Total Angular Momentum and Binding Energy

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Discussion Overview

The discussion centers on the relationship between total angular momentum and binding energy in atomic states, particularly focusing on the comparison between states with different total angular momentum values (J) within the same orbital configuration (2p). Participants explore the implications of Hund's rules and spin-orbit coupling in determining binding energies.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions why states with smaller total angular momentum (J) have higher binding energy, using the example of the 2p1/2 and 2p3/2 states.
  • Another participant introduces the concept of energetic interactions between spin and orbital magnetic moments, suggesting that half-filled orbitals have lower energy configurations due to alignment of magnetic moments.
  • A repeated point emphasizes the photoelectron transition from a filled 2p6 state to 2p5 states, questioning the binding energy differences between j=1/2 and j=3/2 states.
  • One participant acknowledges a mistake regarding the lowest energy state being associated with opposite alignment of spin and orbital moments for j=1/2.
  • Another participant references Hund's third rule, questioning the implications of higher J values leading to lower energy (higher binding energy) states.
  • A later reply reflects on the complexity of spin-orbit splitting in nearly filled shells, suggesting a need for further expertise on the topic.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between angular momentum and binding energy, with no consensus reached on the implications of Hund's rules or the nature of spin-orbit interactions in this context.

Contextual Notes

Participants note the complexity of the interactions involved, including the dependence on orbital filling and the specific configurations of magnetic moments, which may not be fully resolved in the discussion.

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Why, for states with angular momentum l >0, do states with smaller total angular momentum J have a higher binding energy? For example, why does the 2p1/2 state have a higher binding energy than the 2p3/2 state? If the 2p orbital is filled (2p6), wouldn't Hund's third rule indicate that the highest J value would have the lowest energy (in other words, the highest binding energy)?
 
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There is an energetic interaction (typically amounting to a few eV for core levels) between the spin magnetic moment and the orbital magnetic moment. If an orbital is half-filled, the two magnetic moments prefer to line up (have lowest energy). If the orbital is filled (as in the 2p6 configuration) there is only one possible state. Thus in a photoelectron transition:

initial state: 2p6
final states: either 2p5 with spin up, or 2p5 with spin down (non-denegerate).
 
gadong said:
There is an energetic interaction (typically amounting to a few eV for core levels) between the spin magnetic moment and the orbital magnetic moment. If an orbital is half-filled, the two magnetic moments prefer to line up (have lowest energy). If the orbital is filled (as in the 2p6 configuration) there is only one possible state. Thus in a photoelectron transition:

initial state: 2p6
final states: either 2p5 with spin up, or 2p5 with spin down (non-denegerate).

So why would the j=1/2 state (spin -1/2) have a higher binding energy than the j=3/2 (spin 1/2)?
 
Sorry, my mistake - lowest energy [final] state is when the spin and orbital moments are in opposite directions (j = 1/2).
 
gadong said:
Sorry, my mistake - lowest energy [final] state is when the spin and orbital moments are in opposite directions (j = 1/2).

But from Hund's 3rd rule (http://en.wikipedia.org/wiki/Hund's_rules), would the higher J (3/2) have lower energy (higher binding energy)?
 

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