how does the wave mechanical model of the atom differ from the Rutherford's model?

Answer 1

Rutherford's model was based on the electrons having a fixed orbit around the nucleus. It also assumed that electrons were small, hard particles.

Niels Bohr (Rutherford's student) took the next step. Using Quantum Theory developed by Max Planck, he showed that the electrons are in different energy levels around the nucleus. His model is similar to the planets orbiting the sun at different levels. Bohr already included the idea (from Plank and Einstein) that electrons have a dual identity. They act as particles but also act as energy waves.

The wave mechanical model took it one step further by changing electron paths from clear orbits to imprecise orbitals.