Why does the Rydberg equation only work for hydrogen?

Answer 1

The Rydberg equation only works for hydrogen because it is an empirical formula that is based on the Bohr model of the hydrogen atom and can only apply to it and other hydrogenic species. The Bohr model assumes that hydrogen and all subsequent elements have quantized shells with each taking discrete principle energy levels. However, the Bohr model breaks apart past hydrogen due to the presence of two or more electrons in higher atomic numbered elements, which introduces electron-electron interactions that complicate things significantly and can only be explained by more in-depth and rigorous quantum mechanics.