Isotopic Determination of Nitrogen and Carbon By Means of a Microwave Spectrograph A. L. SOUTHERN, H. W. MORGAN, G. W. KEILHOLTZ, AND WILLIAM V. SMITH Oak Ridge National Laboratory, Y-12 Area, Oak Ridge, Tenn. Research on the use of a microwave spectrograph for isotopic analyses was undertaken as part of a program of the Oak Ridge Kational Laboratory to develop new methods of isotope assay. Analytical procedures have been developed for nitrogen 15 in ammonia and for carbon 13 in cyanogen chloride, as being typical of the stable tracer isotopes. Nitrogen 15, in the range 0.38 to 4.5%, can be determined to within approximately 370 of its concentration. For carbon 13, in the range 1.1 to 1070, the average error
T
HE ’techniques of microwave spectroscopy have been employed almost exclusively for the determination of molecular structure parameters and nuclear constants. Some of the earliest papers, however, indicated the possibility of performing isotope analyses by comparing the relative intensities of absorption lines arising from different isotopes. Perhaps the first abundance ratio to be checked in this manner, though qualitatively, was the C137to CIS ratio measured as 0.3 to 1 by comparing the intensity of the C13’CN absorption line at 23,389 Mc. with that of the CISCN line a t 23,885 Mc. (16). Spectra in the microwave region arise principally from transitions b e b e e n different rotational states of a molecule (8). The resulting frequencies are inversely proportional to the moments of inertia of the molecules, which in turn are functions of the nuclear masses. For the great majority of molecules there are no problems in resolving the isotope structure, as the absorption lines can be made narrower than 1 hlc. if necessary. This high resolving power practically eliminates the possibility of confusion with any lines arising from impurities. The principal difficulties in the analysis arise from the relatively large separations of the lines due to different isotopes. Because the microwave components used-oscillator, tuning stubs, wave guide, etc.-are frequency-sensitive, a very careful calibration of apparatus is necessary for accurate results. A high percentage of impurities in a sample does not affect a microwave isotopic analysis, save for a small decrease in sensitivity. With microwave spectrographic technique, isotopic analyses are in general simpler to perform than chemical element or compound analyses. To observe rotational spectra a t microwave frequencies, the compound must be in the gas phase and must have a permanent dipole moment. For use in analysis it is necessary that the absorption be strong, that the gas be nonreactive in contact with the cell, and that the lines lie in a convenient region of the microwave spectrum. Fulfilling these conditions, there are many molecules available for the analysis of the more common stable isotopes: oxygen, hydrogen, nitrogen, carbon, etc. Actual choice of the compound to be used is dependent on the availability or ease of preparation and the accuracy required in the analysis. MICROWAVE SPECTROGRAPH
A schematic diagram of the spectrograph is shown in Figure 1. The source of microwave radiation is a 2K-33 klystron, operated by a well regulated high voltage power supply of convclntional design ( I S , 14). The tube, manufactured commercially, was chosen to oscillate in the region 22,000 to 25,000 Me., to include both the ammonia and cyanogen chloride absorption lines. The microwave energy from the klystron, after passing
is less than 2’30 of the concentration. For each element, samples of know-n enrichment must be examined to determine a standard curve. A complete analysis requires 0.00015 mole of gas, the major portion of which may be recovered. The microwave spectrograph can be used for analysis of isotopes of many of the lighter elements with an accuracy comparable to that for nitrogen and carbon. Accuracy, sample requirements, and characteristics indicate application to both routine and special analyses.
