Question

How many elliptical orbits are added by Sommerfeld in third Bohr's orbit? What was the purpose of adding these elliptical orbits?

Answer 1

Two elliptical orbits were added in third Bohr's orbit.

Purpose of adding was:

$1)$ Failure of Bohr's model to account splitting of line spectra. In an attempt to account for line spectrum structure, Somerfield modified Bohr's atomic model by adding elliptical orbits.