Sommerfeld model and fine spectral lines

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Discussion Overview

The discussion revolves around Sommerfeld's atomic model, specifically focusing on the energy differences in elliptical orbits for electrons and the implications of Einstein's mass-velocity dependence. Participants explore the relationship between kinetic and potential energy in different elliptical orbits, particularly in multi-electron atoms.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how energy differences arise in elliptical orbits for the same quantum number n, questioning the relationship to mass-velocity dependence.
  • Another participant suggests that the energy differences may relate to the precession of the orbital and spin angular momentum, though they acknowledge a lack of expertise.
  • A different participant challenges the connection to spin angular momentum, noting that Sommerfeld's theory predates the discovery of spin and claims it explains the observed phenomena.
  • One participant mentions that in elliptical orbits, the varying speeds of the electron do not cancel out in terms of energy, but they are unsure which parameters remain constant when changing ellipticity.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the explanations for energy differences in elliptical orbits, with multiple competing views presented regarding the role of mass-velocity dependence, precession, and angular momentum.

Contextual Notes

There are unresolved assumptions regarding the relationship between kinetic and potential energy in elliptical orbits, as well as the implications of the model for multi-electron atoms. The discussion reflects varying levels of understanding and familiarity with the Sommerfeld model.

Who May Find This Useful

Students and enthusiasts of chemistry and atomic physics, particularly those interested in atomic models and the behavior of electrons in different orbital configurations.

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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! :biggrin:
 
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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.
 
dlgoff said:
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.
 
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.
 

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