V O L U M E 2 7 , N O . 6, J U N E 1 9 5 5 fusion and leach need not be reworked, as the amount of fluorine retained is negligible for all practical purposes. The slightly greater amount of fluorine retained when phosphate rock was used as the addit'ion material is to be expected because of the presence of calcium and phosphate ions in the rock. Standard samples of phosphate rock, fluorspar, and opal glass were used in testing the procedure on milligram amounts of fluorine. Both the phosphate rock and fluorspar were directly distilled from the perchloric-phosphoric acid medium without preliminary treatment. A 0.25-gram sample m s taken for the phosphat,e-rock test, and 25 nig. n-ere used for the fluorspar. The fusion procedure cannot lie used on phosphate concentrates because of the retention of much fluorine by the residue obtained after leaching the melt. .I 0.5-gram sample for the opal glass was fused, leached n i t h water, and half of filtrate was taken for distillation. For all s:imples, the fluorine was determined by t,itration. The results obtained are compared to the Sational Bureau of Standards certificate values in Table IV and show good agreement. The retention of fluorine in the residue after leaching is again negligible for the opal glass. The direct ilistillntion procedure was applied also to samples
921 from the aluminum phosphate (leached) zone of the Florida phosphate deposits, and again excellent results were obtained. LITERATURE CITED
(1) Brunishola, G., and llichod, J., Helv. Chim. Acta, 37,874 (1954). (2) Dahle, D., and Wichmann, H. J., J . Assoc. Ofic. Agr. Chemists, 19,320 (1936). ( 3 ) Ibid.. 20. 297 (1937). (4j Hoffman', J . I:, and Lundell, G. E. F., J . Research S a t l . Bur. Standards, 3, 581 (1929).
( 5 ) Horton, A. D., Thomason, P. F., and lliller, F. J., ANAL. CHESS., 24, 548-51 (1952). (6) Reynolds, D. S., J . Assoc. Ofic.A g r . Chemists, 18, 108 (1935). (7) Reynolds, D. S., and Hill, W,L., IXD.ENG.CHEM., ~ A L ED., . 11, 21 (1939). (8) (9) (10) (11)
Schlecht, W.G., ASAL. CHEY.,23, 1568 (1951). Shell, H. R., and Craig, R. L., Ibid., 26, 996 (1954). Talvitie, N. A., IND.E m . CHEM.,Ax.4~.ED.,15, 620 (1913). Willard, H. H., and Winter, 0. B., Ibid.. 5 , 7 (1933).
RECEIVEDfor review December 9, 1954. Accepted February 14, 10%. Work completed a s part of a program conducted b y the U.S. Geological Survey on behalf of the Division of Raw Materials of the Atomic Energy Commission, Publication authorized b y the Director, C. 9. Geological Survey.
Absolute Assay of Beta Radioactivity in Thick Solids Application to Naturally Radioactive Potassium ANDREW D. SUTTLE, JR.',
and W. F. LIBBY2
Department o f Chemistry and Institute for Nuclear Studies, University o f Chicago, Chicago, 111.
The method of absolute measurement of beta radioactivity in solids has been found reliable within about 5%. The simplicity of this method and the scarcity of other practical absolute assay techniques led to this study. A wide variety of simple beta emitters display exponential absorption curves when the sample, absorber, and counter are placed close in cylindrical geometry. The absorption coefficient for the material constituting the sample can be used to calculate the absolute specific radioactivity of the solid sample. The absorption coefficients for a given absorbing material vary smoothly with the energy of the beta radioactivity transition, so that reliable values of the energies of such radioactivities can be obtained from the absorption coefficients. The coefficients vary with the atomic weight of the absorber. This effect is only partially elucidated.
