GREPhysics.NET: GR8677 #84

GR8677 #84

Problem

GREPhysics.NET Official Solution

Atomic $\Rightarrow$ }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

danielsw98667
2019-10-24 04:21:47

Confused with the value of J. affordableseoservice.org

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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)

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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.

danielsw98667
2019-10-21 05:45:55

I agree with you that it is too ambiguous. The Southern Institute

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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).

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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.

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