Does Hund's Rule Apply to Electrons in Different n Shells?

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Discussion Overview

The discussion centers on the applicability of Hund's rule to electrons in different n shells, particularly in the context of combining angular momenta and filling subshells. Participants explore the implications of Hund's rule in relation to quantum numbers and total angular momentum.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions whether Hund's rule applies when combining angular momenta of electrons from shells with different quantum numbers n.
  • Another participant clarifies that Hund's rule pertains to filling subshells rather than combining angular momenta.
  • A participant elaborates on the total angular momentum L and total spin S of an atom, stating that Hund's rule indicates the lowest-energy state has the greatest S and L.
  • A later reply reiterates the previous point about the total angular momentum and spin, suggesting that if Hund's rule holds in specific cases, it should hold universally.
  • One participant expresses confusion regarding the previous statements.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the applicability of Hund's rule to electrons in different n shells, with differing interpretations of its relevance to angular momentum and subshell filling.

Contextual Notes

There are unresolved assumptions regarding the definitions of angular momentum and subshells in the context of Hund's rule, as well as the implications of combining angular momenta from different shells.

salsero
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Does Hund's rule also apply when combining the angular momenta of electrons from shells with DIFFERENT quantum number n?
 
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I'm not sure of what you mean. Hund's rule does not have to do with "combining angular momenta", but rather with filling subshells.
 
Suppose there are n electrons with angular momentum quantum numbers L1, L2, L3, ..., Ln. The total angular momentum L of the atom can be any number between the minimum and the maximum of all non-negative combinations +/- L1 +/- L2 +/- L3 ... +/- Ln (in steps of 1). Same about combinations of the spin (the spin quantum numbers of the single electrons are always 1/2) to the total spin S of the atom.

Hund's rule says that the lowest-energy state among all the possible states is the state which has the greatest S and the greatest L (for that S).
 
Originally posted by salsero
Suppose there are n electrons with angular momentum quantum numbers L1, L2, L3, ..., Ln. The total angular momentum L of the atom can be any number between the minimum and the maximum of all non-negative combinations +/- L1 +/- L2 +/- L3 ... +/- Ln (in steps of 1). Same about combinations of the spin (the spin quantum numbers of the single electrons are always 1/2) to the total spin S of the atom.

Hund's rule says that the lowest-energy state among all the possible states is the state which has the greatest S and the greatest L (for that S).

If it's true in two cases, it's true in all (in this case)

Best wishes
 
What?
 

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