the fine spectra cannot be explained alone by the concept of elliptical Orbit alone. justify the statement

Hello Student,

As electrons travel in elliptical path, it will have an angular momentum and this angular momentum must be quantized according to the quantum theory of radiations. Bohr gave that angular momentum as m=nh/2Ω but Sommerfeld used another integer k instead of n. k is an integer known as azimuthal quantum number. n used by Bohr and k used by Sommerfeld are related as: –

n/k = length of major axis/length of minor axis

With increase in value of k, the path becomes more and more elliptical and eccentric. When k=n, the path becomes circular.

Bohr was not able to explain the reason for the fine spectral lines visible by high revolving power spectroscopes but Sommerfeld explained the reason for the same. He said that the energy of the stationary orbit depends not only on n but on k to some extent as well. So when a transition of electron from a higher level to a lower level occurs, it would be different from what proposed by Bohr as there may be more than one values of k. In this way Sommerfeld was able to explain the reason behind those fine spectral lines. Even the frequencies of some of those fine spectral lines came to be in well agreement with the frequencies by Sommerfeld.

Regards
IHE