through a calibrated attenuator and a directional coupler wave meter, traverses the Stark cell. This cell is a 10-foot section of a 1 X 2 inch silver-plated brass wave guide. The Btark cell is joined to the smaller K-band guide by tapers with mica windows to define the vacuum system. The Stark electrode is placed in the center of the cell parallel to the wide dimension and s u p ported on Teflon strips. A 1N26 crystal detector receives and rectifies the microwave energy which passes through the cell. This energy is diminished a t the absorption frequencies of the molecules; also, the absorption frequencies are displaced every half cycle by the 4-kc. square wave (one side grounded to the cell) which is applied to the center electrode. Thus the crystal output contains a 4-kc. note which is amplified by a lock-in amplifier of conventional design with a band pass of a few cycles (fd). A Helmholtz coil phase shifter is used to provide a reference signal of suitable phase to the lock-in amplifier. The output of the amplifier is then displayed on a Brown Electronik strip chart recorder.. Owing to the phase-sensitive nature of the lock-in amplifier, the undisplaced line and the Stark components give deflections in opposite senses. For convenience in test and tune-up procedures, a 60-cycle sawtooth sweep applied to the reflector electrode of the klystron varies the frequency and provides a display of the klystron mode when the output of the crystal detector is connected to the vertical plates of an oscilloscope. The 60-cycle sweep is not used in the actual operation of the spectrograph; instead, the klystron is tuned mechanically by a motor and gear assembly which turns the cavity spacing adjustment screw 1/20 revolution per minute. This corresponds to a frequency scanning speed of approximately 35 Mc. per minute. The Stark cell is provided with heating coils for degassing between samples, which proved to be an important aspect of the ammonia analysis. The large dimensions of the cell used decrease the ratio of surface to volume and hence minimize degassing problems. However, it is believed that satisfactory results can be obtained with guide of smaller cross section. T H E AMMONIA SPECTRUM
The papers of Cleeton and Williams ( d ) , Bleaney and Fenrose (a),and a host of other investigators have clearly established the unique position held by the ammonia molecule in microwave spectroscopy. It was the first molecule found to exhibit a microwave nuclear quadrupole interaction (1, 7 ) and the first to find an engineering application in stabilizing the frequency of an electronic oscillator (6, 16). The reason for ammonia’s unique position lies in the intensity of its absorption, almost 10% in a meter cell for the strongest line. This high intensity is due t o the inversion, or “turning inside out” of the molecule, whose pure rotational spectrum lies in the far infrared. The rotational levels split the inversion spectrum into many lines, clustered in the region 20,000 to 25,000 Mc. Only certain few of these linea possess strong absorption.
V O L U M E 2 3 , NO. 7, J U L Y 1 9 5 1
1001
TUNING
copy by Hughes and Wilson (9). Ammonia possesses a second-order Stark effect given approximately by ( 5 ) : A megacycles = 4.5 [ M K / J ( J
I
mhere E is given in electrostatic units, and is directed parallel t o the high-frequency electric field, so that only transitions corresponding t o A M = 0 are observed. M is the magnetic quantum number ranging from M = 0 to M = J in integral steps, giving rise t o ( J 1) levels corresponding to different values of M . .4typical field of 600 volts per cm. ( 2 electrostatic units) thus splits the 3,3 line into four components displaced from the unperturbed line by 0, 1, 4.5, and 10 Mc. At pressures around 100 microns, this splitting is only partially resolved.
+
I
f
OSCILLOSCOPE RECORDER
Figure 1.
given by Townes (11). Two groups of these lines are given in Table I, columns 1 through 5. The intensities tabulated are the theoretical peak values a t the resonance frequencies and are independent of pressure over a wide range of pressures. In the computation the assumption was made that all lines have equal widths a t a given pressure, the width being caused by collisions among the molecules and the number of collisions being in turn proportional to the pressure. Thus the ratios of peak intensities are the same as the ratios of integrated intensities. Experimentally, Bleaney and Penrose ( 2 )have found that the line widths are proportional to q l C z / J ( J 1). This variation in line width implies an inversely proportional variation in peak intensity which is tahulatrd in the l a p t column of Table I.
+
Table I. Nitrogen Isotope N"
X" N 1'
Selected Isotopic Combinations of Ammonia Line Classification, ( J , R)
2,2 5,4
!:3" 3,2
CALIBRATION AND MEASMREMENTS FOR NITROGEN 15 ANALYSIS
Schematic Diagram of Stark System
A4convenient tabulation of both N14Hgand N16H3lines is
Frequency 22,649.85 22,633.00 22,732.43 22,789.41 22,834.17
Integrated Relative Intensity i n Nl4Ha 320 170 150 720 130
+ 1)I2E2
The Stark cell described requires 3 to 5 uc of ammonia a t 1-atmosphere pressure for an analysis. Thib volume allows the cell to be flushed and measurements to be made on several samples in the wave guide. Each new sample requires several minutes to reach an equilibrium with the walls, during which time the pressure may vary slowly. For an accurate analysis it is essential that the cell be a t equilibrium and the pressure constant. An analysis can be performed in 20 t o 30 minutes, including 10 to 15 measurements of the intensity ratios on the recorder. The present equipment will give results of the accuracy tabulated below with five measurements. -4thorough degassing of the Stark cell between samples is necessary, because of the strong surface adsorption of the ammonia molecule. This can be accomplished by heating the cell a t 200" C. for 1 hour with continuous pumping below 1 micron. The cycle between samples requires approximately 2 hours; thus the total time required for each analysis is about 2.5 hours.
