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 $l=0,1,2,3...$

Alternate Solutions

There are no Alternate Solutions for this problem. Be the first to post one!

Comments

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.

Reply to this comment

Post A Comment!

Bare Basic LaTeX Rosetta Stone
LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...

<a href="http://www6.shoutmix.com/?grephysics">View shoutbox</a>
ShoutMix chat widget

1GHz Smartphone for 1 cent - best deal on a Samsung Galaxy Phone

Free 3D Virtual World. Largest User-Created Fantasy World. Don't Play, Experience. Join Now!

Bored, got time to kill, and want to earn micro-cash by mindlessly clicking on links? Join CrownGPT. Click Offers. Click the Paid to Click button... then click to your heart's delight.

FREE 3D Virtual World Chat - Join Second Life Today!

All-Solutions List | Latest Comments | Unanswered Questions (Cries for Help!) |::| About

This site is not affiliated with ETS, nor is it officially endorsed (yet) by ETS. This site is the work of an individual named Yosun Chang. The solutions, sans user comments and ETS questions, are © 2005 by Yosun Chang except where noted. All rights reserved. / The comments appending particular solutions are due to the respective users. / Educational Testing Service, ETS, the ETS logo, Graduate Record Examinations, and GRE are registered trademarks of Educational Testing Service. The examination questions are © 1997 and © 2001 by ETS.

Bare Basic LaTeX Rosetta Stone