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PHYS 345 Laboratory: Gamma–Ray Spectroscopy and Radon Decay

Purpose: To record and analyze the spectrum of γ rays from various sealed

calibration sources, to become familiar with the use of a high-resolution Ge semiconductor detector and the basic techniques of γ–ray spectroscopy, to understand the three principle interactions of γ rays with matter: the photoelectric effect, Compton scattering, and pair production, and to analyze radon daughter decay.

Apparatus: Canberra Ge semiconductor detector, DSA–1000 Digital Spectrum

Analyzer, liquid nitrogen fill system, data acquisition computer, various 1–10 μCi γ–ray sources, NaI detector, Multi-Channel Analyzer (MCA), radon daughter collection system (shop vac, gauze pad, petroleum jelly, masking tape, sandwich bag, cellophane tape, stopwatch)

References

A.C. Melissinos and J. Napolitano, Experiments in Modern Physics, 2nd Ed., Academic Press, p. 312 – 315, 2003.

B.R. Trees and B.S. Andereck, Laboratory Manual for Physics 115 and Physics 116, 2004 – 2005 Academic Year, Ohio Wesleyan University.

D.W. Preston and E.R. Dietz, The Art of Experimental Physics, Wiley and Sons, p. 316–24, 1991.

EG&G ORTEC 1997/1998 catalog, p. 1.2–1.3, 8–17. Kenneth S. Krane, Introductory Nuclear Physics, John Wiley and Sons, p. 220–

221, 1988. R.B. Firestone and V.S. Shirley (editor), Table of Isotopes, 8th Ed., Wiley and

Sons, p. 1192, C-3, 1996. Instruction Manual, Germanium Detectors, Canberra Industries. R.A. Kaye, PHYS 343 Lab Manual, Purdue University Calumet.

Introduction Nuclei, like atoms, can be investigated from the electromagnetic radiation they emit. Just as the knowledge of the atom was advanced by the study of the photons which are released as the atom undergoes allowed transitions between discrete energy states, so too has nuclear structure been elucidated through studies of the transitions between the discrete energy states of a nucleus. As in an atom, a nucleus in an excited energy state will release a series of photons, called gamma (γ) rays, until it reaches its lowest energy (ground) state. Careful spectroscopy of these transitions can thus be a valuable tool in discovering the energy-level structure (level scheme) of a particular nucleus. A partial level scheme of the 60Ni nucleus deduced from its γ emissions is shown in Fig. 1. Other useful applications of γ–ray spectroscopy include environmental radioactive surveys, bioassays, neutron-activation analyses, and nuclear waste sampling.

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Atomic transition frequencies are usually smaller than nuclear ones and sometimes lie in the visible spectrum, making precision measurements possible with an optical spectrometer. In contrast, the photons emitted in nuclear transitions are usually at relatively higher frequencies (or energies). As a result, γ–ray photons have much higher energies, typically in the range of 0.01 to 10 MeV. Precision measurements of photon energies in this regime involve indirect measurements based on their interactions with matter. In the energy range given above, there are three major interactions: the photoelectric effect, Compton scattering, and pair production. The relative importance of each of these processes as a function of photon energy is shown in Fig. 2. In the photoelectric effect, a γ ray with energy hν is absorbed completely by the atom, causing an atomic electron to either be promoted to a higher energy state, or to be ejected from the atom entirely (ionization of the atom). Of these two possibilities, ionization is much more likely, in which case the ejected electron has an energy hν – E1, where E1 is the binding energy of the electron which depends on the energy shell it was residing in (K, L, M, etc.). The probability of a photoelectric interaction increases rapidly with the atomic number Z and decreases with increasing photon energy (see Fig. 2).