Relative Peak in Nl4Ha 332 190 162 720 170
The close frequency spacing of the W6H3 2,2 and the N14H1 6,4linm was a t first considered to be ideal, as it practically eliminated monitoring problems. In the course of the investigation, however, it proved necessary t o u8e pressures near 100 microns in order to avoid excessive pressure drifts arising from adsorption of the ammonia on the wave guide walls. At this pressure these lines overlapped, so that all data reported here were taken using the N15H83,3 and N14H3 6,s lines. This choice has the advantage of comparing the strongest "SHS line with a relatively weak N"Ha line. Because the integrated (and therefore peak) absorptions are proportional to the isotopic concentrations, a comparison of the X14Haand N16H3absorption lines, together with the theoretical ratios of these lines in normal ammonia, should give an absolute measurement of isotopic concentration. Use of the Stark effect, however, allows the height to be measured from the peak of the main line to the peak of the Stark component. This has the advantage of eliminating the base line, but requires that a calibration curve be employed for the analysis, .I feature of the recording spectrograph is its use of an audiofrequency square wave electric field to modulate the spectrum l i n e frequeocics, a terhnique introduced into microwave spectros-
01 o
I 10
1
PERCENTAGE
Figure 2.
1
20
I
4 0
3 0
l5 0
N15
Standardization Curve for Nitrogen 15 Analysis
In making an analysis, the ratio of the heights of the 3 , 3 N'6H3 and the 6,5 N14H3 lines is measured for each sample. A plot is made of enriched N N%3/normal '6H
E
line heights versus
per cent " 6 , as shown in Figure 2, by using samples of known enrichment. This standard curve can then be used directlv in the analyses of unknown samples. Table I1 shaws the ratios, enriched =/normal N '6H3
mj,
which are obtained with standard percentages of ?;lS. T h e normal gas was examined alternately with the standards in t h e
ANALYTICAL CHEMISTRY
1002 Table 11. Ratios Enriched
70 NIL
y 16 -*
Nl4/
Normal
N Nl' 11
0.00 0.00
1.00 1.86 3.81 4.04 5.31 5.64 7.64 7.59 13.00
2.61 I30
Table 111. 70 N'j 0.38 to 0 . 5 0 to 1.50 to 2 . 5 0 to
0.50 1.50 2.50 4.00
70, N" Deviations fO.02
-0.03 $0.04 -0.09
+0.08 - 0 06 1 0 04
Aberage Deviation Average Deviation rO.O1 70.04 f O . 07 T O . 10
mcwurc~mentsfor the standard CUI'VP. The third colunin s h o w itions of individual samples from the standard curve it?illf. To prepare the standards used in obtaining the above curve, shown in Figure 2, ammonium nitrate enriched in X1j,produced by thr Eastman Kodak Co., was mixed with normal material in thc proper ratios. Analyses of the enriched ammonium nitrate and of the ammonia prepared from it have been made in the Mass Spectrometer Laboratory at, 'IT-12. A further check is given by the fwt that normal ammonia Kith N'jH8 as 0.3801, falls on the straight line of the standard curve. The results from 25 samples of known concentration, consisting of 10 enriched samples and 15 samples of normal material, may be esaniined for average deviation in Table 111. Over a period of time the peak ratios may vary, owing to adjustment of the crystal or of one or more of the ot,her wave guide components. These changes may be made without affecting the accuracy of the analysis, because results are based on the ratio of the line heights for normal material, and any such changes cause the enriched and normal ratios to vary proportionally. The actual absorptions of the 6,5 XI4and the 3,3 ?;Iilines in normal ammonia are in the ratio of 80 to 1. In recording, the height of the 6,5 Nl4 line is reduced by a factor of 10 in the aniplifirr to allow direct comparison of the peak heights. Figure 3 illustratrs typical peaks obtainrd with normal and c~nrichd sanlpll~r.
