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Homework Help: Clausius mossotti equation

  1. Nov 22, 2012 #1
    1. The problem statement, all variables and given/known data

    http://img809.imageshack.us/img809/5676/unavngivetk.png [Broken]

    Additional table info:

    The molarmass ##M_{air}## is ##29 * 10^{-3} g/mol = 29*\frac{10^{-3}}{1000} kg/mol##
    The mass density ## \rho_{air} ## is ##1.3 kg/m^{3}##
    The dielectric constant ## K_{air}## is 1.00059

    My teacher told me to consider the air as 1 molecule.

    2. Relevant equations

    http://img94.imageshack.us/img94/1667/unavngivet2w.png [Broken]

    3. The attempt at a solution

    Here is my approach:

    Basically it is only N we need which is molecules per volume:

    [tex] N = \frac{Molecules}{V} = \frac{N_a n}{V} = \frac{m}{M_{air}} \frac{N_a}{V} = \frac{\rho_{air}V}{M_{air}} \frac{N_a}{V} = \frac{\rho_{air}N_a}{M_{air}} [/tex]

    [tex] \alpha = \frac{3 \varepsilon_0 M_{air}}{\rho_{air}N_a} \frac{K_{air}-1}{K_{air}+1} [/tex]

    Inserting the values:


    [tex]\frac{3(8.854*10^{-12})(29*\frac{10^{-3}}{1000})}{1.3(6.022*10^{23})} * \frac{1.00059 - 1}{1.00059 + 1} = 2.902 * 10^{-43}[/tex]

    The answer in the back of my book says it is supposed to be: ##\alpha = 9.7 * 10^{-41}##

    Can any of you guys spot where I did wrong? (The table values were some I got from my teacher and if my approach is right, then he might have wrote them wrong)
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 22, 2012 #2

    TSny

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    Homework Helper
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    2017 Award

    A quick Google check on the molar mass of air will show an error in this value.

    You used
    [tex] \alpha = \frac{3 \varepsilon_0 M_{air}}{\rho_{air}N_a} \frac{K_{air}-1}{K_{air}+1} [/tex]

    but the denominator of ##K_{air}+1 ## does not agree with the form of the Claussius-Mossotti equation that you quoted.


    Also, does your answer for ##\alpha## correspond to a molecule or an atom?
     
    Last edited: Nov 22, 2012
  4. Nov 22, 2012 #3
    All three things you pointed out gave me the right answer. Thank you ^^
     
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