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I’m doing an x-ray spectroscopy experiment at university. The spectrometer consists of a copper x-ray tube, a collimator, a LiF analyser crystal and a Geiger Muller counter mounted on a goniometer, which rotates keeping the 2:1 ratio with the crystal (we also have several samples for investigating – metal films etc).

We’ve calculated the energy resolution of our spectrometer with this crystal, and obviously for much of our raw data, which consists of an angle and x-ray intensity, it is essential to calculate the wavelength at each angle using Bragg’s law and hence the corresponding energy using E=hc/λ.

Our spectrometer allows increments of 0.1° and our crystal spacing is quoted as 201.4pm. If I assume the uncertainty to hence be 0.05° for the angle and 0.05pm for the crystal spacing, and calculate the uncertainty of λ and E in the standard manner from this (assuming that h and c’s uncertainties are negligible and treating them like constants), then I get some extremely small errors for E. I know something is missing here – I’ve calculated my energy resolution, and I know just from looking at my data that the resolution is not fantastic - the uncertainties should be much larger, and know I’m not including all the relevant accuracy information in my current calculations.

How do I incorporate this (or something more) into my uncertainty calculations for energy?

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  • $\begingroup$ The important factors are the width of the slits of the collimator and the detector aperture. And the distances to the sample. $\endgroup$
    – user137289
    Commented Dec 6, 2017 at 17:35

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You need to make sure that you know the angular uncertainty of the radiation that reaches your detector. This is given by the size of the aperture of the source (or the focal spot size, if there is no separate aperture), the size of the sample, and the aperture in front of your detector. You should be able to draw yourself a simple diagram to show how different rays can arrive at your detector with different angles.

That's likely to be the thing that limits your resolution. The fact that you can read the angle to 0.1° doesn't matter if you accept radiation from a greater range of angles.

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