How did DeBroglie's hypothesis account for the fact that the energy in a hydrogen atom is quantised?
Bohr assumed that electrons move in an orbit around the central nucleus and only certain orbits are allowed.
The electron can be considered as a standing wave. This means that only an integral number of wavelengths can fit into a circular orbit. So we can write:
The wavelength of the electron is given by the de Broglie expression:
The angular momentum of the electron =
This is an important result in that it tells us that the angular momentum of the electron can only take integral values of