# Moseley's law and the determination of the screening constant

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1. May 23, 2017

### Arne H

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...

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

Last edited by a moderator: May 23, 2017
2. May 23, 2017

### 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?

3. May 23, 2017

### 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)...

Last edited: May 24, 2017
4. May 24, 2017