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Moseley's law and the determination of the screening constant

  1. May 23, 2017 #1
    1. The problem statement, all variables and given/known data
    The aim of a laboratory course was to measure the x-ray fluorescene spectra of 20 metallic samples. By comparison of the peaks in the energy spectra with known electronic transitions (e.g. ##K_α## of ##Cu##) the materials were identified.

    After that, Moseley's law
    $$ \sqrt{\frac{E}{R_y}}=(Z-\sigma_{n_1,n_2})\sqrt{1/n_1^2-1/n_2^2} $$
    should be verified and the screening constant ## \sigma_{n_1,n_2} ## should be determined. The problem is, that ## \sigma_{n_1,n_2}## itself is (aside from ##n_1## and ##n_2##) a function of ##Z## (the atomic number), which means it isn't possible to just fit a linear function to the data.

    2. Relevant equations
    Moseley's law:
    $$\sqrt{\frac{E}{R_y}}=(Z-\sigma_{n_1,n_2})\sqrt{1/n_1^2-1/n_2^2}$$

    3. The attempt at a solution
    At first I tried to fit the data, but that does not seem to make much sense to me..

    Sorry for the equations, I am new here and don't know how to properly compile LaTeX equations... :sorry:

    Moderator's note: LaTex edited. See e.g. https://www.physicsforums.com/help/latexhelp/
     
    Last edited by a moderator: May 23, 2017
  2. jcsd
  3. May 23, 2017 #2

    kuruman

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    What if you plotted ##\frac{\sqrt{\frac{E}{R_y}}}{ \sqrt{1/n_1^2-1/n_2^2} }## vs. ##Z## and fitted a straight line to that? Do you see how you can extract Moseley's constant from the fit?
     
  4. May 23, 2017 #3
    Well, the curve actually shows a linear behaviour (I assume, you mean that ## \sqrt{1/n_1^2-1/n_2^2}## is constant ##\Leftrightarrow## the data has to be fitted for every transition found (## K_\alpha ##, ## K_\beta ##, ## L_\alpha ##, etc) seperately). But the problem is that ## \sigma ## seems to be also a function of ## Z ## (## \sigma < 0 ## for ## Z \geq 55## according to my course instruction)...
     
    Last edited: May 24, 2017
  5. May 24, 2017 #4

    kuruman

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