What is the spin quantum number of an atom in 4P state?

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Discussion Overview

The discussion revolves around the spin quantum number of an atom in a 4P state, focusing on the concepts of spin-orbit coupling, term symbols, and angular momentum in atomic physics. Participants explore the definitions and relationships between quantum numbers in this context.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asserts that for an atom in a 4P state, the spin quantum number s is 3/2, referencing the relationship between the exponent in the term symbol and the value of S.
  • Another participant seeks clarification on how a term symbol is constructed, specifically mentioning the form 2S+1LJ and noting that the value of J is omitted in the current discussion.
  • There is a question regarding the meaning of the term "4P" and the construction of term symbols, indicating some confusion about the terminology used.
  • One participant confirms that the angular momentum quantum number l is 1 for a P state and asks how the value of s is determined.
  • Another participant explains that the notation used is a legacy from earlier atomic physics, linking the uppercase letters used for total orbital angular momentum to the nomenclature of orbitals.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the terminology and relationships between quantum numbers, indicating that there is no consensus on the clarity of the concepts discussed.

Contextual Notes

Some participants express uncertainty about the notation and relationships involved in term symbols and angular momentum, suggesting that further clarification may be needed. The discussion does not resolve these uncertainties.

shedrick94
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If an atom described by spin-orbit coupling is in a 4P state, why is the spin quantum number s=3/2?
 
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I guess you mean 4P. How is a term symbol built up?
 
That's the terminology in the question yes. I don't quite understand what 4P means though? What do you mean by term symbol?
 
The description of the angular momentum of a state is called a term symbol. In Russell-Saunders (LS) coupling, it has the form 2S+1LJ. In your particular case, the value of J has been omitted.
 
So the angular momentum quantum number is l=1 as it's a P state? How is the value of s determined?
 
shedrick94 said:
So the angular momentum quantum number is l=1 as it's a P state? How is the value of s determined?
The exponent is 2S+1, so for a quadruplet, 2S+1 = 4 means S=3/2.
 
Sorry I've never seen this notation before so I wasn't aware of the relationship. So why do we have L=P then?
 
shedrick94 said:
Sorry I've never seen this notation before so I wasn't aware of the relationship. So why do we have L=P then?
It's a legacy from the earlier days of atomic physics. It follows the same nomenclature as orbitals: s, p, d, f, etc., but with uppercase letters (just as the total orbital angular momentum is L, instead of l for the orbital angular momentum of a single electron).
 

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