2505

1332

0

1173

1332

4+

2+

0+

60Ni

Figure 1. Partial level scheme of the 60Ni nucleus. Gamma-ray transitions between the levels are indicated by arrows and labeled by their energy in keV. Each discrete energy state (indicated by a horizontal line) is labeled by its energy relative to the ground state (values on the right, in units of keV), its discrete angular momentum quantum number (values on the left), and its parity, or reflection symmetry state (in this case, even or “+” parity, indicated by the superscript symbol on the angular momentum quantum number). The Compton effect is essentially an elastic collision between a photon and an electron. During this interaction, the photon gives only a fraction of its energy to an electron (assumed initially at rest), and its energy is therefore decreased partially. This effect becomes less prominent with increasing photon energy, but the decrease is less rapid than for the photoelectric effect (see Fig. 2). In the pair-production effect, a photon of sufficiently high energy is converted into an electron-positron pair. (A positron is the antiparticle of the electron, having a positive charge +e.) In order to maintain conservation of energy and momentum, the photon energy must go into the rest-mass energy and the kinetic energy of the electron-positron pair, and the process must take place within the field of a nucleus (or of another electron), which supplies the remaining recoil momentum in the “reaction”. The minimum energy threshold necessary for this effect is set by elementary relativistic considerations at 1.022 MeV, the amount equivalent to two electron rest masses. The probability for pair production increases with photon energy (see Fig. 2). Up to energies of about 10 MeV,

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the probability as a function of Z remains constant with energy, but at higher energies, the probability starts to decrease for increasing values of Z. Since the cross sections for both the photoelectric and Compton effects decrease with increasing photon energy, pair production is the dominant interaction mechanism for very high-energy photons (see Fig. 2).

Figure 2. The cross section for the interaction of photons with matter as a function of photon energy (expressed in units of the electron’s rest mass, mc2). The cross section σThomson is the classical cross section derived from the simplified assumption of a plane-polarized electromagnetic wave scattering from a free electron. From the Experiments in Modern Physics text. Radioactive materials are composed of atoms with unstable nuclei having an overabundance of protons (or neutrons) compared to the number of neutrons (or protons). These nuclei become more stable by releasing energy through γ decay (if they are in an excited energy state), or through alpha and/or beta decay once they are in their ground state (or in some cases a relatively long-lived metastable state), transforming into a different isotope. Sometimes, as is the case for radon-222 (222Rn), the nucleus decays into yet another unstable nucleus, which itself undergoes radioactive decay. This chain of decays continues until a stable nucleus is reached. Each unstable parent nucleus decays to a subsequent daughter nucleus. Modeling a long decay chain can be very complicated, because the rates at which the different nuclei decay into each other can vary greatly. As a result, the abundance of one element can actually increase even if it’s decaying, because its parent nucleus in the chain is decaying more rapidly. The decay of any one nucleus is a completely random event based on probability. This probability depends on which isotope it is. Every nucleus of a given isotope has the same probability of decaying in any given time interval. A large collection of identical nuclei has the same probability to decay as does any single nucleus in the collection. In these cases, it is convenient to describe the amount of time required for one half of the original number of nuclei to decay, called the half-life of the isotope, which is a fundamental property of that nucleus. Half-life is inversely related to decay probability: a high (low) probability of decay corresponds to a short (long) half-life. Simple (one-step) radioactive decay is described mathematically by , (1) 2/1/2ln

