Experiment 2This experiment consists of three parts: Measuring the resolution of the NaI detector,calibrating the energy of the detector in terms of the channel number, and finally you willdetermine the energies (and the uncertainties of your measurements) of the photopeaks ofBi207.1. Resolution of the NaI DetectorIn the introduction to this experiment, we discussed what is meant by the resolution ofthe detector and how to measure it. You are to determine the resolution of the photopeak atfive different energies. For this part we will use three isotopes, which will also be our energystandards:22N a,137Cs, and60Co. To do this, you need to first record a spectra for eachisotope. Then, using the fitting program developed by previous Cal Poly Physics students,find the channel number of the peak center, C0, and the width parameter σ. As discussedin the introduction, the Full Width at Half Maximum (FWHM) is related to σ by:F W HM = 2qln(2)σC0(1)As calibration standards, you will use22N a,137Cs, and60Co. The CRC lists the energys ofthe primary gamma rays of these sources to be:137Cs: 661.64 KeV22N a: 511.0034 and 1274.5 KeV60Co: 1173.237 and 1332.501 KeVa) Using the curve fitting program find the channel number and σ for each of the five energiesof the standards.b) Make a graph of σ versus energy E. Comment on the relationship between σ and E.c) Show your data and calculations for the FWHM for the Cs137photopeak. Note: themanufacturer of the detector claims the FWHM should be between 6% and 8%.2. Energy Calibration of the MCAIn this part you will first calibrate energy of the Multichannel- Analyzer, then determinethe energies of the two gamma rays of the207Bi decay and the uncertainty of your values.1Use the five standard energies to estimate how the channel number of the photopeak C isrelated to the energy E of the gamma, that is E(C). Once you have determined your bestestimate for the calibration line (curve ?) E(C), then determine the energies of the two pho-topeaks of Bi207. When we used older detectors, there were a number of things to considerin calibrating the MCA. Some important properties are:a) The detection system is not exactly linear.At some level of accuracy the function E(C) is not linear.b) There is an offset, E(0) is not necessarily zero energy. For example,channel number 10 might correspond to the zero of energy.c) The amplifier gain can drift in time.Suggestions for Calibrating the MCAa. For some of the amplifiers in the lab, the drift in gain is quite significant. To correctfor this problem, you can measure two samples at the same time. For example, you cancollect data with both N a22and Cs137together,60Co and137Cs together, as well as137Csand Bi207together. In these combinations, the photopeaks of the two isotopes don’t overlapeach other. With proper scaling guided by the137Cs peak, you can account for amplifierdrift. In your writup, explain how you corrected for amplifier drift.b. You can try different expressions for E(C), the energy of the photopeak as a functionof channel number. Each computer has EXCEL installed on it. You can use EXCEL (oranother spreadsheet) to try linear and/or quadratic fits of the standards. Try various fitsand see how much your predictions of the Bi207photopeak energies vary to estimate youruncertainty of these energies.Note: With the newly purchased detectors, the amplifier drift is expected to be minimaland the calibration function E(C) is expected to be quite linear.3. Find the channel number of the Compton edge for Cs137. After you havecalibrated the MCA, determine the energy of the C s137Compton edge. You will use thisvalue in one of the questions.Laboratory Writeup for Experiment 2Your lab writeup will consist of the following:1) (6 points) Show the data for the peak center and σ for the energies of the five standards.The graph of σ versus E for the energies of the five standards, and a discussion of your results.22) (2 points) Show your measurements and calculations for determining the FWHM for theCs137photopeak.3) (6 points) Determine the energy and uncertainty of the main photopeaks of207Bi. Discussin detail how you corrected for amplifier gain and the type of fit you used to obtain yourvalues. Show all your data.4) (2 points) Measure the channel number and detemine the energy of the Compton edgefor137Cs. You will use this value in the question below.5) (4 points) The ”Compton Edge” corresponds to the maximum transfer of energy fromphoton to free electron. This occurs when a ”head on” collision takes place between photonand electron. The incident photon (E0= hν) is backscattered (180 degrees scattering angle)and emerges with energy E′= hν′where ν′< ν. Use conservation of energy and momentumto show that the kinetic energy Kelectronof the electron at the Compton Edge isKelectron=2E202E0+ m0c2where m0c2is the rest energy of the electron and E0is the energy of the incoming gamma.What is the kinetic energy K for the Cs137662KeV gamma ray? Does it correspond to theenergy of your Compton