Bohr`s theory oft hydrogen atom enabled calculation of energies and redii associated with various permissible orbits in the hydrogen atoms the calculated values were found to be in good arrangement with the experimental values . Bohr`s theory could not explain the emission of these fine spectral line in the hydrogen spectrum. however, a few years later the use of spectroscope of high resolving powers revealed the presence of fine structures (i.e., groups of very fine lines) in the spectra of hydrogen and hydrogen -like species (He+, li2+, Be3+, etc). Bohr`s theory could not explain the emission of these fine spectra . The theory was , therefore extended by sommerfeld by putting forward the idea of elliptical orbits.
According to sommerfeld, an electron revolving around a central positively charged nucleus is so influenced by the nuclear charge that it is set into motion in elliptical orbits with the nucleus situated by the nuclear charge that foci . Thus, while according to Bohr`s theory, electrons move in circular orbits, In the latter case, there will be a major axis and a minor axis having different lengths. As the orbital broadens, the length of the two axes becoms closer they become equal when the orbit becoms circular, as shown in fig below . Thus the circular orbits is only a special case of elliptical orbits.
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