Quantitative Interpretation of Gamma-Ray Spectra Kurt Liebscher and Hamilton Smith Department of Forensic Medicine, Glasgow University, Glasgow, W.Z., U . K .
A peak fraction method of interpretation of gammaspectra is described. A computer technique i s proposed for work under varying conditions which consists of successive applications of a series of procedures. Curves are smoothed and calibrated peak fraction areas are calculated. For peak fraction calibration, the points of inflection on a third order approximation curve are used. The shape of the peak fractions is checked with normalized Gaussian curves. This method permits work without a catalog of standard spectra and gives better results than spectrum stripping in the lower energy region of composite spectra. I t is suitable for the interpretation of trace elements in biological materials.
A GAMMA-RAY SPECTRUM consists of peaks corresponding t o the total absorption of photons and continuous contributions arising from Compton scatter, backscatter, and other minor effects. The total absorption peak, or “photopeak” has the shape of a Gaussian distribution ( I ) . I n most of the practical applications of gamma-ray spectrometry, conclusions are drawn from photon energies and count numbers of the various photopeaks in a spectrum (together with other information from various other sources, such as half-life, chemical form, etc.). Therefore, methods have been developed, and are still being improved, to differentiate between photopeaks and counts due to other effects and, thus, t o translate a gamma-ray spectrum into a list of photon energies and corresponding activities. As Covell has pointed out, there are two main types of photopeak evaluation methods, referred to as the “stripping technique” and the use of a “calibrated fraction” of the photopeak area ( 2 ) . The stripping technique is of practical value only if the statistical error for all parts of the curve is small, and it requires a catalog of gamma spectra of individual nuclides measured under exactly the same conditions as the sample in question. F o r the determination of a calibrated fraction of the photopeak area, that part of the peak area can be used which lies above a straight line drawn through the points of inflection of the rising and falling parts of the curve (3). However, these points are largely influenced by statistical errors. Covell recommends a method in which the number of channels t o be used and the energy increment represented by each channel are found by use of a standard radiation source. The same number of channels is then used in each evaluation. The application of either of the afore-mentioned methods implies tedious computations. Therefore, automatic electronic computers have been used. Most of the computer programs have been written in Fortran and apply some variant of the stripping technique. The peak fraction method is only occasionally applied, such as in a program, which, by subtracting a n exponential curve from the total curve, results in individual peak curves ( 4 ) . (1) R. E. Connally and M. B. Leboeuf, ANAL.CHEM., 25, 1095
(1953). (2) D. F. Covell, ibid., 31, 1785 (1959). (3) L. D. McIsaac, U. S. Naral Radial. Defense Lab. Rept. USNRDL-TR-72 (1956). (4) J . Picard, Rapport du Commissariat a I’Energie Atomique, CEA-E-3024 (1966).
Generally programs are used by large research establishments and, therefore, they are written to suit the special needs of their particular users. There are, however, some smaller departments and those whose activities are not solely limited t o the application of gamma spectrometry or non-destructive activation analysis. These institutions, generally, d o not use their own reactors, counting equipment, and computers, but have access to other peoples’ equipment. This means, that conditions vary, and usually there is not much time and manpower for collecting catalogs of standard data, adjusting programs, and trying optimal radiation and cooling times. Only a small computer or only part of its memory may be available. With a view t o this situation, a technique has been developed and a program written, which may serve as a n easily adaptable basis for various working conditions. Independence of any catalog of standard data and applicability to poor statistical data were essential in this study. I n order to achieve versatility by variations of the basic program, it had to be divided into several successive steps. Although the whole program should not need a large memory, it may be desirable to further reduce the storage requirements by running each step separately. METHOD
