Sommerfeld model and fine spectral lines

[Absentee]

Hey guys! First time posting on this site. Been reading for quite a while and really loving it! :thumbs:!
I'm a chemistry student and reading my book in general chemistry I couldn't understand two things about Sommersfeld's atomic model.

I believe i understand the whole concept but what bothers me is the energy difference in different elliptical orbits.

What my textbook says is that for the same quantum number n, different elliptical orbits have a slightly different energy which is related to Einstein's mass-velocity dependence.

But what does it mean? I could understand that the highest velocity can be measured in the most elongated ellipse because electron gets as close as he can get to the nucleus so his kinetic energy rises due to the higher velocity and larger mass. But on the other hand, on that same ellipse he gets in the position where he is as far as he can get relative to nucleus so that's where his velocity should be the smallest, and so would mass - so that kinda cancels out, am i right right?
So what is this all about?

Also, what i read is that in atoms with more than one electron (with large number of electrons) the outer orbit electron while orbiting in elliptical orbit penetrates the inner orbits and gets really close the the nucleus and his potential energy gets lower. So the more elongated ellipse is, the lower overall energy is. But in that same ellipse he gets the furthest from the nucleus, and shouldn't that increase potential energy and kinda cancel out whole effect?

Could you help me? Thanks!

 

[dlgoff]

What my textbook says is that for the same quantum number n, different elliptical orbits have a slightly different energy which is related to Einstein's mass-velocity dependence.

I believe it has to do with the precession of the orbital and spin angular momentum. But I'm no expert.

 

[Absentee]

I believe it has to do with the precession of the orbital and spin angular momentum. But I'm no expert.

I believe it's not related with spin angular momentum because Sommerfeld theory was proposed before spin was known. So according to my book, Sommerfeld theory explained this phenomena. But i just don't quite get it.

 

[Khashishi]

In an elliptical orbit, the fast part and the slow part don't quite cancel out. I'm not familiar enough with the model to know which parameters are held constant as the ellipticity is changed.