The Bohr–Sommerfeld Model for Energy of Electron in Hydrogen Atom

  • Dr. Motiur Rahman Ansari


This paper discusses Bohr-Somerfield quantization theory and tries to explain how all earlier propositions about energy at atomic level failed to correspond to observed facts and further how this model solved the mathematical discrepancies leading to a near perfect model of energy exchange at the atomic level. The author has attempted here to show the historical connections, logical justifications as well as mathematical expressions for the energy of electron in hydrogen atom and prove how Bohr’s celebrated theory of atomic structure is an application of Planck’s theory of quanta to the Rutherford nuclear atom in an attempt, extraordinary fruitful, to define the nature of the orbits in which the electrons might revolve round the nucleus and to explain the origin of spectral lines of the elements. It further shows how Sommerfeld extended the model so as to include elliptical orbits. The introduction of the elliptic orbits has no new energy for the electron of the hydrogen atom. Bohr had also solved the dilemma arose due to the Rutherford’s atomic model and he admitting the failure of the classical theory, applied with remarkable success of the quantum theory to the Rutherford nuclear atom with revolving electron, which leads us to understand the significance of the Bohr’s atom model.

 Keywords: Electromagnetic theory, Model, Electrical attraction, Energy, Atom.