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Sommerfeld's Atomic Model, Extension to the Bohr Model

Sommerfeld's atomic model, extension to the Bohr model

Sommerfeld's atomic model is an extension of Bohr's atomic model. The new model was developed by the German physicist Arnold Sommerfeld and his assistant Peter Debye in 1916. The model was made with the help of Albert Einstein's theory of relativity. Sommerfeld discovered that electrions in certain atoms reached speeds close to the speed of light.

The basic modifications of the Sommerfil model with respect to Borr's are:

  • Electrons move around the nucleus of the atom, in circular or elliptical orbits.

  • From the second energy level there are one or more sublevels at the same level.

  • The electron is a tiny electric current.

The current model of the atom, known as the atomic orbital model, could not have been formulated without the earlier models derived from Bohr's hypotheses.

    What Were the Limitations of Bohr's Atomic Model?

    Bohr's atomic model was seamless when it came to the hydrogen atom. On the other hand, when it came to atoms of other chemical elements, the electrons of the same energy level had different energy.

    For the hydrogen atom and the He + ion, this does not affect the spectrum, because both types of shells are energetically equal. However, for multi-electron atoms, the number of possible energy levels increases. In the spectrum, this manifests itself in a greater number of spectral lines.

    What Was Sommerfeld's Solution to the Limitations of the Bohr Model?

    Regarding these cracks, Sommerfeld postulated that within the same energy level there were sublevels, with slightly different energies. Furthermore, from theoretical calculations, Sommerfeld had found that in certain atoms the speeds of the electrons reached an appreciable fraction of the speed of light. Sommerfeld also performed these calculations for relativistic electrons.

    Sommerfeld's atomic model introduced two basic modifications:

    • Relativistic velocities.

    • In atoms, electrons move in circular and elliptical orbits unlike Niels Bohr's model in which electrons only rotate in circular orbits.

    The eccentricity of the orbit gave rise to a new quantum number that determines the shape of the orbitals: the azimuthal quantum number.

    During elaboration, a principal quantum number n = n '+ k. The secondary quantum number n 'determines the angular (radial) momentum and eccentricity of the ellipse. For n '= 0 circular orbits arise. The lateral quantum number k describes the angular momentum that the hydrogen electron can take.

    What Is the Wilson-sommerfeld Formula?

    The Wilson-Sommerfeld formula represented a key element for the definition of a Bohr-Sommerfeld model.

    In this model, electrons were supposed to travel around the nucleus in elliptical orbits, as opposed to Bohr's original model in that they moved in circular orbits.

    The Bohr-Sommerfeld model contemplated an addition to the restriction on the quantization of the angular momentum of the electron with an additional quantization restriction of the radius determined through the "Wilson-Sommerfeld quantization restriction formula":

    Sommerfeld's atomic model, extension to the Bohr model

    Where is p Is the moment dq represents the differential of the generic coordinate function q (t) and n are natural numbers and h is Planck's constant.


    Published: August 18, 2021
    Last review: August 18, 2021