from my notes/biki:
Because these orbiting electrons can be thought of as waves, where the shell number relates to the number of waves, if you have non integer number of waves then the wave will not join and will collapse. So electrons can only exist where a whole number of waves is possible. This coincided with the specific orbits that Bohr had postulated. Since the electron could exist as a wave it was in a non-radiating energy level as also postulated by Bohr.
image:
http://www.boredofstudies.org/wiki/images/f/f2/Sci_phys_quanta_de_broglie.png