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 Error creating thumbnail: Unable to save thumbnail to destination SpecTech equipment Error creating thumbnail: Unable to save thumbnail to destination SpecTech equipment (back) Error creating thumbnail: Unable to save thumbnail to destination 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 Error creating thumbnail: Unable to save thumbnail to destination Settings Menu 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. In the settings menu, select "Amp/HV/ADC" 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 Error creating thumbnail: Unable to save thumbnail to destination 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. [math]\displaystyle{ \Pr = \frac{e^{-\lambda} (\lambda)^k}{k!} }[/math] 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. [math]\displaystyle{ f(x)=\frac{1}{\sqrt{2 \pi \sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}},\,\! }[/math] 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! Citations/Acknowledgements Thanks to Richard's notebook for the Gaussian function Thanks to Dan's notebook for the Poisson distribution function Thanks to Emran for being my lab partner.