Mathematical analysis of a Bohr atom model Academic Article uri icon


  • Bohr proposed in 1913 a model for atoms and molecules by synthesizing Planck's quantum hypothesis with classical mechanics. When the atom number Z is small, his model provides good accuracy for the ground-state energy. When Z is large, his model is not as accurate in comparison with the experimental data but still provides a good trend agreeing with the experimental values of the ground-state energy of atoms. The main objective of this paper is to provide a rigorous mathematical analysis for the Bohr atom model. We have established the following: (1) An existence proof of the global minimizer of the ground-state energy through scaling. (2) A careful study of the critical points of the energy function. Such critical points include both the stable steady-state electron configurations as well as unstable saddle-type configurations. (3) Coplanarity of certain electron configurations. Numerical examples and graphics are also illustrated. © 2006 American Institute of Physics.

author list (cited authors)

  • Chen, G., Ding, Z., Hsu, S., Kim, M., & Zhou, J.

citation count

  • 5

publication date

  • February 2006