I am conducting an experiment in which I investigate the relationship between the counts per second detected by a Geiger Counter and the distance between said Geiger Counter and the source of radiation. Attached is a graph of the counts per second over time at a fixed distance. My question is: why so much variation between the data points? Is it by virtue of systematic errors?
Best Answer
It is difficult to provide a complete answer as you have not provided enough information about the experiment.
Your graph, which clearly shows the variation in values of the count rate, exaggerates the variation by having a false origin.
It is not clear as to whether or not a count rate of say $249$ is the result of a reading taken over a period of one second or an average of a reading taken over, say, $10$ seconds.
This matters because radioactive decay is a random process in that one cannot precisely state when a particular nucleus will decay. Statistically with such a process if $N$ is the count in a given time the error in the count is $\pm \sqrt N$. So you one off reading of $249$ has an error of $\pm\sqrt 249 \approx \pm 16$ and it could be shown as an error bar on your graph.
Another thing which could have been important is whether or not your readings are corrected for background radiation as the background count rate which can fluctuate during the course of a day. However as the background count rate was probably less than 1 per second that will not be a significant factor.
I have read off approximately 40 values of count rate from your graph and found the mean count rate to be $236\pm22$ per second.
As you have quite a number of readings the count rate should follow a Normal distribution which means that approximately $68\%$ of the readings should be in the interval $236\pm22$ (range $214-258$), $95\%$ in the interval $236\pm2 \times 22$ (range $192-280$) and $99\%$ in the interval $236\pm3 \times 22$ (range $170-302$). A cursory glance at your data shows that the fluctuations you have observed are as to be expected.
There are also tests which could be used to test whether the distribution of count rates is Normal. There are many ways of getting this done including the use of Microsoft Excel.
Here is a visual comparison.
Using the experimental mean and standard deviation the blue dots shows what the data points would be if the distribution was normal and the orange dots are the data points from your experiment. It looks very much as though your data follows a Normal distribution.
Is it by virtue of systematic errors?
With radiation detectors one source of systematic error is the possibility of the detector not being to count all the particles which reach it due to the detector having a dead time and this error increases as the count rate increases. Given that the your range of count rates is relatively small this is unlikely to be a source of error with your experiment.