Bohr model

In 1911, fresh from completion of his PhD, the young Danish physicist Niels Bohr left Denmark on a foreign scholarship headed for the Cavendish Laboratory in Cambridge to work under J. J. Thomson on the structure of atomic systems. At the time, Bohr began to put forth the idea that since light could no long be treated as continuously propagating waves, but instead as discrete energy packets (as articulated by Planck and Einstein), why should the classical Newtonian mechanics on which Thomson's model was based hold true? It seemed to Bohr that the atomic model should be modified in a similar way. If electromagnetic energy is quantized, i.e. restricted to take on only integer values of hυ, where υ is the frequency of light, then it seemed reasonable that the mechanical energy associated with the energy of atomic electrons is also quantized.

However, Bohr's still somewhat vague ideas were not well received by Thomson, and Bohr decided to move from Cambridge after his first year to a place where his concepts about quantization of electronic motion in atoms would meet less opposition. He chose the University of Manchester, where the chair of physics was held by Ernest Rutherford. While in Manchester, Bohr learned about the nuclear model of the atom proposed by Rutherford. To overcome the difficulty associated with the classical collapse of the electron into the nucleus, Bohr proposed that the orbiting electron could only exist in certain special states of motion - called stationary states, in which no electromagnetic radiation was emitted. In these states, the angular momentum of the electron L takes on integer values of Planck's constant divided by 2π, denoted by ? = h/2π (pronounced h-bar). In these stationary states, the electron angular momentum can take on values ?, 2?, 3?... but never non-integer values. This is known as quantization of angular momentum, and was one of Bohr's key hypotheses.

He imagined the atom as consisting of electron waves of wavelength "λ = h/mv" endlessly circling atomic nuclei. In his picture, only orbits with circumferences corresponding to an integral multiple of electron wavelengths could survive without destructive interference (i.e., r = n?/mv could survive without destructive interference). For circular orbits, the position vector of the electron r is always perpendicular to its linear momentum p. The angular momentum L has magnitude "mvr" in this case. Thus Bohr's postulate of quantized angular momentum is equivalent to "mvr = n?" where n is a positive integer called principal quantum number. It tells us what energy level the electron occupies.