Explain Bohr- Sommerfeld model of an atom. What is the merit of this model? What are its limitations?

Explanation

The allowed electronic orbits for the main quantum numbers by Bohr-Sommerfeld model
1) In an attempt to account for the splitting of line spectra, Sommerfeld modified Bohr's model by adding elliptical orbits.
2) While retaining the first of Bohr's circular orbit as such, he added one elliptical orbit to Bohr's second orbit, two elliptical orbits to Bohr's third orbit, etc. such that the nucleus of the atom is one of the principal Foci of these elliptical orbits.
3) He was guided by the fact that, in general, periodic motion under the influence of a central force will lead to elliptical orbits with the force situated at one of the Foci.
Limitation : This model failed to account for the atomic spectra of atoms of more than one electron.