Electrons fly on certain orbits around nucleus. why do not they radiate waves and crash to the nucleus? How to fill the gap between classical physics and quantum physics?
 A: In classical physics an electron is a particle with a single location. When the electron orbits an atom, its position changes over time and it accelerates. An accelerating charge radiates light and so the electron loses energy and falls into the atom.
In quantum mechanics an electron doesn't have a single well-defined position. Rather, there are multiple versions of it spread out over a finite region. The wave function is a quantity defined everywhere in space that describes how these different versions interact and gives the probability of finding an electron in a particular region: it's like a sort of blob of fog whose intensity gives the probability of finding the electron. The different versions interact with one another to form a sort of blob in position and momentum which can't be compressed too much. If you compress the electron so that it has a narrow momentum distribution then it spreads out in position and vice versa.
As a result, on a small enough scale the electron doesn't have a single well defined trajectory at all. The force exerted by the proton on the electron pulls the wave function close to the proton but can't make it shrink too much as I described. As a result, the collection of different versions of the electron sit around the atom without changing their position or momentum overall even though you can't really say that any individual version of the electron is still. So the electron cloud doesn't accelerate.
If you look at the electron on a large enough scale and don't pay attention to the small scale, then the electron looks a bit like a particle because the blob (wave function) is concentrated in a small enough region that you don't see the details. The position of the whole blob can change over time under some circumstances and when this happens the charge can be said to accelerate and it radiates. But that approximation fails near atoms.
A: Adopting Planck's idea of quantized energy levels, Bohr hypothesized that in a hydrogen atom there can be only certain values of total energy (electron kinetic energy plus potential energy) for the electrons.
These allowed energy levels correspond to different orbits for the electrons as it moves around the nucleus, the larger orbits associated with larger total energies.
Bohr assumed that an electron in one of these orbits does not radiate electromagnetic wave. For this reason, the orbits are called stationary orbits or stationary states. 
Bohr recognized that radiation-less orbits violated the laws of physics. But the assumption of such orbitals was necessary because the traditional laws indicated that electron radiates electromagnetic waves as it accelerates around a circular path, and the loss of the energy carried by the waves would lead the the collapse  of the orbit. 
