Limits of the Bohr model

Bohr's model, with its planet-like electron, correctly predicts the gross features of hydrogenic atoms, especially the frequencies they emit or absorb.

A hydrogenic atom has a nucleus of charge +Ze and a single electron: hydrogen, singly ionised helium (He⁺), doubly ionised lithium (Li²⁺).

Limit (i): it cannot be extended even to two-electron atoms such as helium. Each electron is attracted by the nucleus and also repelled by every other electron, and the model contains no electron–electron force.

In the solar system, planet–planet gravity is tiny next to the sun's pull. In an atom, the electron–electron force is of the same order as the electron–nucleus force, because the charges and distances are comparable. That is why the planet picture fails for many-electron atoms.

Limit (ii): it predicts the frequencies of hydrogen's lines but not their relative intensities; some visible lines are strong and others weak, because some transitions are favoured over others.

Complex atoms need quantum mechanics, which gives a fuller picture; in it Bohr's orbits become regions where the electron is found with high probability.