0TteNN −=

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where N0 is the initial population of nuclei at time t = 0, N is the number of radioactive nuclei remaining at some later time t, and T1/2 is the half-life. The rate of radioactive decay is called the activity R, and is given by NR λ= , (2) where λ, the decay constant, is equal to ln2 / T1/2. Since R is directly proportional to N, it follows the same time dependence as N (see Eq. 1). The worldwide abundance of a radioactive species is partially related to its half-life. Members of a species with a very short half-life will have almost all disappeared by this point in the Earth’s history, and even if their population is being fed by a parent decay, they will decay quickly and not build up in the environment. A species with a long half-life will build up easily and stick around for some time. However, a state of equilibrium can be reached by any chain, and in this state the relative abundances of the species are inversely proportional to their decay probabilities. In this experiment, the equilibrium proportions of radon’s daughters will be collected and analyzed. Experimental Apparatus and Technique Historically, photon detectors were conceived as solid-state ionization chambers. To obtain a high electric-field, low-current, solid-state device for detection and possibly spectroscopy of the radiation, conduction counters (highly insulating diamond crystals) were first used. However, such crystals were quickly rejected because of poor charge collection capability. After the highly successful development of silicon (Si) and germanium (Ge) single crystals for transistor technologies, the conduction-counter concept was abandoned, and silicon and germanium semiconductor detectors were developed. A semiconductor detector is essentially a large Si or Ge diode (allowing current flow in only one direction) operated in reverse bias mode such that nearly all free charges are removed by an applied electric field. For high-resolution spectroscopy of photons, Ge detectors have an advantage over Si detectors because of the relatively higher number of electrons which are liberated following photon interactions (see Introduction section). These electrons are collected by an electric field produced by the reverse bias between two electrodes mounted on the Ge crystal. The resulting collected charge is proportional to the energy deposited in the detector by the incoming photon. This charge is later converted into a voltage pulse by a charge sensitive preamplifier in series with the detector. Since Ge has a relatively small energy difference between its valence and conduction bands (0.72 eV), these detectors must be cooled in order to reduce the thermal generation of electrons to an acceptable level. Otherwise, electronic noise induced by the resulting “leakage current” ruins the energy resolution of the detector. Such currents could also damage the detector irreparably. Liquid nitrogen (LN2), having a temperature of 77 K, is the common cooling substance for such detectors. The detector crystal is mounted in a vacuum chamber which is attached to an LN2 storage vessel (dewar), comprising what is called a “cryostat.” The sensitive detector surfaces are thus protected from moisture and condensable contaminants. In this experiment, you will be working with a Ge detector called a Reverse-

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Electrode Germanium (REGe) detector, a schematic of which is shown in Fig. 3. The semiconductor crystal is fabricated from high-purity Ge and is formed to have a coaxial cylindrical geometry with a diameter of 55 mm and a length of 50 mm. A major advantage of the coaxial geometry compared with, say, a planar crystal geometry is that it has a relatively high efficiency for collecting high-energy γ rays (> 1 MeV) due to a relatively large interaction volume. To collect the charges liberated by photon interactions, the Ge is fabricated with an ion-implanted p–type outer electrode and an n–type lithium-diffused inner electrode located in a cylindrical bore concentric with the crystal (Fig. 3). (This electrode orientation is opposite from the conventional coaxial detector, owing to the “Reverse Electrode” name.) The Ge crystal is placed in a cylindrical static vacuum enclosure with a thin circular beryllium (Be) window.

Figure 3. A schematic view of the REGe detector crystal.

This, in conjunction with the extremely thin (0.2 μm) outer electrode, reduces the attenuation of low-energy γ rays and extends the energy response down to about 5 keV, giving this detector a dynamic energy range of about 2000:1, as demonstrated by the γ detection efficiency as a function of γ–ray energy (Fig. 4). The Ge is also kept in thermal contact with a dipstick-like “cold finger” assembly extending from the liquid nitrogen storage dewar (not shown in Fig. 3) in order to maintain the crystal temperature approximately equal to that of liquid nitrogen. γ-ray energies are measured from the number of free charges they produce in the Ge crystal. First, the γ ray liberates individual electrons from atoms in the crystal through Compton scattering, the photoelectric effect, and/or pair production (see Introduction section). These free electrons have a very short range in the crystal, and therefore lose energy very rapidly by creating a plethora (~106) of electron-hole pairs. All of this energy is absorbed, and corresponds to the energy deposited in the detector by the original γ ray. If the original γ ray, after a series of interactions with the crystal, is eventually absorbed completely via the photoelectric effect, then the energy deposited in the crystal is the total γ-ray energy. If it eventually scatters out of the crystal, then the deposited energy is less than the total γ-ray energy. Linear amplifiers integrate the total resulting charge collected by the detector electrodes and convert it to a voltage signal. Initial amplification is performed by a preamplifier module mounted inside of a cylindrical shell on the outer cryostat casing. Further amplification and signal shaping is performed by an external amplifier module.