The proposed method of peak area evaluation proceeds as follows: The curve obtained from the gamma-ray spectrometer is smoothed. T h e points of inflection of the smoothed curve are determined and a straight line is drawn through any pair of points of inflection. This straight line is subtracted point-by-point from the part of the curve above it. (The remaining curve should be a Gaussian distribution.). The differences thus obtained are summed u p giving the area of the calibrated peak fraction. The ordinate values of a theoretically exact Gaussian curve are calculated in such a way that the area and the points of inflection are the same as for the curve which was previously cut off by the straight line through the points of inflection. This theoretical curve is compared with the one actually found in order to exclude all parts of the curve other than those approximately Gaussian-shaped. DISCUSSION
Curve Smoothing. Independence of any catalog of standard data can only be achieved, if the peak fraction method is applied. However, in calibrating the peak fraction as well as in determining the peak fraction area, some statistically variable data are involved in subtractions. Therefore, statistical errors are often amplified. I t is necessary to minimize these errors before the calculations are started, in such a way that the spectrum curve becomes smooth, that the calibrated area remains unchanged after smoothing, and that as much as possible of the available information is used in the calibration of the peak fraction. Gamma-ray spectrum curves are generally given in the form of discrete points representing the values of a function for a number of equidistant arguments. The constancy of the argument increment is a n advantage in smoothing. Every single point of the curve is replaced by another point found using one of the following methods: The new point is VOL. 40, NO. 13, NOVEMBER 1968
1999
the center of gravity of two or more old ones: the curve is folded with a Gaussian distribution, or new points are found by least square fits of specified order to a given number of old points. Each one of these methods is repeatedly applied until the curve is sufficiently smooth. The center of gravity method is often applied in statistics (5). In its simplest form, the new point is halfway between two old ones. If this procedure is carried out twice, every point x i is replaced by
xi-I
+ 2xr +
Xt+l
4
This method is widely used in physics and meterorology and is referred to as the “trapezoid rule”. Folding a spectrum curve with a Gaussian distribution means multiplying several consecutive points by factors which are themselves values of a Gaussian distribution curve. The products are then added and the sum is assigned to the central argument. The folding of two Gaussian distributions results again in a Gaussian distribution (6). If the sum of the abovementioned factors equals one, the new distribution curve has the same area as the old one. The fraction calibrated by the points of inflection also remains unchanged. The whole curve is flattened and broadened. The standard deviations of the new curve (uz), the old one (uo), and the curve of the factors (al)are connected by the relation UfL
= u:
+ us
I n a formula applied by Picard ( 4 ) :
+ + 0.18256(xi-1 + xr+J + 0 . 6 2 6 2 0 ~ 1
x i is replaced by 0 . 0 0 4 3 4 ( ~ ~ - ~xi+..>
The standard deviation of the curve of factors is uf = 1.5 channels. A new point constructed halfway between two old ones can also be regarded as a n application of this method, since the two factors in the formula are points o n a Gaussian curve with uI = 0 . 5 channel. x i is then replaced by 0.5 xi-0.5
+ 0.5
xi+0.5
Smoothing by a least square fit requires a t least two points more than the order of the curve to be fitted. The point halfway between two old points can be regarded as the simplest fit of this type, if a single point is taken as a curve of order 0. The next higher grade would be a straight line fitted to 3 points. This gives as the replacement formula for the middle one: x t is replaced by
xi-1
+ x i + xr+1 3
Least square fits to curves of order 0, 1, or 2 necessarily flatten all maxima and minima. However, a least square fit to a curve of 3rd or higher order does not have this disadvantage. Its simplest form, a 3rd order curve through 5 points is, therefore, recommended by Yule (7). H e uses a replacement formula calculated by Savitzky and Golay ( 8 ) : (5) K. Mader, “Handbuch der Physik,” vol. 3, H. Geiger and K. Scheel, Eds., H. Thirring, Sub-editor; Julius Springer, Berlin, 1928, p 533. (6) L. Janossy, “Theory and Practice of the Evaluation of Measurements,” Oxford University Press, London, 1965, p 114. (7) H. P. Yule, ANAL.CHEM., 38, 103 (1966). (8) A. Savitsky and M. J. E. Golay, ibid.,36, 1627 (1964). 2000
ANALYTICAL CHEMISTRY
x i is replaced by
-3(xi-?
