# User:Randy Jay Lafler/Notebook/Physics 307L/2010/11/29

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## Poisson Statistics

### Purpose

• Measure the background radiation by using an NaI detector, and create a poisson distribution.
• Everything but the calculations is the same as in Emran's notebook because we worked on it together.

### Equipment

SpecTech equipment
SpecTech equipment (back)
UCS30 Software
• Computer
• Windows XP Professional Version 2002 Service Pack 3
• Intel Celeron CPU 2.26 Ghz
• 1.96 GB of RAM
• NaI detector
• TN-1222 Detector Base
• Tracor Northern
• Model # TN-1222
• SN 880067
• Bicron Mod 2N2/2
• SN CK-091
• +1200 Volts, 1300 Max
• Spectech Universal Computer Spectrometer, UCS 30
• Connected to computer with USB Cable
• Manufactured by Spectrum Techniques inc. Oak Ridge Tennessee 37830
• Input channel connected to detector Input channel
• POS High Voltage channel connected to detector HV channel
• Spectrum Techniques UCS30 Software
• UCS30 Version 2.10.7, Friday January 23, 2009 - 2:41 PM
• SN. 505, FW Rev. 6
• 2006-2007 Spectrum Techniques, Inc.

### Safety

• High voltage, so beware of shock.
• We measured the background radiation, so there is no danger of radioactive substances.

### Setup

SpecTech equipment
Channel Settings
Dwell time
• Turned on the power supply.
• Opened the Spectrum Techniques UCS30 Software on the computer.
• In the Mode menu, set the software to MCS Internal.
• We set the High Voltage to 1000V.
• We also set the channels to 256.
• Then we set the dwell time to 80ms initially.

### Procedure

• Press go.
• We changed the dwell time to 80, 100, 200, 400, 800, 1000ms and ran the experiment again.
• For each of these we plotted the occurrences verse the number of counts.
• Next we plotted the Poisson distribution for each dwell time and the Gaussian distribution for the 1000ms dwell time.

## Data

Poisson Statistics XL DocSJK 05:50, 21 December 2010 (EST)
05:50, 21 December 2010 (EST)
This link doesn't seem to work. (Same is true for your Balmer lab)

EMQ Comment (l=14:13, 21 December 2010 (EST)) I fixed it for you. Poisson distribution function

### Calculations

We plotted the number of occurances verse the number of counts to obtain the graphs the manual asked us for. We also plotted the Poisson distribution function on each graph by using this formula.
$\Pr = \frac{e^{-\lambda} (\lambda)^k}{k!}$ For the graph of the 1000ms dwell time we also plotted the Gaussian distribution function to compare with our data as well as the Poisson distribution. As you can see they are very similar. This is the Gaussian function we used.

$f(x)=\frac{1}{\sqrt{2 \pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}},\,\!$

### Error

• The error in our graphs is because we chose to follow the manual and use the lowest number of channels. We used only 256. If we had used more channel we would have gotten more measurements, and therefore a better result. Despite this, all of our graphs except the 800ms and 1000ms graphs match the Poisson distribution closely.
SJK 05:51, 21 December 2010 (EST)
05:51, 21 December 2010 (EST)
It's still pretty good!