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# Physics for Scientists and Engineers - Lab 12 PreLab

For this assignment you will choose two possible experiments for your lab final. For each of those experiments give:

• A title
• A list of the independent and dependent variables
• A list of the governing equations
• A paragraph explaining the principles being tested.

# Physics for Scientists and Engineers - Lab 12

## Nuclear Gamma Ray Spectra

### Objectives:

• To use a NaI crystal detector and nuclear spectrometer to obtain and analyze a gamma ray spectrum of nuclear decay.
• Measure the absorption of gamma radiation by matter.

### Equipment:

• NaI crystal detector
• Multichannel analyzer (nuclear spectrometer)
• Sources: 60Co, 22Na, 137Cs
• Lead and Aluminum absorber sets
• Computer with Spectrum Analysis and Graphical Analysis software

### Physical Principles:

Nuclear decay

The nucleus of an atom with an atomic number Z and an atomic mass A can be thought to be composed of (Z) protons and A-Z neutrons. The mass of an atom is then about A×mproton since the masses of the proton and neutron are nearly equal. The proton and neutron can decay into one another according to the reactions

$p \ \to \ n \ + \ e^+ \ + \ \nu \ \ \ \ \ \ \ \ \ n \ \to \ p \ + \ e^- \ + \ \bar{\nu} \ \ \ \ \ \ \ \mbox{(1)}$

where e- is the electron, e+ is a positron (a particle with the same mass as the electron but charged positively with the same (magnitude of charge) and a neutrino (a particle with zero rest mass moving at the speed of light). Such reactions occurring in the nucleus results in electrons (or positrons) being ejected from the nucleus with a resulting change in nuclear species.

$^A_z X \ \to \ ^A_{z+1} Y \ + \ e^- \ + \ \bar{\nu} \ \ \ \ \ \ \ \mbox {(2)} \ \ \mbox {Electron Emission}$

$^A_z X \ \to \ ^A_{z-1} Y \ + \ e^+ \ + \ \nu \ \ \ \ \ \ \ \mbox{(3)} \ \ \mbox{Positron Emission }$

The resulting nucleus will be in an excited state and will make transitions to lower energy states by emitting high energy photons called gamma particles.

Detection of gamma rays

Gamma rays passing through a sodium iodide crystal may collide with an atomic electron freeing it to move through the material. This electron will collide with many other atoms in the crystal leaving them in excited electronic states. As these atoms decay the visible light emitted is collected by a photo detector giving a voltage pulse which can be counted electronically. The size of the voltage pulse is proportional to the energy of the incident gamma ray.

The photo detector becomes very useful when it is coupled with a sorting device called a multi-channel analyzer which sorts the incoming voltage pulses according to the energy of the gamma ray. The voltage pulses from the photo detector are sorted into bins referred to as channel numbers. The spectrum must be built up over time and in general, the longer the counting time, the more accurate the spectrum obtained.

The distribution of the numbers of gamma rays with energy is the gamma ray spectrum and varies depending on the gamma ray source. In this lab we will be determining the gamma ray spectrum from three different gamma-emitting sources.

Features of a typical gamma ray spectrum A typical gamma ray spectrum is shown in figure 2. The number of counts is plotted as a function of channel number (gamma ray energy) for the radioactive isotope 22Na. There are a few features to notice from this spectrum.

• 22Na emits gamma rays of two distinct energies. These appear as broad peaks and are marked along with their energies in the figure. The highest energy peak at 1.274 MeV is emitted when the 22Na nucleus decays from an excited state. The peak at 0.511 MeV results from positron emission and corresponds to the rest energy of an electron (or positron).
• Some of the 0.511 MeV gamma rays undergo Compton scattering with electrons in the crystal, loosing much of their energy to the electrons. In the extreme case of a head-on collision, the gamma rays are completely backscattered 180 degrees. This results in the “backscatter peak”, , predicted by conservation of energy and conservation of momentum to be at

$E_{{\gamma}'} \ =\ \frac{E_\gamma }{1\ +\ \frac{2\, E\gamma}{m\,c^2}} \ \ \ \ \ \ \ \mbox{(4)} \ \ \mbox{Backscatter Peak}$

Where mc2 = 0.511MeV and Eγ' is the energy of the backscattered gamma rays in MeV and Eγ is the energy of the incident gamma rays in MeV.