+ Xi+,) + 12(xt-1 + x ~ + I+ ) 17x1 35
Of all the formulas mentioned in this section, Picard’s is the most exact one. Yule’s formula is of advantage, if too many peaks tend to interfere with each other. Constructing new points halfway between old ones is the simplest method, the only one which meets all the three mentioned principles and is not influenced by the background. It has been used in our curve evaluation program. Two smoothing steps were always carried out together, using the trapezoid rule. This modification is easier to deal with, because, unlike application in single steps, it does not call for intermediate argument values. Calibration of Peak Fraction. A fraction of the peak area may be calibrated by any reproducible method. It is done practically always by intersecting the peak curve by a straight line connecting the two points of inflection o n its rising and falling parts. The area between this line and the curve is proportional to the total number of registered photo-effects. It is important to mention in this connection that the factor of proportionality is the same for all Gaussian curves. It is, therefore, not affected by any method of smoothing as long as the smoothed curve is Gaussian again. The use of a straight line for calibration implies the assumption that the energy dependence of the number of interfering counts is linear, apart from statistical fluctuations. Although this is not exactly true, the energy range over which the line is extended is so small that normally linearity can be assumed. Because the second derivative of a linear function is zero, the position of the points of inflection on the energy scale is the same for a photopeak with or without interfering background, even if the interference is strong. In Covell’s method, the statistical error of only two channels affects the total peak fraction area. The effects on these two channels of a shift in energy calibration cancel each other only if their statistical errors are small. However, experiments carried out with moderate statistics need objective numerical determination which makes use of all available information. The coordinates of 4 points o n the curve have been used t o find coordinates of a point of inflection, two of the curve points being o n either side of the latter. Through these 4 points a n approximation curve of 3rd order was laid. The radius of curvature is infinitely large at the points of inflection and, therefore, the error induced by this approximation is negligible. Spectrometers are usually designed for a linear correspondence of pulse height and quantum energy so that the mean energies, which are represented by the various channels, are equidistant. With this condition satisfied, Newton’s interpolation formula can be used. We insert 4 points representing the channel numbers n, n 1 , n 2 , and n 3 and the numbers of counts y z , J ’ ~ +ye+?, ~ , respectively. Thus we find:
+
y = yn
+
Ayn(x
1 2
+
+
- n) + - A 2 j S n ( x- n)(x
- n - 1)
+
where x and y are the coordinates of any point on the curve of 3rd order. Hence,
and
If this value is introduced in Newton’s interpolation formula, we find Y p o i n t of inflection
=
Yn
+ A ~ n ( 1- r> -
Table I. Area of Photopeak Fraction of 137Cs (Photon Energy 0.662 MeV) Measured for 1.0 Min
Measurement no. 1 2 3 4
where
r
=
Calibrated peak fraction obtained by: Covell’s method (counts) Computer (counts)
A2y,/A3yn
I n this way both coordinates of the point of inflection can be determined. Any curve of third order has one point of inflection. Consequently, the above-mentioned procedure will give the same result if it is applied to any set of points on such a curve. If we repeat this calculation several times, with n - 1 , 2 , 3, . . . . , we will find the points of inflection of all third order curves laid through any four adjacent points of the spectrum curve. But we want each point of inflection only once, that is when it 1 and n 2, beis between the points with the arguments n cause with this selection of reference points o n the spectral curve the approximation is the best one. This condition is obviously fulfilled when
+
+
-1 I A2y/A3y 5 0 In the computer program, a point of inflection is calculated only if these conditions are valid. A t the point of inflection, the second derivative of the spectrum curve, or of its approximation, is zero. If the third derivative is negative, that indicates that the second is descending. That, in turn, means that the first derivative is concave from below, having its greatest value a t the point of inflection. Thus, the point of inflection is o n the rising part of the Gaussian curve. If the third derivative is positive, the point of inflection is o n the falling part of the curve. This distinction is necessary for deciding where to place the left and right limits of the calibrated fraction. By subtracting the values of each point o n the line connecting the points of inflection from the spectrum curve values and by summing up the resulting differences between each pair of points of inflection, we find the area enclosed by the curve and the straight line. Construction of a Gaussian Curve. Some criterion is needed to show that the area calculated in this way is actually the area of the top part of a Gaussian peak. There is n o interest in, and it would be better to eliminate, other maxima of the spectrum curve, such as Compton edges. The top part of a theoretical Gaussian curve of equal area and half-width is calculated in order to compare the theoretical and the actual curves. The difference between a point o n the Gaussian curve and the line connecting its points of inflection is
This formula is used in a computer procedure, which generates a Gaussian distribution curve between two given points of inflection and adapts this distribution to a given peak fraction area, so that each channel of the actual gamma-energy distribution curve can be compared with the corresponding figure of the idealized Gaussian peak distribution. In the main program, the area enclosed between the actual and the idealized curve may be calculated and given as a percentage of the whole peak fraction. This may help the workers involved to decide o n the reliability of the curve shape.
