What is the basis for the quantum mechanical model are the atom?

BOHR atomic model could only explain colour spectra for single electron species . rest of colour spectra couldn't be explained.

There are many factors which lead to the development of quantum theory

photoelectric effect says that if a metal is exposed certain frequency of light then it emits electrons. electron emitted moves in wave form due to it's energy

according to BOHR theory electrons have their own energy so according to Planck and Einstein electron must move in wave form