Question

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

Answer 1

Hint: We know that the Sommerfeld model of an atom is an extended version of Bohr’s atomic model, which was formed by Sommerfeld to explain the fine spectral line phenomenon which Bohr was not able to explain. According to him electrons move in elliptical orbits in addition to circular orbits. The elliptical shape of the orbits is due to the influence of a centrally located nucleus.

Complete Step by step answer: Sommerfeld suggested that orbits are made up of sub energy levels which are $s,p,d,f$ .These subshells possess slightly different energies.
So, Bohr’s third orbit means that $n = 3$ , where n is the quantum number given by Bohr which determines the energy of the electron.
Sommerfeld introduced a new quantum number called the Azimuthal Quantum $(l)$ number which determines the orbital angular momentum of an electron.
So, we now see that: -
When $n = 3$
$l = 0,1,2$
Which means that $3s,3p,3d$ subshell will be present.
Let us have a look on the Sommerfeld atomic model when $n = 3$ :-

So we see that two elliptical orbits are added by Sommerfeld in the third Bohr’s orbit.
The purpose of adding these elliptical orbits was that as Bohr was unable to explain the splitting of line spectra so, in an attempt to account for spectrum structure, Sommerfeld modified Bohr’s atomic model by adding elliptical orbit. By Retaining the first of Bohr’s circular orbit Sommerfeld added two elliptical orbits to Bohr’s third orbit.

Note: Sommerfeld atomic model also showed some defects which are:
-Sommerfeld did not predict the exact number of lines which are actually present in the fine spectrum.
-This model was not able to explain the behaviour of a system having more than one electron.
- It does not explain the Zeeman and Stark effect