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In this experiment, the analog voltage signal from the preamplifier is first converted into a digital signal using an analog-to-digital converter module in the Canberra DSA–1000 Digital Spectrum Analyzer prior to receiving this second stage of amplification. The resulting digital number is assigned to a “channel” number depending on its value. The larger the input voltage signal from the detector preamplifier, the larger the channel number assigned to it. A computer running the appropriate control software then histograms the data according to the number of times each channel received an “event” or “count” from the detector. A picture of the Ge detector and DSA–1000 module is shown in Fig. 5.

Figure 4. REGe detector efficiency as a function of photon energy for a detector end-cap to source spacing of 2.5 cm. The notch in the curve at 11 keV is caused by excitation of the Ge K shell by incoming photons and subsequent escape of a significant fraction of K-shell X rays.

Figure 5. The REGe detector and DSA–1000 Digital Spectrum Analyzer. Channel number is converted to γ-ray energy by measuring the γ-ray peak positions in a spectrum from a source with known γ-ray energies. Since channel number is directly proportional to γ–ray energy, a linear least-squares fit to the peak positions measured in channels results in an equation which converts channel number to energy (see Eq. 3). Each peak in the spectrum has a finite width (i.e. more than one channel wide) due to the fluctuations in the number of electrons produced from each interaction

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with a γ ray of a particular energy. The integrated area of a spectral peak is proportional to the intensity of the corresponding γ ray (once corrected for detector efficiency). A sample γ–ray spectrum is shown in Fig. 6. Data Acquisition Software Data will be acquired and analyzed using the Canberra GENIE–2000 Gamma Acquisition and Analysis program. This software performs the data histogramming mentioned in the previous section, and also provides several display and analysis functions. To begin acquisition, you must first select the “Open Datasource” option under the File menu. Next, choose the “Detector” option as the input source. Finally, select “GE1” as the specific detector choice. This will set the histogram to receive a maximum range of 8192 channels from the DSA–1000. Your instructor will give you further instructions and training on other specific program options in order for you to obtain a γ–ray spectrum successfully and analyze the results.

Figure 6. A sample γ–ray spectrum as obtained with the GENIE–2000 data acquisition software used in this experiment. Radiation Safety In this experiment, you will be using sealed 1–10 μCi γ–ray sources. While these are relatively low-intensity sources, it is nevertheless important to practice sound radiation safety procedures. A useful rule of thumb is to utilize the ALARA (As Low As Reasonably Achievable) safety principle. This principle stresses two important aspects of minimizing exposure: minimize the time handling a source, and maximize the distance between you and the source. The latter follows from the fact that γ radiation obeys the inverse-square law for emission from a point source. Your instructor must train you in the use and handling of the radioactive sources before you begin the experiment.

