new law of nature for the atomic scale, to be justified later (see de Broglie's explanation, section 15.6.4). …