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Accuracy of Spectrometer Measurement

An experimenter uses an X-ray spectrometer which has a rotating drum scale and a pointer to measure angles. A view of this scale is shown in the attachment.

a) It is expected to measure an X-ray peak which occurs at an angle of around 31.6 degrees. After viewing the scale and pointer, with what accuracy will you quote the result?

b) A preliminary set of measurements are made in which little care is taken in making the measurements (e.g. not always approaching from the same direction, careless estimation of position etc). Five repeated measurements in degrees are as follows:

30.8, 31.3, 31.8, 31.7, 32.2

Is this acceptable? - if not, why not?

c) The mechanical linkages in the spectrometer are adjusted to remove 'backlash', and care is taken to always approach the measurement in the same direction. Five repeated measurements in degrees are as follows:

31.2, 31.3, 31.7, 31.6, 31.7

Is this acceptable? If so what is the measured angle of the peak.

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(a)
Least count of the measuring scale = 0.5 degree

As the pointer is between 31.5 and 32.0

Hence, measured value will be = 31.5 + 0.5/2 = 31.75 = 31.8 (rounded off to 1st ...

Solution Summary

Through an example problem, accuracy of measurement is discussed.

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