However, this was not actually the object of our considerations; we want to gain another perspective by applying minor conversions. We use the following equations:

  VI  

Hence:

  VII  

This conversion is aimed at clearing the Sommerfeld fine structure constant of c because then, as is well known, we obtain the speed of the electron on the innermost orbit of the hydrogen atom. This provides better understanding and clarity in our equation. Thus, in the denominator one finds the speed of the electron on the lowest orbit of the hydrogen atom.

Considering equation VII carefully and using our imagination, we may ask, that if equation VII is the equation of the emission, what does the equation of a steady orbit look like? Here we integrate over a closed area. Perhaps for a steady orbit we have to integrate over an annular surface? We will attempt it since such an experiment will not cost more than a failure. Actually, how often a wrong calculation has resulted in a reasonable idea! Consequently, we will replace the denominator by such an integral over a ring surface (Fig. 2):

  VIII        is replaced by the diameter of the electron ( eØ ) has to be used.