by interactions of the quadrupole moments of the C135and S14 nuclei into some twenty-two components covering a region of approximately 40 >I (f'?'). C. To simplify measurements it was necessary t o obtain one main line of maximum height for each isotope. This Ras done by using a pressure of 100 microns and a Stark voltage of 750 volts per centimeter, causing the many components to coalesce into one very intense line and two satellite lines of lox intensity. These satellite lines are obscured by the Stark components of the main line. Figure 4 shows tracings of the cyanogen lines obtained with different concentrations of C13. A i sin the previous analysis, the height of the stronger line has heen reduced h j a factor of 10 to allow direct comparison of the heights. The separation of thr isotopic cyanogen chloride lines is 124 Nc., which is ideal for purposes of comparison by the recorder technique. Because both lines correspond to the same transition and thus have identical widths, the peak heights may be assumed proportional to the integrated areas and thus t o the relative concentrations. Measurements are made for this analysis, as for ammonia, from the peak of the main line to the peak of the high frequency Stark component, and again a calihlation c u r w must be prepared. C4LIBRATIOY AND MEASURE,MENTS FOR CARBON 13 ANALYSIS
The Stark cell requires 2 to 3 cc. of cyanogen chloride a t 1 atmosphere for an analqsis, allowing measurements to be made on several samples. In practice, the first sample put in the syskm has given results of the accuracy tabulated in Table V,
Table IV. J = O + l 1+2 2-3
First Three Transitions c i a 0 2 ~ 1 4 M, C . 11879 237.59 35638
ClW13N14. >IC. 11941 23883 35824
SAMPLE PREPkRkTION
Each of the standard samples was prepared in a vacuum by the dry reaction of calcium hydroxide and ammonium nitrate under low heat. The gas \vas dried by contact with calcium oxide and then quantitatively transferred to the wave guide. Samples of nitrogen conipounds must be transformed into ammonia for analysis by the microwave methods described above In the case of ammonium mlts, the sample may be obtained by reaction with calcium hydroside or any convenient hydroside. For other compounds, nitrogen fixation procedures such a9 the formation of ammonia by thr Iijeldahl method ma)- be used. The sample required for an analysis represents approvimately 0.002 g a m of nitrogen or 0.00015 mole of ammonia. T H E SPECTRUM OF CYANOGEN CHLORIDE
The spectrum of cyanogen chloride is that of a linear molecule with moderately strong rotational lines spaced equidistant throughout the microwave spectrum. -4tabulation of the first three transitions is given in Table IV. The J = 1 + 2 transition falls in the same general region as t h e ammonia lines discuMed above and thus was chosen for the carbon isotope analysis. The carbon isotope lines are each split
0 38
Figure 3.
I. 3
25
Recorder Traces for Ammonia 125-micron pressure
V O L U M E 23, NO. 7, J U L Y 1 9 5 1
1003 more readings are taken to averagt. out the small random variations introduced by the electronic system. The values $tion-n in Figure 5 are independent of variations in crystals and wave guide adjustment?. Table V shows the data taken to establish the standard curve and indicates the accuracy obtainable from ten comparisons of the line ratios. In general, the per cent error is less than 2% of the C13 concentration, as indicated in Table V. The C13 in the form KC131 used for standardization was purchased from the Eastman Kodak Co., Rochester, N. Y., and the sample was etandardized by the Y-12 N a s s Spectromet,er Laboratory. SAMPLE PREPARATION
Figure 4.
Recorder Traces for Cyanogen Chloride 100-micron pressure
Proper isotopic ratios of C13 and C'* were prepared from standard K C W solutions and the carbon was completely precipitated in the form of silver cyanide. The sam le was then filtered and transferred to a glass system where chforine gas reacted with silver cyanide to form cyanogen chloride. Ercess chlorine was removed with amalgamated copper turnings. A411 carbon samples were sealed in glass break-seals containing sodium pyrophosphate, which prevents polymerization in the presence of moisture ( I O ) , and stored until use. Immediate use in analysis would eliminate the need for this drying agent. The samples were then attached to a glass vacuum system and admitted t o the wave guide cell as required. In tracer work the carbon is oft'en present as carbon dioxide and must be transformed into cyanogen chloride for analysis. Carbon dioxide can be reduced to potassium cyanide with potassium and ammonia with yields of 90 to 96% (5). DISCUSSION
Figure 5 .
