explain sommerfields atomic model in great detail?how is it related to DeBroglie's equation?
Sommerfeld extended Bohr Theory and gave his postulates.
According to him, the stationary orbits in which electrons are revolving around the nucleus in the atom are not circular but elliptical in shape. It is due to the influence of the centrally located nucleus. The electron revolves in elliptical path with nucleus at one of its foci. So there will be a major and a minor axis of the path. He said that with the broadening of the orbit, the lengths of the two axis approach to equal value and ultimately become equal i.e. the path become circular. So we can say the circular path is just one special case elliptical path.
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/2? 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.