Fine structure, and hyperfine structure

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Discussion Overview

The discussion revolves around the applicability of equations related to fine structure and hyperfine structure in atomic spectra, particularly focusing on one-electron atoms and their implications for larger atoms or ions with more than one electron.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the equations discussed are applicable only to one-electron atoms or if they also extend to larger atoms, such as helium.
  • Another participant references a book by Gerhard Herzberg, noting that the spectra for hydrogen-like ions can be derived using the atomic number Z, specifically mentioning He+, Li++, and Be+++ as examples of one-electron systems.
  • A different participant points out that while these ions are indeed one-electron systems, they inquire whether the equations would also apply to two-electron systems, suggesting a potential difference in applicability.
  • One participant asserts that the equations are only valid for nuclei with a single electron, providing an example of a carbon ion with one electron and its ionization energy.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the equations to one-electron versus multi-electron systems, indicating that multiple competing views remain without a consensus.

Contextual Notes

There are unresolved assumptions regarding the conditions under which the equations apply, particularly concerning the transition from one-electron to multi-electron systems.

Denver Dang
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Hello...

I was just reading about that, and I have one question.
In the chapter I've jut read about, the overall headline is about one electron atoms, so I was just wondering, since the overall equation got Z (Atomic number) in it, if this was for larger atoms as well, or ONLY one electron atoms, or maybe even Helium as well ?

I hope you know what I mean :)


Regards.
 
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I picked up my old "atomic spectra & atomic structure" book by Gerhard Herzberg and is says:

Spectra of hydrogen-like ions. Taking Z=2... gives the spectrum which would be emitted by an electron moving about a nucleus with charge 2; that is, the spectrum of He+. Analogously, for Z=3 and Z=4, we obtain the spectra of Li++ and Be+++.
 
But they have one electron as well, since they are ionized, don't they ?
I mean, would it also count for a two electron system, or is that completely different ?
 
I think the equations apply only to nuclei with only one electron: For example, the ionization energy of a carbon nucleus with only one electron is 62 x 13.6 eV. This would be a C+++++ ion.

Bob S
 

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