How can the electron be a wave? I read about Rutherford's failed attempt to describe the atomic model. Then I read about Bohr's model and his postulates. Ok, that was fine. But then I read in my book  a statement that shocked me:

One and the most important discovery of quantum mechanics was that electron behaves as wave....

Now, how can an electron, a particle revolving around the nucleus in a quantized orbit, be a wave?
 A: If one wishes to get a clear image about what is a quantum object, it is very recommended to read the Feynman's path integral,
https://www.scribd.com/doc/227963184/Feynman-Hibbs-Quantum-Mechanics-and-Path-Integrals-pdf#scribd
The electron behaves as a wave because inside an atom, it behaves as a quantum object, not as a classical object. A classical body has a trajectory. But a quantum object has a wave, a wave-length, produces interference as a wave. In the atom, the movement of the electron doesn't fit the classical laws of movement, i.e. rotates with some velocity around the nucleus. It is even difficult for us to say if it rotates. The best description we can give for the dynamics of the electron in the atom, is the wave-function.
Why is it difficult to say that it rotates? In the classical mechanics, an object that rotates around a rotation axis has an angular momentum along that axis. And in the plane perpendicular to that axis, the projection of the angular momentum is zero. But, for instance, in a hydrogen atom the electron on the lowest energy level has angular momentum zero. So, does it rotate? Hard to say.
A: When you get into quantum physics things start to get a little strange - to say the least. What you have to understand is that electrons (or any other particles for that matter) are simply modelled as particles because that matched most closely with their behaviour, as understood at the time.
As we have developed a better understanding of quantum mechanics, we understand that the particle model simply does not describe the observed phenomena well enough. We do, however, realise that some of the qualities of electrons can be described by wave theory.
I personally don't think it's correct to say an electron is a wave, simply that it behaves like a wave. In quantum mechanics, in order to begin to understand it, you need to suspend a great chunk of what you have considered to be axiomatic thus far (i.e. that particles are particles and waves are waves).
