Using a Geiger–Müller tube to prove inverse square law

[beatlemaniac]

Homework Statement

Today our class used a Geiger–Müller tube for the first time, and we conducted a short experiment to prove that Newton's Inverse Square Law also applies to radioactivity. We recorded the number of clicks from a small sample of Strontium-90 for ten seconds at halved distances, as shown below...


Distance from sample (m) = 0.24
No. of clicks = 5, 6, 7, 3, 2
Average = 4.6

Distance from sample (m) = 0.12
No. of clicks = 5, 13, 5, 4, 6
Average = 6.6

Distance from sample (m) = 0.06
No. of clicks = 18, 21, 21, 27, 28
Average = 23

Distance from sample (m) = 0.03
No. of clicks = 42, 30, 45, 50, 44
Average = 42.2

Distance from sample (m) = 0.015
No. of clicks = 114, 97, 82, 96, 94
Average = 96.6


As you can see the number of clicks seems to be doubling as the distance is halved, not squaring as we expected. Any ideas on we were doing wrong?

Homework Equations

$$\textit{Bq}\propto\frac{1}{d^2}$$

The Attempt at a Solution

?

This is my first post on the site so I hope I have adhered to all your conventions and what not :)

 

[Troels]

As you can see the number of clicks seems to be doubling as the distance is halved, not squaring as we expected. Any ideas on we were doing wrong?

That may be due to the constant of proportionality. Can you think of a sure way to test if a given set of points follow a power law?

Hint: It involves plotting them in a special kind of chart with special scales on the axes ;)

 

[tomcue]

Dear student,

Thank you for sharing your experiment with us. It is great to see that you are exploring the application of Newton's Inverse Square Law to radioactivity using a Geiger-Müller tube.

Firstly, I would like to commend you on your experimental design. You have taken multiple measurements at different distances and calculated the average, which is a good practice to ensure accuracy in your results.

Now, let's address the issue you have encountered - the number of clicks not squaring as expected. It is important to note that while Newton's Inverse Square Law applies to the propagation of light and other electromagnetic waves, it may not apply to the emission of radioactive particles. This is because radioactive decay is a random process and the number of particles emitted in a given time is not constant. This can lead to variations in the number of clicks recorded by the Geiger-Müller tube.

To account for this, you can repeat your experiment multiple times and take the average of the results. This will help to reduce the effect of random fluctuations and give a more accurate representation of the relationship between distance and number of clicks.

Additionally, it is also important to consider the limitations of the Geiger-Müller tube. It may not be sensitive enough to detect all the particles emitted by the sample, especially at larger distances. This could also contribute to the variations in your results.

In conclusion, while your experimental setup and approach are sound, it is important to keep in mind the limitations of the equipment and the nature of radioactive decay when interpreting your results. I hope this helps to clarify any confusion you may have had. Keep up the good work in your scientific explorations!