• The energetic electrons appear in the spectrum as a plateau of energies below the so-called Compton edge. The maximum amount of energy that can be imparted to an electron occurs when the gamma ray collides head-on with the electron. This energy defines the Compton edge.

From conservation of energy, the Kinetic Energy of the recoil electron, KEe, is given by

$KE_e \ =\ E_\gamma \ -\ E_{{\gamma}^'} \ \ \ \ \ \ \ (5)\ \ \ \mbox{Compton Edge}$

Note: Each gamma ray peak has its own corresponding Compton edge and backscattered peak.

• You will also observe a sharp peak at very low energies of the spectrum. This is due to noise in the photo multiplier tube and is not related to the nuclear gamma-ray spectrum.

Absorption

The intensity, I, decreases exponentially with the distance, x, that the radiation travels through a material.

$I\ =\ I_0\ e^{-k\,x}\ \ \ \ \ \ \ (6)$

where I0 is the intensity entering the material and k is the absorption coefficient characteristic of the material.

## Procedure

### A. Nuclear Spectra

Data Collection

1. Make sure that gamma ray sources are fresh.
2. On the computer with the Nuclear Spectrometer, double click on the UCS30 icon on the desktop.
3. Set the high voltage to 900 V (selecting on), the course gain to 8, the LLD to 1.7, the fine gain to 1.5, and the ULD to 32.9.
4. Under the Settings menu choose Preset and set the real time for 120 seconds.
5. In the Display menu, check that the Pixel Size is set to 2 points.
6. Place a 22Na source into the next to top slot in the detector holder
7. Click on the green Start icon to accumulate a spectrum.
8. Save the file using the format Na22yourinitials.spu in the My Documents folder.
9. Erase the spectrum using the eraser icon
10. Collect spectra for 137Cs and 60Co. Save these files in the same way.
11. Email the files to yourself.
12. At your station computer copy the files from your email and double click on the UCS30 icon to start the program.

Calibration

1. In order to calibrate your energy scale using 22Na
1. Open the spectrum file you want to analyze.
2. Click on the Strip Background menu item, select Load Backgound and open the 22Na spectrum.
3. Right click any point in the spectrum window, select Energy Calibration, click on 2 point calibration and OK for keV.
4. Then click the cursor at the middle of the tall narrow peak near the center. Enter the energy for this peak as 511 in the keV box (the rest mass of an electron) and click OK.
5. Now click the cursor at the middle of the peak near the right end of the spectrum. Enter the energy for this peak as 1274 in the keV box and click OK. Now the horizontal axis is calibrated in KeV and all the features of the spectum and the background spectrum can be read by placing the cursor at the feature and recording the value of the energy following the Energy: label below the graph.
2. In this way compare with accepted values and predicted values of the backscatter energy and Compton edge.
3. For the 60CO and the 137Cs, open the spectra into UCS30. Next go to Background and Load Background Spectrum. Select the 22Na as a background. Now the spectrum of sodium shows up as well. Use the sodium peaks to set the .511 MeV and 1.274 MeV points in a calibration. Now you can find the locations of the peaks and other features of the spectrum of the new element.
Source/Peak Published Energy (MeV) Observed Energy (MeV) Predicted Back Scattered Energy (MeV) Observed Back Scattered Energy (MeV) Predicted Compton Edge (MeV) Observed Compton Edge (MeV)
22Na0.511 0.511
22Na 1.274 1.274
60Co 1.173
60Co 1.333
137Cs 0.6616

Data Collection

For this portion the lab will be split into two groups. Repeat spectrum measurements of the 137Cs source, with 4 different thicknesses of absorbers between the source and the detector.

Data Analysis

1. Use the UCS30 program to measure the counts for the peak.
2. Plot the number of counts vs. thickness of the absorber, including error bars.
3. Fit the data to the appropriate function.
4. Compare the fit values with those that are commonly accepted for this problem.
5. Plot the same data on a linear graph, and use the linear fit to compare to the same values.
6. Compare with the generally accepted value of absorption for lead of k = 1.19 cm-1 for 0.6616 MeV gamma rays.