Attenuation of Gamma Rays in Binary Compounds A Versatile Illustration of Beer's Law E. W. Kleppinger and S. W. Yates University of Kentucky, Lexington, KY 40506 While Beer's law, or the Beer-Lambert law, is familiar to all chemists, students whose main contact with it has heen a UV-visible spectroscopy experiment in an analytical chemistry course, quite understandably, may not grasp its broad applicability. Beer's law describes the decrease in intensity as lieht nasses throueh a medium and relates this decrease to the concentration of the interacting species present. While s~ecificmodes of interaction withmatter varv with the energy of the electromagnetic radiation, the end result for all radiation is an exponential attenuation as thickness (or concentration) of interacting species is increased. This relationship is usually expressed as A = rbe
(1)
where A is absorbance, c is the molar absorptivity, b is the pathlength in centimeters, and c is concentration of ahsorber in moles per liter. Many excellent student experiments have been developed for demonstrating the analytical application of Beer's law in the UV-visible1 and IRZ regions. Pedagogically, however, these experiments necessarily suffer from several shortcomings. Since ambient light is an interference, the source, sample, and detector must all be concealed from view inside a light-tight "black box" or spectrometer. Moreover, the relatively low energy of even UV.radiation precludes the use of a pure absorbing species of any significant thickness; the absorber must be dissolved in a nonabsorbing solvent, and concentration cannot be varied easily by simple addition. In most spectrometers, cells of fixed dimensions are used and pathlength cannot be varied. Finally, experiments utilizing only UV-visible or IR radiation fail to demonstrate the much wider applicability of Beer's law. We have developed an experiment, based on depth-gauging principles,3 which uses gamma radiation to illustrate Beer's law. There are several advantages of using y rays as a "light"source. Because of the higher energies of y rays, finite thicknesses of Dure materials can he used as attenuators. Monuchrvmatic lsingle ray) sources are inexpensive and rendilv nvnilnhlr. Furthermore, the entire assemblv (source. sampie, and detector) is in plain view. Sample thickness (or pathlength) is continuously variable by simple addition of material since no nonparticipating solvent is present. Finally, by bringing the experiment out of the domain of traditional UV-visible spectroscopy, this procedure demonstrates the wide applicability of Beer's law. This experiment could also he used in anuclear chemistry context toillustrate the properties of y rays as well as the requirements for agood y-ray absorber.
In nuclear chemistry, the attenuation of electromagnetic radiation in matter is usually described as
where x is the absorber thickness (in g/cm2-units of surface density, obtained from the product of density and thickness) a n d l oand I are the beam intensities before and after attenuation. The linear absorption coefficient, fi, is in units of cm2/ g and varies with y-ray energy and absorber. Values of fi have been tabulated for the elements for various y-ray energies4and are additive for compounds (i.e., ir = mlpl mzpz . . .,where m = weight percent). The attenuation relationship can also he expressed in more traditional terms as
+
-log(I/I,)
'
. . ..
741
In depth gauging, the attenuation of radiation incident on an absorber is used to gauge absorber thickness. 'Storm, E.: Israel, H. I. Nocl. Dat. Tables 1970, 7. 565. The sources required in this experiment are below the activity level requiring a government license; little or no shielding is necessary.
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Journal of Chemical Education
(3)
= px
where the left side is comparable to absorbance, fi can be equated with the molar absorptivity, and x corresponds to a combination of the usual concentration and pathlength terms of eq 1. Experiment The experimental setup is depicted in Figure 1. A sealed, monoenergetic'3"Cs source is attached to the hottom of a 12mm-thick lead hrick directly below a 3-mm hole drilled in the brick. This arrangement provides some collimation of t h e y rays and ample radiation ~hielding.~The detector is a 5 X 5-cm NaI(T1) crystal located far enough above the collimator to leave space for a short graduated cylinder. Data are accumulated with a multichannel analyzer (MCA) and are printed out for subsequent analysis. Figure 2 shows a typical '"Cs y-ray spectrum where the shaded portion is the area of
Analysis
-,
Paper presented at the National Meeting of the American Chemical Society. Washington. DC. August 1983. Diehl-Jones. S. M. J. Chem. Educ. 1983, 60. 986. Allpress, K. N.;Coweli, B. J.; Herd, A. C. J. Chem. Educ. 1981,58,
+
System
Detector
h Sample
P ~-J-L
Source Figure 1. Block diagram of experimental setup.
Collimator
Llnear Absorption Coewicients (a) In cm2/g for Several Elements as a Function of y-Ray Energy in MeV
ENERGY
hand, a simple Geiger counter can be purchased for as little as $200, hut there is some attendant loss of accuracy with such a setup. The experimental procedure we have adopted allows us to teach several aspects of the interaction of electromagnetic radiation with matter. The student collects spectral data with no source (i.e., a background spectrum), with the source and lead brick collimator in place, with a graduated cylinder between source and detector, and with several different amounts of either water or carbon tetrachloride6in thecylinder (Fig. 3). The source is then replaced with an unknown which emits a sinele r rav. In our case. the unknown was "Mn produced biirradiating a sample of MnO~forseveral hours in a 252Cfsource: however. an additional purchased source, such asS4Mn,would be eq"ally suitable. he attenuation of the unknown y ray in various thicknesses of Hz0 and CCla is measured.
