Why could the Bohr model not fully explain atoms with more than one electron?

The Bohr atomic model, developed by Danish physicist Niels Bohr in 1913, was highly successful in describing the hydrogen atom and other single-electron systems, such as the singly ionized helium atom. However, it could not fully explain the structure or spectra of atoms with more than one electron.12

The model’s limitations in multielectron systems stemmed from several factors:

• Complexity of Interactions: Bohr’s model relied on the assumption that electrons travel in fixed, circular orbits governed by quantized angular momentum. In atoms with multiple electrons, the complex electrostatic interactions between the electrons themselves, in addition to their attraction to the nucleus, could not be accounted for by the simple orbital rules Bohr established.2
• Incomplete Quantum Description: The model lacked the necessary framework to describe the fine details of atomic structure, such as the splitting of spectral lines caused by spin-orbit interaction or magnetic field effects (the Zeeman effect).23
• Need for Wave Mechanics: Understanding multielectron atoms required the development of quantum mechanics, which represents electrons using wave functions rather than simple orbits.12