49368 48444 49034 48981 49673 48898 49306 48903 47548 48056 48254 49792 47738 48392 48987 49071 49598 48977 48888 49280
5
6 7 8
9 10 11 12 13 14 15 16 17 18 19 20
Mean 48859 Standard deviation 4~619 Relative standard deviation 1.27
44178 44125 44094 43794 43867 43895 43724 44030 43812 441 52 44061 44088 44433 43830 43902 43901 43906 44124 44105 44 108 44006 i177 0.40
Table 11. Area of Photopeak Fraction of 137Cs (Photon Energy 0.662 MeV) Measured for Various Lengths of Time Duration of measurement, min
Calibrated peak fraction obtained by: Covell’s method, cpm Computer, cpm
0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 Mean Standard deviation Relative standard deviation
45030 45605 45077 45565 44944 44679 44624 45064 45324 45451 45608 45641 45782 45781 45613 45509 45469 45458 45557 45708 45739 45756 45915 45818 45918 45922 45884 45853 45910 45830 45932 45965 45985
42960 43360 43333 43288 43322 43483 43494 43348 43310 43309 43231 43206 43262 43288 43288 43352 43282 43269 43290 43295 43261 43272 43317 43345 43294 43275 43279 43275 43287 43 300 43280 43278 43255
45573 f371 0.81
43294 i84 0.19
VOL. 40, NO. 13, NOVEMBER 1968
0
2001
0
0
24Na
MEASURED VALUES
0
I
-
SMOOTHED SPECTRUM
CJ
CALIBRATED PEAK FRACTION
*.
2 0 OOO
.,
3 8 ~ ~
I *
. 4
.
3% I
I * .
'
I .
-
t 6 10 000
L
U
-
1
. .
* .
* C
a U
,
0
I
1
40
60
50 CHANNEL NUMBER
?' . 4.
.
Figure 2.
80Br
photopeak expanded from Figure 1
.*I
0 0
100 Channel
200 Number
Figure 1. Gamma-ray spectrum of thermal-neutron-irradiated hair
Main Program. The above considerations enable us to write computer procedures for curve smoothing, points of inflection, straight lines through two points, and theoretical Gaussian curves. I t is easy now to use these in a main program for gamma-ray spectrum evaluation. I t is necessary, of course, to take into account whether one spectrum only or a set of spectra will be evaluated at a time and, in the case of a whole set, whether there is some connection between the various spectra of the set. In most cases peak areas from various spectra will be compared. This is the usual technique in activation analysis, where each peak of the sample spectrum is related to a corresponding peak in a standard spectrum. In such a case, it is of advantage to make sure that the smoothing procedure is equally often applied to all spectra, because equality of conditions contributes to accuracy. I n many other cases it will be better to continue smoothing as long as smaller maxima and minima are removed from the curve. The number of points of inflection is twice the number of either of these. Once it ceases to diminish, this may be taken as a criterion that the curve has reached a high degree of smoothness. I t is usual to measure a standard spectrum with two easily determined peaks as a n aid for energy calibration. If such a spectrum is the first one in a set, the procedure for a straight line through two points can be applied t o interpret channel 2002
ANALYTICAL CHEMISTRY
Table 111. Area of Peak Fractions of 137Cs (0.662 MeV) and 6oCo(1.173 MeV and 1.332 MeV) in Mixed Spectra Measured for 1.0 Min Each Measurement no. 1 2 3 4 5 6 7 8
9 10
Calculated by computer, cpm 1.332 MeV 1.173 MeV 0.662 MeV 12299 13858 49322 12241 13891 4941 1 12052 49441 13828 12225 13913 49431 12165 13894 49624 12220 13946 49365 12200 13907 49499 12268 13988 49944 12259 13895 49533 12129 13949 49754
12206 Mean f74 Standard deviation Relative standard 0.61 deviation
13907 f47
49532 rt 193
0.34
0.39
Calculated bv Covell's method cum 1
2 3 4 5
6 7 8
9 10
11540 11676 11337 11313 11048 11295 11509 11605 10962 10942
11323 Mean Standard deviation +282 Relative standard 2.49 deviation
13873 14063 13432 14100 13655 13848 13710 14198 13813 13649
66163 66367 66531 67246 66600 66275 66750 67449 67587 67793
13834 240
66876 f598
1.73
0.89
Table IV. Area of Peak Fraction of 137Cs (0.662 MeV) and W o (1.173 MeV and 1.332 MeV) in Mixed Spectra of Various Composition Calculated bv comouter Measuring time, min 0.662 MeV 60Co 1S7Cs 1.332 MeV, cpm 1.173 MeV, cpm Counts cpm 1.0 None 45293 48733 69 ... 0.1 45293 48731 1.0 5354 53540 0.2 45301 48734 1 .o 53505 10701 0.3 45310 48731 1 .o 53589 16077 0.4 45319 48730 1 .o 53590 21436 0.5 45323 1.0 48731 53550 26776 45332 1 .o 0.6 48731 32131 53553 45336 1 .o 0.7 48730 37501 53574 45345 48728 1.0 0.8 42917 53646 45357 0.9 1.0 48730 48335 53705 48727 45360 1 .o 1. 0 53725 53725 Mean 45324 48735 53598 Standard deviation h25 +2 +72 0.055 Relative standard deviation 0.004 0.13 Calculated by Covell’s method 1.0 1 .o 1.0 1.0 1.0 1.0 1.0 1 .o