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Experimental Procedure Detector Setup and Calibration First, fill the detector dewar with liquid nitrogen until it is full. Have your instructor train you and demonstrate the procedure. You will know it is full when liquid nitrogen comes out of the dewar vent hose. When finished, sign and date the detector LN2 fill log sheet attached to the lab table on which the detector is located. Set up the electrical connections between the Ge detector and the DSA–1000 module as shown in Fig. 7. Verify that the detector temperature status is “Cold” as indicated by an LED on the outer sleeve of the vacuum chamber (once the DSA module is switched on). Also make sure that the high-voltage (HV) output of the DSA–1000 is set for the –5 kV range (reverse-bias mode). A close-up view of the indicators and connections on the front and rear panel of the DSA–1000 module are shown in Figs. 8 and 9. If the detector is cold, activate the high voltage to the Ge crystal through the GENIE–2000 software. While the voltage is ramping up to the preset operating value (–3000 V), monitor the reconstructed output from the amplifier in the DSA–1000. It should look triangular and have a mostly stable, flat baseline when a test source is placed in front of the detector (Fig. 10). Once the detector has reached full bias, place the 60Co source a few cm from the detector and record a spectrum for several minutes, then repeat for the 152Eu source. Be sure to save your spectra to disk. Then acquire a 60Co source spectrum using the NaI detector and the Multi-Channel Analyzer (MCA)1. (The spectrum should look similar to Fig. 8.20 in the Experiments in Modern Physics text.) Compare the 60Co spectrum obtained with each detector. What are the advantages of using a Ge detector? (Note that the NaI detector is a scintillation detector that operates fundamentally different from that of the Ge detector.) Finally, acquire a spectrum with the 137Cs source placed 2.5 cm from the detector (you will need this spectrum for part of the analysis).

Figure 7. Electrical connections (signal and power) for the experiment.

1 See Appendix A for a discussion of how to set up and use the MCA. To obtain a spectrum of γ-ray counts vs. energy, select Yes/Enter for the PHA option, rather than the MCS option, and select all the default options that follow. Then continue with last five steps of the procedure in Appendix A.

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Figure 8. The front panel of the DSA–1000 module.

Figure 9. The rear panel of the DSA–1000 module.

Figure 10. Output waveform from the DSA–1000 representing the amplified voltage signals from the Ge detector, as viewed with the Digital Oscilloscope feature of the GENIE–2000 software. Radon Decay In this portion of the data acquisition, you will make direct measurements of the activity of the radon daughter products captured from the lowest level of the science building. Follow the procedure given below.

• Prepare a filter to place over the intake hose of a shop vac by spreading a thin layer of petroleum jelly in a circle with a diameter of (roughly) 5 cm on half a gauze pad. Tape the pad over the end of the hose of the shop vac with masking tape.

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• Start the shop vac in the predetermined location and allow it to run for at least 30 minutes. Before the time is up, finish the next step and be ready with a sandwich bag and cellophane tape.

• To make sense of the decay data to be collected, it is necessary to make a measurement of the background radioactivity2 which will be subtracted from the radon decay data. You will need to collect a background spectrum using the Ge detector as well as a counts/time interval measurement using the NaI detector and the MCA, without a sample (or calibration sources!) beside the detectors. Collect data for at least 20 minutes, or as long as possible, and calculate the average background count from the MCA spectrum.

• When the 30 minutes have elapsed, you will have to move quickly to get the gauze from the shop vac to the MCA to begin taking data. Turn off the shop vac and start your stopwatch immediately. Untape the gauze and put it in the sandwich bag. Using cellophane tape, attach the bag to a mount (the Styrofoam protective sleeve for the NaI detector works pretty well) so that it can be “seen” by both detectors. Start the NaI and Ge detector data collection (using the MCA and GENIE–2000 software, respectively) after a whole number of minutes since the time you turned off the shop vac. Record that number. If you move quickly you should be able to start at the two-minute mark.

• The NaI and Ge detectors should acquire data for at least two hours to collect adequate statistics. The data values from the MCA can be read at any time, so let the MCA run and you can return later to record the activity for each minute. Be sure to also save the resulting spectrum from the Ge detector.

Data Analysis and Discussion γ−ray Source Spectra The spectra that are observed from a typical γ–ray source are the emissions from decaying excited states in the daughter product following the beta decay of the parent source material in the encapsulated source disk. (The daughter product following alpha or beta decay is typically left in an excited state.) For example, the γ rays observed from a 60Co source are actually those emitted from the 60Ni nucleus, the daughter product following the beta decay of 60Co (see Fig. 1 in this document and Fig. 8.20 in the Experiments in Modern Physics text). Using the spectra that you record from the 60Co and 152Eu sources and their known decay energies, determine an energy calibration for the Ge detector using the particular (software controlled) amplification gain setting that you used for the DSA–1000. Since the amplification is linear, we expect an equation of the form Eγ = A + B × (Channel number) , (3)

2 Background radiation results from the activity of the surrounding environment as well as Compton-scattered events from a radioactive sample. It is necessary to make measurements of the background activity so that the average can be subtracted from the radiation of the sample, thus giving a better indication of the sample’s true activity. It is also important in order to understand the true γ−ray spectrum of a sample when performing high-resolution spectroscopy with the Ge detector.

