# How to work out energy uncertainty values for an x-ray spectrometer?

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?

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