The evidence that Bohr's model works is in the fact that, the moon is able to move around its orbital without crashing to the continent like Australia and it is also supported by Millikan's Oil Drop experiment that explains how an atom can exist only in definite amounts of quanta, hence "stationary states."
Bohr calculated an equation that gives simplistic values for the radii or energy level shell at which the electrons could orbit in a "stationary state" where there is neither emissions nor absorptions of energies explained by the discontinuous transition between the different energy level shells.
On the other hand, multi-electron elements have more electrons and more energy levels. . Hence when electrons are excited can move from one energy level to another: either higher or lower and in the process energy is given out. Therefore, electrons are many hence energy relationships cannot be done directly or not "solved".(Nelkon, p188)