Moseley's law and the determination of the screening constant

[Arne H]

Homework Statement

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.

Homework Equations

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

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...

Moderator's note: LaTex edited. See e.g. https://www.physicsforums.com/help/latexhelp/

 

[kuruman]

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?

 

[Arne H]

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)...

 

[kuruman]

Yes, you have to sort out the transitions and group them by $n_1$ and $n_2$ values. See here for example
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/moseley.html