The theory published in 1913 by Niels Bohr to explain
the line spectrum of hydrogen. He assumed that a single
electron of mass m traveled in a circular orbit of
radius r, at velocity v, around a positively charged
nucleus.

The angular momentum of the electron would
then be mvr. Bohr proposed that electrons could only
occupy orbits in which this angular momentum had certain
fixed values, h/2p, 2h/2p, 3h/2p,...nh/2p where
h is the Planck constant. This means that the angular
momentum is quantized, i.e. can only have certain
values, each of which is a multiple of n. Each permitted
value of n is associated with an orbit of different
radius and Bohr assumed that when the atom emitted
or absorbed radiation of frequency v, the electron
jumped from one orbit to another, the energy emitted
or absorbed by each jump is equal to hv.

The idea
of quantized values of angular momentum was later
explained by the wave nature of the electron. Each
orbit has to have a whole number of wavelengths around
it, i.e. nl = 2pr where l is the wavelength and n a
whole number. The wavelength of a particle is given
by h/mv, so nh/mv = 2pr, which leads to mvr = nh/2p.

Modern atomic theory does not allow subatomic particles
to be treated in the same way as large objects, and
Bohr's reasoning is somewhat discredited. However,
the idea of quantized angular momentum has been retained.