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As part of a an experiment, I was to determine the minimum wavelength emitted by an x-ray source through analysing the detected count rate (detected by a GM counter) of a diffracted x-ray source, via a crystal; NaCl.

From the experimental data, we are able to plot a graph of count rate against x-ray wavelength.

What I do not understand is that the lab manual had asked us to determine the minimum wavelength via linear regression of the points close to the end of the spectrum. The plots and linear regressions are shown below:

enter image description here

Is there any scientifc reason behind the linear regression? Or is it just a experimental approximation due to the lack of resolution in wavelength?

Why can't we take minimum wavelength to be the point where the count rate meets the background count rate?

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  • $\begingroup$ Are you sure that the linear regression was not for determining Planck's constant from these data? $\endgroup$
    – user137289
    Commented Feb 14, 2018 at 15:42
  • $\begingroup$ @Pieter The minimum wavelength found through linear regression was used to determine the plank's constant through the Duane-Hunt relation. But my question is about the need for linear regression to determine minimum wavelength $\endgroup$
    – Tian
    Commented Feb 14, 2018 at 16:10

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I believe its due to thermalisation & defects states which may mean that you have a spread of minimum values of X-ray emission.

The density of states should be roughly linear near the band gap (i.e. conduction and valence bands), which means that a linear regression is normally taken until this intersects with the background/zero level.

This is also common practise in photoelectron spectroscopy.

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