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where Eγ is the γ−ray energy, and A and B are constants to be determined. Plot energy versus channel number for the γ–ray energy peaks you observe in the spectra, and perform a linear least-squares fit to these data. You can first obtain a rough two-point calibration using the 60Co source, then improve your calibration with the multiple lines of the 152Eu source. Once the detector is calibrated properly, locate and determine the origin of the full-energy photopeaks and the “Compton edge” and “single-escape” peaks (see Fig. 11) in the Ge 60Co spectrum.

Figure 11. Pulse-height spectrum for (a) an ideal γ-ray detector and (b) a real γ-ray detector for a monoenergetic source. The “Compton edge” occurs at the maximum Compton electron kinetic energy Kmax, and the “single-escape” peak occurs at an energy of hν − m0c2, where hν is the total γ−ray energy and m0c2 is the rest energy of an electron (511 keV). From The Art of Experimental Physics text. Measure the area (and the uncertainty in the area) of the peaks corresponding to the 1173 and 1332 keV γ rays from the 60Co source, and the 122, 245, 344, 778, 964, 1086, 1112, and 1408 keV γ rays from the 152Eu source using the analysis features of the GENIE–2000 software. These areas are proportional to the intensities of the associated γ rays. Compare the relative intensities (based on your measured areas) of each γ−ray with the accepted values given in the Table of Isotopes or online from www.nndc.gov. How do the values compare? The intensity analysis thus far has not taken into account the ability of the Ge detector to collect the radiation incident upon it, which depends on the efficiency of the detector. Depending on the application, there are various types of efficiencies that can be calculated for the detector. First, estimate the absolute efficiency of the Ge detector at a detector–source spacing of 2.5 cm by taking the ratio of the number of detected counts for some time interval divided by the total number of expected counts emitted by the source during that same time interval. (Note that there is also a Ge crystal-to-window distance of 0.5 cm.) This is most easily accomplished by using the 137Cs source, which

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has only a single γ−ray emission at 661.7 keV. Note that your calculation will depend on the value you use for the current activity of the source. Next, modify your efficiency value to incorporate the number of expected counts within the solid angle subtended by the detector (see the Experiments in Modern Physics text), and compare your result with the manufacturer expectation (Fig. 4). Note that the diameter of our Ge detector is 5.5 cm. Finally, calculate the relative efficiency as a function of γ−ray energy using the 152Eu source. The energy dependence of the relative efficiency ε is given by the following commonly-used parameterization:

( ) ( ) ( ){ } 22logloglog

γγγε

EDECEBA +++= , (4)

