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When performing this experiment with a cup source and GM Tube it says that you should start at a distance several times the diameter of the GM tube in order to obtain accurate results (https://www.imagesco.com/nuclear-science/geiger-counter/experiment-4.html). Which is why this link starts taking readings at 16cm as its many more times the diameter of the GM Tube he used. Please someone explain why starting, at say 3cm, would not give accurate results?

Thanks

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    $\begingroup$ The source is not a point source. You want it looking more like all the gammas come from the exact same place, not over an area. $\endgroup$
    – Jon Custer
    Feb 8 at 14:29
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In the experiment described in the link the percentage error would double when one squared the distance compared with the percentage error in the distance so measuring a larger distance reduces the percentage error but of course this would decrease the count rate which would therefore there would be a larger error in the count rate than if the distance was smaller and hence the count rate was larger. So there must be a compromise between the acceptable errors in distance and count rate.

The further the detector is from the sealed source the better the approximation is that it is a point source although the type of source you are likely to be using will be very small in dimension, $\approx$ 1 mm.
As the source is sealed there might be an error associated as to locating the precise position of the source so a greater distance between the source and the detector will reduce the error produced by not knowing precisely where the source is located.
The error in locating the source can be eliminated by using the procedure and analysis described in Testing the Inverse Square Law for Gamma Radiation.

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