Standardization Curve for Carbon 13 .Analysis
Thv actual analysis may be performed in 50 minutes or le+, comprising ten measurements of the line ratios on the recorder For degassing the sypteni between samples, it hits been found sufficient to pump on the cell for 45 minutes a t a pressure belon 1 micron. Thue the full cyrlr for an analysk runs slightly over 1.5 hours. It ha$ been found sufficient to determine the ratio of the line heights for normal cyanogen chloride once each day for coniparison against samples of unknown concentration. Although the ratios for normal ryanogeii chloride and for the standard enriched samples vary slightly from day to d a ) , the ratio of these values, plotted in Figure 5, remains constant. The plot of ClC'35 enrivhed cIc12?J c1C'3x/ -____ normal clclzxline heights vi'rsus per c m t ~
carbon 13 is essentially a straight line in the 1 to 5% C13 range. A b w e 5% there is a gradual curve, due to slight nonlinearities in the characterietics of the syetem. Results are reliablr when ten or
The reEults shown for the abovo analyses are those to be expected under the usual laboratory conditions. They represent intermittent, operation, changing of crystals and small variations in wave guide geometrl-, and operation in the same area as other the source of intcnrmitelectronic equipment Tvhich provc~lt o tent noise. The molecule cyanogen chloride m:iy I K employed for the analysis of thr chlorine and nitrogen isotopes, in addition to cartmn, u.*ing thr sanw procrdure and obtaining about the same accu~~;icy as for Cia. By p r o l ) ( ~rhoice of molecule the smie samples may, in fact. Iw uscd for the :iiialyt& of two or more c>lenients. Carbonyl sulfidr nnd sulfur dioxide may tmtli be ~xaniincdfor the analyses of the sulfur a i d the oxygen isotopes, I\ hile N eoniparipon of the HDO line i L t 22,307 Mc. with t,ht. water line at 22,235 N c . allow F a determination of hydrogen-deuterium mixtures. These are a fev suggerted molesules, and do not twgin to exhaust the compounds T\ hich might be used for isotope analysis. A l i d of microwave molecules and their absorption frc.quencies has bwn published by Kisliuk :ind Townes ( 1 I ).
Table 1.. standards,
'> CLJ 1 11 2 00 3 00 4 00
Standardization Curve Data ~
~
~
5 00 i 00
1.00 1.92 2.71 3.69 4 50 6.55
00 I O 00
9.63
s
~
7.4:
~
h
~
0.00
+o.
10
-0.04 4-0.04
-0.07 +0.06 -0.06
0.00
ACKNOWLEDGMENT
Tht) authors express their appreciation to L. 0. Gilpatrick of the Isotope Chemistry Section for his careful work in the chemical preparation of the cyanogen chloride standards used in this inveetigation, and to R. F. Hibbs for the mass spectrometer analj-sw. Also. thanks are extended to M. W. P. Stmndbwg of
d
ANALYTICAL CHEMISTRY
1004 the Massachusetts Institute of Technologj , \rho kindl? -upplied the circuit for the square wave modulator, and t o I,. G. Larikford and G. W. Cartel for the excellent machine work i n th(3 con+tructionof the Stark cell used in this investigation LII EK i n H E CITED
Bailey, B. P., Kyhl, It. L.. Strandberg, M. W. P., \.an Vleck, J. H., and Wilson, E B., Jr., Phys. Rev., 70,984 (1946). 12) Rleaney, B., and Penrose, R. P., Proc. Phys. SOC.,59,418 (1947), 60, 83, 540 (1948); -\-u~uFP. 157,339 (1946); Proc. Roy. Soc., A189,358 (1947). ( 3 ) Calvin, Heidelberger, Reid, Tolbert, and Yankwich, “Isotopic Carbon,” New York, John Wiley & Sons, 1949. (4) Cleeton, C. E., and Williams, K.H., Phys. Rev., 45,234 (1934). (5) Coles, D. K., and Good, W. E., Ibid., 70,979 (1946). (6) Garcia de Quevedo J. L., and Smith, W. V., J . A p p l i e d Phus., (I
1
19, 831 (1948). (7) Good, W. E.,Phys. RPV., 70,213 (1946). ( 8 ) Gnrdy. W., Rei, M o d i r n Ph!is 20,A68 (1948)
Hughes, K . H . . and N.ilsoii, E:. H., ,Jr., Phgs. R e i . . 71, 562 (1947). Kharasch, Stiles. Sensen, arid Lewis, Ind. ETIY.Chem., 41,2840 (1949). Kisliuk, P.. aiid Townes, (‘. H.. . I . Research S a t l . Bur. Stcindnrds, 44,611 (1950). IIichels, W.C., and Bedding, E:. I)., Reo. Sci. Ircstrun~mts.20, 566 (1949).