where coefficients A, B, C, and D are constants to be determined. Your instructor will show you how to perform a least-squares fit to your measured 152Eu peak areas using existing software in order to determine these coefficients. Once these coefficients are determined, write a Perl program to correct any user-input γ−ray energy and peak area (including the uncertainty in the area) for detector efficiency. Perform the efficiency correction for your 60Co and 152Eu source data, and compare the corrected relative intensities with each other. How do the results compare with the accepted intensity values after performing the correction? Do your relative efficiency values follow the expected trend with γ−ray energy for a REGe detector (see Fig. 4)? Of the three interactions between photons and matter given previously, which ones are responsible for the peaks you observe in your spectra? Notice that your collected spectra also include background counts. Give some possible causes for the background counts that you observe. Estimate the average number of electrons N that are excited across the 0.72 eV band gap of Ge by the absorption of both the 1173 and 1332 keV γ rays emitted by the 60Co source. N is subject to statistical fluctuations of N1/2. Compute the variation in N (ΔN) and the fractional variation in N (ΔN / N). What is the corresponding intrinsic variation in the measured energy of these γ rays? This result is interpreted as the minimum intrinsic resolution of the Ge detector. Note that it should be similar to (but likely smaller than) the measured full-width-at-half-maximum (FWHM) resulting from a Gaussian fit of these spectral lines in your data obtained with the GENIE–2000 software. Radon Decay Data Radon-222 (222Rn) is a member of a long decay chain whose progenitor is uranium-238 (238U). The immediate parent of 222Rn is radium-226 (226Ra), which has a half-life of about 1600 years. When 226Ra undergoes an alpha decay it produces 222Rn. The end of the decay chain (for our purposes) is lead-210 (210Pb) ⎯ it has a long half-life and can be considered effectively stable for the length of time that data will be collected. The detectors we are using detect only the γ rays that accompany the beta decays of the intermediate daughter products lead-214 (214Pb) and bismuth-214 (214Bi). (The daughter nuclei produced following the beta decays are left in an excited state, which decays to the ground state through γ rays.) Thus, the activity being measured is that of 214Pb and 214Bi. Radon, a gas under laboratory conditions, does not collect on the gauze like the lead and bismuth “dust”, but even if it did it would be undetectable by the Ge and NaI detectors.

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See www.nndc.bnl.gov for more information about the decay chain from radon to lead. Make a plot of the experimental data for the background-corrected radon daughter activity (the number of decays per minute) as a function of time. This is the experimental “decay curve” representative of the radon daughter activity. Then obtain a theoretical decay curve by programming a spreadsheet to simulate the decay of radon’s daughters. The simulation should include the decays of 218Po, 214Pb, and 214Bi. Normalize the theoretical decay curve to the experimental one by adjusting the initial activity of each species in the decay chain so that the theoretical activity at two minutes matches your experimental activity at two minutes (or whatever time you started data collection). (Note that at time t = 0 the decay chain is in equilibrium, so the initial activity of each species is the same.) Then superimpose the normalized theoretical decay curve with the experimental one for comparison, and include this plot in your lab report. Use the Ge radon spectrum you recorded and the “Peak with NID Report” function of the analysis software to measure the energies and areas of the peaks in the spectrum. This peak report function will include the tentative parent nuclide responsible for the decay peaks that you see. Do the results make sense, based on the decay chain you are analyzing? Include the peak report table in your lab report. Map out the decay chain of 238U to 206Pb in a figure in your lab report. Plot A vs. Z or Z vs. N. Label the nuclei and draw an arrow to indicate the decay and label the type of decay (being sure to distinguish between β+ and β– decay). Some nuclei may decay by more than one path. Plot the most probable decay. What aspect of the radon daughter decay curve gives information about the abundance of radon (and its daughters) in the area that was vacuumed? What aspect of the decay curve would not change even if the abundance were ten times larger? Explain. Appendix A: Use of the Multi-Channel Analyzer (MCA) To set up and collect data with the MCA, follow these steps:

• Press “Setup” • Press “Acquire” • Select “No / Clear” to PHA option and “Yes / Enter” to MCS option • Press “Enter” again to choose the default sweep number • Choose a dwell time of 60 seconds and press “Enter” • Press “No / Clear” twice to change units to seconds and press “Enter” • Press “Enter” again to choose the default preset integral • Press “Setup” • Press “1 / 4” • Press “Erase Data” to get rid of the lines • Press “Acquire” to begin data collection • To reset for new data, press “Erase Data” and then “Acquire”

Every minute a data point will appear representing the number of events detected by the NaI detector in that minute. You can read the value of any point by moving the screen cursor, much like on a digital oscilloscope. The arrow keys can be used to expand or compress the axes of the graph.