1.0 1.0 1.0
None 0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.9 1 .o
Mean Standard deviation Relative standard deviation
32297 32309 32306 32312 32322 32325 32328 32343 32343 32339 32341 32324 116 0.050
numbers in terms of photon energy units. The coordinates of the two points are the channel number and the known energy values of the calibration peaks in MeV or keV. RESULTS This program was used t o calculate a few test samples. Twenty measurements, under the same conditions, of a 137Cs standard were calculated both by the computer program and by Covell’s method, the latter using about the same halfwidth (Table I). There was only one peak, very good statistics, and virtually n o background. These are the best conditions for the application of Covell’s method. The relative standard deviation found using this method was 1.27%, three times that found using the proposed method (0.40%). I t was not possible to get equal areas in both methods, because in Covell’s method the number of channels under consideration must be a n integer (in this case it was 5 ) , while in the proposed method it was determined by the position of the points of inflection. Therefore, the fraction used in Covell’s method was, by chance, larger than the fraction calculated by the computer. A similar result was achieved, when the peak was calculated for 33 measurements of different duration varying from 0.1 minute to 3.3 minutes (Table 11). In measurements of mixed spectra consisting of the two 6oCopeaks at 1.173 MeV and 1.332 MeV and the 137Cspeak, the proposed method also yielded better results than Covell’s method (Tables I11 and IV). I n these spectra the 137Cspeak is superimposed upon the Compton continua of the two 6OCo peaks. Here the portion of counts, which must be subtracted, is much larger than in the simpler case of 13iCsalone. There-
42559 42560 42555 42564 42571 42576 42577 42572 42575 42584 42580 42570 i10
0.023
446 7364 14385 20974 27570 34509 41234 47777 54857 61325 68113
-
...
73640 71925 69913 68925 69018 68725 68254 68571 68138 68113 69522 =kt1842 2.66
fore, the more elaborate computer method can give more accurate results. A pure W o peak has a small escape peak a t 0.662 MeV (1.173 MeV - 0.511 MeV = 0.662 MeV). O n the other hand, 13’Cs gives a small contribution to the 1.332 MeV peak of 6oCo. Each of these additions amounts to about 70 cpm in the measurements listed in Table IV. They were not taken into account when this table was calculated. A sample with 7 peaks has been chosen to serve as a n example of the practical application of the proposed method. A strand of human head hair was irradiated with thermal neutrons for 10 minutes. The gamma-ray spectrum obtained 80 minutes later is shown in Figure 1. I t is dominated by 24Na and 38Clpeaks. The results of the computer evaluation are shown in Table V. The identification of 80Br,T I , and 24Na was confirmed by the decay constants. The backscatter peak, the annihilation peak, and the peak at 0.85 MeV had composite decay curves. As is shown it was possible t o determine the small 8oBrpeak in the presence of very large 24Naand 38Clpeaks. This part of the spectrum is marked in Figure 1 and shown in detail in Figure 2. Here the dots denote the measured values while the smoothed curve is drawn out. The shaded area is the peak fraction under consideration. CONCLUSIONS A method of gamma-ray spectrum evaluation by computer is proposed for work under varying conditions. I t consists of successive application of a series of procedures. Curves are smoothed and calibrated peak fraction areas are calculated. F o r peak fraction calibration, the points of inflection o n a VOL. 40, NO. 13, NOVEMBER 1968
2003
Curve smoothing can show up peaks in statistically poor spectra and smaller peaks in the vicinity of large ones. Comparison with normalized Gaussian curves eliminates statistical fluctuations and Compton edges, but not Gaussianshaped peaks like backscatter peaks. Results have been found to be better than those obtained by the application of Covell’s method with similar width of the calibrated peak fraction. However, it should be noted that the width is fixed by the proposed method, while Covell’s method leaves the choice of the most suitable width open. The method is applied in this department for the simultaneous determination of trace elements in biological material and the program (Algol 60) is available on request.
