Bohr’s Model for Hydrogen Atom

Why was a change in the Bohr Model of atom required? Due to which important development (s), concept of movement of an electron in an orbit was replaced by, the concept of probability of finding electron in an orbital? What is the name given to the changed model of atom?

When an electric discharge is passed through hydrogen gas, the hydrogen molecules dissociate to produce excited hydrogen atoms. These excited atoms emit electromagnetic radiation of discrete frequencies which can be given by the general formula.

$\overline{\mathrm{\nu }}=109677 \left(\frac{1}{{\mathrm{n}}_{\mathrm{i}}^2}-\frac{1}{{\mathrm{n}}_{\mathrm{f}}^2}\right)$

What points of Bohr’s model of an atom can be used to arrive at this formula? Based on these points derive the above formula giving description of each step and each term.