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  GR8677 #84
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Verbatim question for GR8677 #84
Atomic}Spectroscopic Notation

Given the order in which energy levels are filled in atomic configuration 1s 2s 2p 3s 3p 4s 3d and the number of electrons in sodium, one can fill it up like 1s^2 2s^2 2p^6 3s^1. There is a net spin from the missing electron in the 3s valance shell, and thus S=1/2. The valance 3s shell has l=0 (and L=S), since s=0;p=1;d=2;f=3. J=l+S=1/2. Thus, the form should be ^{2(1/2)+1}S_{1/2}=^{2}S_{1/2}

Not even knowing anything about spectroscopic notation, one can deduce the right answer as well as the general form: ^{2S+1}(L)_{J=l+S}, where L can be either S,P,D,F... depending on whether l=0,1,2,3...

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Comments
andyferd
2010-11-12 17:35:33
When is it correct to assume ETS is asking for the spectroscopic notation of the electron rather than the atom? In a problem on a different test they give the spectroscopic notation of an atom and ask for the state of the electron after a transition (I can't remember which other practice test it is)NEC
faith
2010-10-23 23:51:18
there's ambiguity in yosun's solution although it too arrives at the correct answer.

for J
>half filled shell, J=|L+S|
< half filled shell, J=|L-S|
=half filled shell, J=S (since no net orbital momentum)

hence knowing just the value spin which is 1/2, will immediately gives the answer, B. ( and the valence electron is in sub shell s will give notation S)

to clarify S notation can be a lil confusing. S represent spins while S also is use to represent the sub shell s.
NEC
wikiwert
2010-09-15 21:55:13
This excercise is solved using Hund´s Rule; this should be mentioned in the solution (for other atoms, other problems arise, as the one mentioned by student2008).NEC
student2008
2008-10-14 03:02:16
Yosun, you're not quite right writing J = l + S, since J may take any of the values in the range {\mid l - S\mid }\le {J} \le {l + S}, separated by 1.

Otherwise, the information about J would be redundant.
NEC

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