Quantum Numbers & Electron Energy

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Discussion Overview

The discussion revolves around the quantum numbers that influence the energy of an electron within an atom, specifically focusing on the hydrogen atom and the implications of different quantum mechanical theories. Participants explore the roles of principal quantum number (n), azimuthal quantum number (l), and total angular momentum (j) in determining electron energy levels.

Discussion Character

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

Main Points Raised

  • One participant suggests that the principal quantum number (n) and azimuthal quantum number (l) are related to electron energy, but expresses uncertainty about their roles.
  • Another participant clarifies that in the hydrogen atom, energy is determined by either the principal quantum number (n) alone or both (n) and total angular momentum (j) in Dirac's theory, which incorporates relativistic effects.
  • A participant indicates that changing the azimuthal quantum number (l) affects the total angular momentum (j) and thus the energy level, suggesting that (l) indirectly influences energy in Dirac's framework.
  • There is a reiteration that according to Schrödinger's theory, only the principal quantum number (n) changes the energy of the electron, with no consideration for spin or relativistic effects.

Areas of Agreement / Disagreement

Participants express differing views on the influence of quantum numbers on electron energy, particularly regarding the roles of (n) and (l). There is no consensus on whether (l) affects energy levels in all contexts, as some participants assert it does while others maintain it does not in Schrödinger's theory.

Contextual Notes

Limitations include the lack of clarity on how different quantum mechanical models apply to multi-electron atoms and the implications of relativistic effects and spin on energy levels.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of quantum mechanics, particularly those exploring atomic structure and the role of quantum numbers in determining electron energy levels.

SeReNiTy
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Hi i was wondering what quantum numbers can change the energy of a electron within a atom. I thought it would be n and l since its the energy and sub energy numbers, but i was wrong. Can someone explain it in some more deatail please?
 
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For the simplest of them all,the H atom,without taking into account hyperfine structure Hamiltonian and the Lamb shift due to the interaction to virtual photons,it's EITHER "n" (Schrödinger's theory) or "n" and "j" (the latter is the sum between "l" and "s") in Dirac's relativistic theory.

The best analysis of the H & He atoms is found in [1],while in the general case,a good approach on atomic physics is found in [2].

I don't know what u mean by "sub energy numbers.

For a multielectronic atom,the problem of computing total angular momentum operator is not that simple.Read more in [3]

Daniel.

-----------------------------------------------------------------------
[1]Bethe & Salpeter:"Quantum Mechanics of One and Two Electron Atoms"
[2]R.E.Moss:"Advanced Molecular Quantum Mechanics".
[3]Bransden & Joachain:"Atom's and Molecule's Physics".
 
I think that is way above my level now, I'm only first year university dexter! :biggrin:

Now my question was changing which of the quantum numbers will change the energy of the electron in the atom. I know that if you change the "n" number obviously the energy of the electron will change cause it has either been promoted or demoted to a higher/lower energy level but i was thinking if you change "l" the angular momentum number you should also change the energy of the electron as s,p,d,f subshells also have different energy levels as I'm led to believe! :confused:
 
Yes,i said that in the formula of energy levels (in Dirac's theory) "l" is included indirectly by means of "j"...So varying "l" means varying "j" and therefore changing the energy level.

Daniel.
 
dextercioby said:
Yes,i said that in the formula of energy levels (in Dirac's theory) "l" is included indirectly by means of "j"...So varying "l" means varying "j" and therefore changing the energy level.

Daniel.

So in other words your saying sticking purely to shrodingers theory only "n" changes the energy of the electron?
 
That's right.

Daniel.

P.S.No spin involved in SE,nor relativistic effects...
 
dextercioby said:
That's right.

Daniel.

P.S.No spin involved in SE,nor relativistic effects...

Thanks dexter, this forum is always a great resource! :smile:
 

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