Figure 2. Gamma-ray specnum fw '%s.
Calculations Students carry out calculations that can be categorized under three headines: " "checkine" of exnerimental results versus theoretical predictions; using the depth-gauging princinle to determine the thickness of the eraduated cvlinder bottom; and finally, determining p, and hence the energy, for the unknown y ray. First, observed attenuation of the '37Cs y ray in both Hz0 and CC4 is compared to theoretical attenuation in the following way: the student obtains values of p, the linear ahsorntion coefficient, as a function of y-ray enerw for the nppr~~riateele~nenrsirom the literature (sic tahlei).'l'hen r is calrdated for H20 and CC14at various 1 -ray energies and log-log plots of attenuation versus energy are constructed; from these plots, pvalues for '37Cs can he determined. Substitution of p and I, the depth of liquid in the graduated cylinder (g/cm2), into eq 2 yields theoretical attenuation values that are comnared eranhicallv with the exnerimental attenuation versus {hicknessdata (see Fig. 4). Second. the thickness of the " eraduated cvlinder bottom is estimated. I t is necessary to assume the glass is SiOz and determine the linear absorption coefficient for Si02 a t 662 keV. Then, given the density of SiOn, eq 2 can he used to calculate the thickness of elass reauired to nroduce the ohserved attenuation. ~ e n e r a l l y the , cylinder bottom thickness can he determined within 10%. Third, p values for the unknown y ray are calculated from eqs 2 or 3 using the experimentally determined attenuations in various depths of Hz0 or CC14. Using the prepared graph of p versus y-ray energy, the calculated linear absorption coefficient can be used to determine the unknown y-ray energy. This exercise is, of course, only an intellectual one if the y rays are "energy analyzed" as is generally the case when a NaI(TI) detector and MCA are used.
-
0.0cm (No Attenuation)
)55 0.65 075
0.55 0.65 0.75
ENERGY (MeV)
Figure 3. Auenualion of the full-energl %s
peak as a function of depm for
both H20and CCI,.
the full-energy peak and isequated with intensity (0ineq 2. There are several possibilities for alwrnative setups. For instance, the multichannel analyzer could he replaced with a sinrlechannelanalvzer and scaler with a windowset tocount onG the full-energy peak. In this case, the actual area of the '37Cs spectrum measured would include both the shaded neak and the hatched nortion of the hackeround in Finure - 2. An even simpler setup would involve a Geiger counter used in d a c e of the NaI(TI) detector and MCA. With this arraigement, no energy discrimination is obtained, and events from the entire spectrum of Figure 2 are counted. Although the cost of equipment needed for this experiment is not prohibitive, it can he more expensive than what is required for a traditional Beer's law experiment. A spectrometer (Spectmnic 20) currently costs about $1000, while the source, collimator, NaI(T1) crystal, and associated electronics may cost several thousand dollars. On the other
-
Since students should avoid contact with CCI,, the instructor might wish to provide various amounts of CCi, in sealed cylinders. Volume 64
Number 2
February 1987
173
This experiment can also he used as a vehicle to demonstrate the limitations imposed on any determination by the uncertainties associated with measured quantities. For example, the maximum and minimum thicknesses of H 2 0and CCL that can be determined by depth gauging depend on the background count rate and the statistical uncertaintv associated with an unattenuated count rate, respectivel;. The student might also he asked to calculate the range of thicknesses of Hz0 and CCll that could he determined with this particular experimental setup.
Depth (g/crn2) Flgure 4. Plots of attenuation of y rays in H P and CCi+ The salld lines are themtical atlenuatianr, and the x's are experimental student data.
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Journal of Chemical Education
Summary Student results for this exoeriment have been excellent. Curves for experimental and iheoretical attenuation in both Hz0 and CCL are virtuallv indistinauishahle (Fie. 4). Obtaining and fi values for the compounds versus y-ray energy is the initial step of the data analysis. Once this information is plotted, the analysis is straightfoward and most students find the excellent results they obtain well worth the effort expended. A wide variety of principles caqbe taught with this experiment. In the analvtical realm. a concrete and visual illustration of Beer's lawis provided'in such a way as to emphasize its aoolicabilitv to electromaenetic radiation in eeneral. In the fikld of r a d i ~ c h e m i s t rt~h,e student learnsabout the properties and detection of y rays, and obtains information on the effectiveness of various absorbers. Two relevant applications of the theoryused in this procedure should be pointed out. Depth gauging as such can be used, for example, in industry for quality control, while information on absorbers for y rays is useful in designing shielding for.gamma radiation.
