User:Cristhian Carrillo/Notebook/Physics 307L/2010/11/24

Poisson Distribution

• Note that Ginny was my lab partner.

Purpose

This simple experiment was intended to help us gain familiarity with the Poisson distribution which is the second most important statistical distribution in physics. In this lab we study the distribution of radioactive decays. The Poisson distribution describes the restults of experiments where one counts events that occur at random but at a different average rate. This distribution is of significant importance in all of atomic and subatomic physics.

Equipment

Power Supply

Detector

Most of this experiment was done on the computer

• We combined the scintillator and the Photo-Multiplier Tube (PMT)

This was used to detect the background radiation in the lab.

• Spectech Universal Computer Spectrometer power supply (This supply gives a bias voltage to the detector).

Brief explanation on how the lab works

The scintillator absorbs cosmic radiation and sends a beam of light down the tube to the PMT. The PMT will then create a signal voltage that a card on the computer will detect. After the card detects the signal, it will send the information to the UCS 30 software which will count the number of radiation events in a given window of time.

Setup and Procedure

SpecTech equipment

Settings Menu

Channel Settings

Dwell time

The setup was very simple, and in fact it was already setup when we started the lab. Since Brian Josey's setup and procedure section was exceptionally good, I copied and pasted from his notebook so that you can have a very detailed procedure on how to perform the experiment.

1. Turn on the computer and log-in if necessary,
2. Turn on the Spechtech, it has to be turned on first before the software,
3. Double click on the icon for the software on the desktop of the computer,

Like the set up, the procedure is pretty basic, the only issue is that the user interface on the computer doesn't make much sense. To set up the data collection, you want to set the cut off voltage fairly high before collecting the data. So the step by step process for collecting data is as follows:

1. Under mode select "PHA (Amp In)"
2. Under Settings Select "High Voltage On", and set it to an appropriate value, we used 1200 V. This value is used to adjust the sensitivity of the detector, and a higher voltage will decrease the sensitivity to only the most energetic radiation
3. Under mode, select "MCS (Internal)"
4. Under Settings, select MCS, and then pick your appropriate dwell time, which is how large each bin is for the number of events counted.
5. To collect data, hit the green "Go button" and let it run its course
6. When it stops, save it to a file or USB drive, but save it as a "comma separated variable (*.csv)"
7. Import it into Google docs

From this point, the procedure is actually in the data analysis. We did every single dwell time between 10 ms and 1 second. The values for these are then, 10, 20, 40, 80, 100, 200, 400, 800 ms and 1 s.

Calculations and Analysis

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[math]\displaystyle{ \Pr = \frac{e^{-\lambda} (\lambda)^k}{k!} }[/math]

[math]\displaystyle{ f(x)=\frac{1}{\sqrt{2 \pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}},\,\! }[/math]

Acknowledgements

I would like to thank Ginny my lab partner for the help and her hard work. I would also like to thank Brian Josey for his setup and pictures and also Randy Lafler for the pictures on the options to click on for the experiment. And of course, I would like thank Katie Richardson and professor Steve Koch for helping us get started with the lab.