Montgomery, “Techniques of Microwave Measurements,” Vol. 11, SIIT Radiation Lahoratory Series, Xew Tork, McCraw-Hill Book C‘ runrc,!ifs, 21,120 (1950). Smith, TI-. V., (;ai& cle Qurwdo. .J. I,.. Carter, R. I,.. and Bennett, W. S.,J . A p p l i e d Ph,p.. 18, I112 (1947). Townes, C. H., Holden, A . S . , arid Merritt. F. K.. P h y s . Rcu., 71,64 (1947). I hid., 74, 1113 (1949). UECEIYED April 10, 1Q50. Based o n work perfornied under contract for the .iromic Energy Commission b y the Isotope Research and Production Division, Oak Ridge National Laboratory, Y-12 Area, Carbide a n d Carbon Chemicals Division. Iinion Carhide and Carbon Corp.. Oak Ridge. Tenn.
Detection of Trace Quantities of Radioactive Materials in Waste. Streams PAUL K. FIELDS W D GRAY L. PYLE -4rgonne Yational Laborutory, Chicago, Ill. Some general considerations in determining microquantities of radioactive isotopes are presented. In order to concentrate on the radiochemical problems, the general analytical chemistry has been limited to uranium, as an example of an alpha emitter, and to 1131, as an example of a beta emitter. A fluorophotometric method and a radiochemical method of determining uranium are discussed. Some of the problems encountered in analyzing and identifying betaemitting isotopes are illustrated by a procedure for isolating Ii31from a waste solution. Certain corrections must be applied to the recorded beta count to obtain the absolute disintegration rate.
T
HIS paper is intentfed to serve as a brief introductioii to radiochemistry for waste disposal scientists who have had little or no experience in the field of radioactivity. In order to wnplify the coverage of such a broad and complicated subject, the general analytical chemistry is limited here to only two rlem ~ i i t s IJranium is taken as an example of an alpha emitter xiid 1‘3’ an example of a beta emittrr. IC
PERMISSIBLE LEVELS OF RADIOACTIVITY
. i t a recent Riastme Disposal Symposium (11) lO-’microcurie per milliliter of alpha and beta activity mas proposed as the probablt. niasinium permissible c.oncentrat,ion of general radioactive contaniinant,s in a water supply outside a controlled area. This, with other considerations diwuwtd below, must be kept in mind when < h i d i n g on the volumrs ( 1 1 \\ aste solutions to he taken for an;rly-
lost in qaniple‘~of VWIOUS suifiic~derislties can he seen in Tahle I (6). In beta counting a larger aliquot must be taken than in alpha counting, because the natural background of a beta counter is about 25 counts per minute whereas that of the alpha counters is practically zero. Therefore, 1 liter of the solution may be evaporated to dryness under alkaline conditions. The solid residue, when spread over an area of approximately 6 sq. cm., would be about 50 mg. per sq. cm. This sample could be counted with an end-window Geiger counter, the windows of which are generally about 8 sq. cm. in area. Only the very soft betas would be missed by this method; these would require special techniques. Examples of isotopes emitting soft betas-Le., beta rays with very low energies-are Ci4 and 8%
*is.
The following prwcdure would probably be satisfactory for crlet,ecting the presenw of this level of activity. For ail alpha assay, about 25 ml. could be evaporabed to dryness in a flat metal .dish about, 10 sq. cm. in area. Assuming lo-’ microcurie prr milliliter, the sample would contain 2.5 counts per minute, lwel of alpha activity that can easily be determined iii a11 ordiI I : I I . ~ alpha counter. Unless there was more than the usual amount of nonvolatile material in the water, this aliquot aould give :I dry residue of a little less than 1 mg. per sq. cm. .Ilt,hough this is a little thick for alpha counting, the amount of alpha activity could he determined with fair accuracy, provided t,he inat
