First workable theory of internal structure of atoms was proposed by Niels Bohr in 1913. The main postulates of this theory are: 1. Nuclear model, 2. Idea of permitted stationary states, 3. Energy transition in discrete units, or quanta. Bohr’s theory was successful, albeit through apparently blind assumptions on quantization of angular momentum, in explaining the stability of atoms. It was also fairly successful in explaining the line spectrum of Hydrogen atom.
The wave mechanical model was, however necessitated to rectify certain drawbacks encountered by the Bohr theory, especially in the light of two concepts, viz. the wave-particle duality proposed by de Broglie in 1924, and Heisenberg’s uncertainty principle in 1927. Bohr theory also failed to give any real explanation of why the electrons were restricted to only certain orbits. This was resolved by imagining a wave associated with the electron moving in a Bohr orbit. If this wavelength does not divide the path-length (circumference of the orbit), a whole number of times, then the waves woud destructively interfere. Thus there will be certain permitted orbits. The uncertainty aspect was resolved by considering orbitals instead of waves as “a region in the 3D-space around the nucleus, guided by a set of mathematical conditions, where the probability of finding the electron is maximum”. The wave mechanical model uses the Schroedinger equation to predict the probabilities of where the electron may be positioned at any given time (without saying with any certainty where the electron actually is).