# Determining Threshold Voltage and Plateau from experimental data

I’ve been trying to figure out how to interpret the following data from the Geiger muller tube

There are only seven data points. Where does the plateau begin? Has the data collection begun after the number of counts has reached the plateau? What does this say and the threshold voltage. I feel like it’s ambiguous.

• What you need to include are the error bars in the count rate. If the total count is $N$ then the error due to statistical fluctuations is $\sqrt N$. May 16, 2018 at 8:08
• The plateau runs up to 700 or 750 volt. The GM works at least at 500 volts. So 600 V is a good voltage to run this device on. That is usually the quantity that one is interested in.
– user137289
May 16, 2018 at 11:44

## 1 Answer

Short answer: You can't tell, it is indeed ambiguous.

Slightly longer answer: This is a typical example of the discrepancy between theory and experiment. I don't know whether this is your data or someone else's data but apparently, there is some deviation from the theory due to an unknown influence in the experimental set-up. Another possibility is that the theory is so highly idealized that it is not applicable to you case. You would need more data points to make a statement about the plateau or even better, you should identify why the curve is not like in theory. If you absolutely have to estimate the boundaries of the plateau, I'd say it lies between data points 1 and 5. The uncertainty of this estimation is very high though. The fact that the data doesn't have any error bars makes it even more difficult.

• I have updated the picture, its just a sketch. I have done a weighted linear regression ($\sigma _{CountRate} = \sqrt{\frac{N}{t^2}} = \sqrt{N}, ~ as~t = 1$). I then did a chi squared value GOF test which output a very large number (p-val < 0.001) if I use the first 5 or 6 points. I suppose I will simply have to explain why the experiment deviates from the theory as you said May 16, 2018 at 15:19
• Sounds like a pragmatic approach to me. Sometimes experiments are just not what you want them to be
– lmr
May 16, 2018 at 17:03
• @frozenbooger A couple of additional comments here. (A) Your data is too sparse; you need at least twice as many points to really compare to what you expect. (B) If this data is representative then either you've grossly under-estimated your random errors or you have a significant systematic error of some kind. May 16, 2018 at 17:04
• @dmckee I agree, there seems to be significant systematic error. This data was given to me to analyze with no detail as to any errors in the collection process. The only error I am aware of is that counts will follow a poisson distribution, thus $\sigma_{counts} = \sqrt{N}$ May 16, 2018 at 17:59