Derivation of Formula for the Calculation of Wave Number Of Spectra Of Radiations Due To Effect Of Nuclear Motion

According to the Rutherford and bohr’s atomic model, the nucleus of the atom is assumed to be stationery and therefore the wave number of spectra of radiation emitted from the atoms of substance when they are excited or jump back from a higher energy level to their ground state was given as 1/W=R_(S ) Z^2 (1/〖n_1〗^2 -1/〖n_2〗^2 ) where W = wave length , Z= atomic number, RS = Rydberg constant for stationery nucleus, n1 and n2 are the respective energy level 1st and 2nd . But in reality not only the electrons that are revolving round the nucleus, both the electrons and the protons are revolving around a centre of their mass, this centre of mass is close to the position of the nucleus both not the exact position of the nucleus, therefore the nucleus undergo a nuclear motion and not static as assumed in the above wave number relation. it is a known fact that the electrons are negatively charge and are equal in number as the protons s that are positively charged . this electrons in their orbit repel each other while being attracted by the nucleus, this make the electrons and the nucleus to revolve around their common centre of mass in order to balance the repulsive and attractive force between the electrons and the electrons & protons respectively. this is how the concept of nuclear motion come into being.