Table V.
Evaluation of Neutron-Irradiated Hair Sample Peak fraction calibrated by points of inflection Width. Area. Energy, Channel channels counts MeV Comment 7.18 3135 13.59 0.237 Backscatter 41.79 Annihilation (80Br, 6.48 4321 0.511 C4Cu, 38Cl,z4Na) 53.55 80Br 5.17 312 0.625 66Mn, 2;Mg 76.38 0.847 8.19 2602 Z4Na 10.43 33835 130.07 1.37 38C1 10.99 24601 158.87 1.65 3 8 ~ 1 2.17 13.29 25986 212.92
ACKNOWLEDGMEYT The authors thank Professor Gilbert Forbes for his support and encouragement during the course of this study. They also thank the Scottish Research Reactor Centre and the Computing Department of Glasgow University for the use of equipment and facilities.
third order approximation curve are used. The shape of the peak fractions is checked with normalized Gaussian curves. The peak fraction method was chosen, because it permits work without a catalog of standard spectra and gives better results than spectrum stripping in the lower energy region of composite spectra.
RECEIVED for review August 10,1967. Accepted July 1, 1968. -
Direct Determination of Lead-210 by Liquid ScintiI lation Counting I
William D. F a i r m a n a n d Jacob Sedlet Argonne National Laboratory, 9700 South Cuss Ace., Argonne, Ill. 60439
The soft betas, 15 and 61 keV end-point energies, the internal conversion electrons, and unconverted gamma rays from z10Pb are efficiently detected in a liquid scintillation counting system. The overall counting efficiency (cpm/dpm) is 97-98%. The background counting rate in the 210Pb window is 20 cpm for polyethylene vials and 40 cpm for low-potassium glass vials. It is possible to determine 0.98 t 0.58 pCi of separated 21oPb at the 95% confidence level in a 100minute sample counting period, with polyethylene vials. The Z10Pb can also be measured in the presence of its daughter activities, ZlOBi and 2lOPo. Both the 3lOBi beta (1.160 MeV end-point energy) and the 210Po alpha (5.305 MeV) are counted at essentially 100% efficiency. There is no interference between the 210Pb and Z1OPo spectral counting regions. The 210Bi beta spectrum overlaps the zloPb and 2l0Pospectral regions; 23 and 50% of the ZlOBi beta particles appear in the lead and polonium regions, respectively. However, an energy range covering approximately 27% of the bismuth spectrum is completely free of zloPb and zlOPo activity. It is thus possible to determine the concentration of each component of a lead-bismuth-polonium-210 mixture.
THEDETERMINATION of 2loPb is important in such fields as radium toxicity studies, atmospheric tracer studies, and uranium mining operations. The direct measurement of this radionuclide has always been difficult because of the low energy of its beta particles. If the zloPb in a sample is in secular equilibrium with its daughters, zlOBiand zloPo,one or both daughters can be separated and measured immediately to determine the amount of 2loPb ( I , 2). If, however, there is doubt as to whether secular equilibrium has been established, then it is necessary t o purify the lead from its decay products and wait for the 210Bior z1OPo to grow in significantly, before (1) E. S. Ferri and H. Christiansen, Piibl. Health Repts., 82, 828 (1967). (2) C. W. Sill and C. P. Willis, ANAL.CHEM., 37, 1661 (1965). 2004
ANALYTICAL CHEMISTRY
the zloPb can be determined from the daughter activities This growth period results in a delay of days to weeks before measurements can be completed. Current procedures have used one of the above indirect methods for determining zloPbconcentrations because of the ease of measurement of the energetic beta (1.160 MeV endpoint energy) from zlOBior the alpha (5.305 MeV) from ZlOPo, as contrasted with the previously believed difficulty of measuring the disintegrations from zloPb. Lead-210 decays by the combined emission of beta and gamma-rays and internal conversion electrons to the ground state of *loBi (6). Nineteen per cent of the beta emission is directly to the ground state with a maximum beta energy of 61 keV. Eighty-one per cent of the beta emission is t o the 0.04652-MeV level of zlOBiwith a maximum beta energy of 15 keV. The 0.04652-MeV level is highly converted in its rapid (
