The Bohr model fails for multi-electron atoms because it treats each electron as moving only in the Coulomb field of the nucleus. In atoms with multiple electrons, electron-electron repulsion and shielding change the energies, so the simple Bohr energy-level equation no longer applies.
For hydrogen, there is one proton and one electron. The electrostatic attraction is described by a simple inverse-square force, allowing the Bohr model to predict discrete energies:
where is the principal quantum number. This correctly predicts the main hydrogen emission and absorption wavelengths.
In helium, however, each electron experiences both attraction toward the nucleus and repulsion from the other electron. Inner electrons also produce shielding, reducing the effective nuclear charge experienced by outer electrons. The net potential is therefore not the simple Coulomb potential assumed by the Bohr model.
| Case | Why the Bohr approach succeeds or fails |
|---|---|
| Hydrogen | One electron experiences a simple nuclear attraction, so its energy mainly depends on . |
| One-electron ions such as | The model remains useful, with energies proportional to . |
| Multi-electron atoms | Electron-electron repulsion and shielding make the energy depend on more than . |
A common misconception is that the Bohr model fails for every atom other than hydrogen. It can also describe hydrogen-like ions containing exactly one electron, such as and . Its major failure is with atoms or ions containing two or more electrons.
The model also assumes electrons occupy definite circular orbits. Modern quantum physics instead represents electrons using wavefunctions and orbitals, explaining spectral details that the Bohr model cannot predict.
This is HL content in E.1 Structure of the atom. For an Explain question, link the failure explicitly: multiple electrons cause repulsion and shielding, these alter the electrostatic potential and energy levels, and therefore the Bohr equation cannot reproduce multi-electron spectra.
