Term symbols & degeneracy

  • Thread starter osskall
  • Start date
47
0
Hi!

I've finally made some effort to understand spectroscopic term symbols ([tex]^{2S+1}L_J[/tex]) and after having thought a few times that I'd understood but then running into trouble again, now I'm fairly convinced that I got it right. But some things bother me though.

Apparently I was locked too much in the idea that e.g. triplet states have to have unpaired electrons. I thought the number of unpaired electrons was reflected in the value of S. Hence I couldn't imagine a triplet microstate (of e.g. the configuration [tex]p^2[/tex]) with [tex]M_S=0[/tex] as one of the states having only paired electrons but had to rather think of it as something virtual/unimaginable in between the all-unpaired-spins-up and all-unpaired-spins-down microstates. But it seems like the number of unpaired electrons for a certain microstate is only related to [tex]M_S[/tex] and that some of the states unpaired electrons actually do belong to a triplet state.
And thus similarly, for e.g. the [tex]^4[/tex]S states of [tex]p^3[/tex], there are, besides the obvious states [tex]\underline{\uparrow~~}~\underline{\uparrow~~}~\underline{\uparrow~~}[/tex] and [tex]\underline{\downarrow~~}~\underline{\downarrow~~}~\underline{\downarrow~~}[/tex] two microstates where one electron has opposite spin to the other two. There are 6 such microstates with [tex]M_L=0[/tex] which all look similar, but, yet, two of them (one with [tex]M_S=1/2[/tex] and one with [tex]M_S=-1/2[/tex]) will have the same energy as the above mentioned states with all spins paired and the other four will have higher energy (belonging to either [tex]^2[/tex]D or [tex]^2[/tex]P where in any case all states only have one unpaired electron). This is somewhat hard to grasp for me. According to this, states that look completely similar are splitted and states that have either (in this case) 3 or 1 unpaired electrons and thus should have different energy are actually degenerated...
Is this correct?

When it comes to deriving the term symbols, there's nothing to it any more, but understanding it seems to be something totally different.

PS: I'm now basing my understanding of term symbols on http://www.chem.ufl.edu/~itl/4412/lectures/ATermSym.html [Broken], where the approach also is illustrated graphically for [tex]p^2[/tex] and [tex]p^3[/tex], since this approach no longer leads me to any contradictions except for the one mentioned here.
 
Last edited by a moderator:

Want to reply to this thread?

"Term symbols & degeneracy" You must log in or register to reply here.

Related Threads for: Term symbols & degeneracy

Replies
4
Views
6K
  • Posted
Replies
1
Views
2K
  • Posted
Replies
4
Views
3K
  • Posted
Replies
3
Views
4K
  • Posted
Replies
6
Views
19K
  • Posted
Replies
1
Views
4K
  • Posted
Replies
3
Views
3K
  • Posted
Replies
7
Views
1K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top