T
HE possibility of calculating the absolute quantities of radio-
activity from relatively simple measurements on solids has always been interesting. A prescription has been outlined (3, 7 , 8, 11). The possibility of converting the count rate obtained from the radiations from a solid sample to an absolute measure of the specific radioactivity of the sample seems t o exist in a general way. This is true, however, only in so far as the absorption of beta radiation is accurately exponential under the conditions of measurement. These conditions are that the source, absorber, and detector be in relatively intimate contact, as, for example, in the arrangement in which the absorber is wrapped directly around the wall of the Geiger counter and the source is placed directly over it (8). It is apparent that the contact can allow some appreciable distance between the Geiger counter and the source and 1 Present address, Research a n d Development Division, Humble O il and Refining Co., Baytown, Tex. 2 Present address, U. S. Atomic Energy Commission, Washington, D . C.
the absorber, providing that the cylindrical geometry is maintained. This is revealed by data given in this paper, in 11hich in the one instance the abeorptiori curve is measured with the sample as the wall of the counter, and in the other instance as a cylindrical sample surrounding a counter n i t h about 1 cm. between the sample and the n-all of the Cciger counter. I n both instances the absorption curves are exponential. The absorber must lie close to the counter because the chance of recording the beta rays scattered in the absoiber dependq strongly on this juxtaposition (5). Under the condition that the absorption curve is accurately exponential, one can write that the fraction of the radiation coming from a n infinitesimal thickness, dx,of material a t a depth, 1 -2 2, from the surface of the sample, \vi11 be e - h where G is the ratio of 3.ir to the solid angle subtended by the sensitive counter volume a t the position of the tiny element of the sample being considered, and X is the reciprocal of the mass absorption coefficient for the beta radiation. It is of course equal t o the 1 half thickness times -. Therefore an expression can be n ritten ln2 for the total radioactivity, total count rate, expected from a sample for which it is assumed that G is not dependent seriously on the depth of the sample being considered and has been averaged over its area.
R (c.p.m.)
=
AuX/G
(1)
where A is the area of the sample in square centimeters, u is the absolute specific radioactivity of the sample in disintegrations per minute per gram of sample, A is the reciprocal of the a b s o r p tion coefficient of the radiation in units of grams per square centimeter, and G is defined above. This equation holds if the source is thick as compared with A. For finite thickness, it becomes :
ANALYTICAL CHEMISTRY
92 2 ahere x now is the thickness of the source. Equation 1’assumes that the material is supported on a backing of the same atomic number and composition as the sample itself. It is implicit in the exponential absorption law that scattering is an integral and important part of the phenomenon, and the requirement for cylindrical and/or close geometry is one that obviously derives primarily from considerations of scattering. I n fact, Johnston and Willard ( 5 ) have shown in a most dramatic manner the tremendous effects of geometry and scattering on count rates with conventional end-B indow counters. The question which remains t o be discussed most completely iq: How accurately can u be determined by the use of Equation 1 or l’? The answer to this question depends in the first instance on the general validity of these equations, and then on the accuracj n i t h which each of the factors in the equation, R, A , G, and A, can be measured. All involve errors. It seems that under most conditions, the one that is most likely to contribute is R itself, though G and X are by no means negligible sources of error. The methodology of the techniques suggested here will in the hands of careful investigators develop to the point where the relative magnitudes of these different sources of error will become well known, and procedures for handling them become well developed. It is the authors’ experience a t the present time that the over-all error involved in the routine determination of u by the present method is between 5 and 10%. The method appears to be applicable in general to beta radioactivities which have a simple decay scheme-that is, a transition betn-een two single levels, and two levels only-even though they may be as highly forbidden as wme of the long-lived natural radioactivities. In all these cases exponential absorption curves are obtained under the conditions of close cylindrical geometry which have been described. It apparently is not very important that the beta radioactivities hltve the same degree of forbiddeiiness in the sense of the theorv of beta decav, since potassium-40, phosphorus-32, and tritium all seem to fit. The restriction that only heta emitters ~ h i c hdecay by a transition between just two levels can be used might a t first sight be thought to be so limiting that the method aould have little general applicability. However, most of the long-lived isotopes of greatest chemical applicabilitv are simple beta emitters. Thev
include tritium (hydrogen-3), radiocarbon (carbon-l4), sodiuni22 ( 3 years), sodium-24 (15 hours), phosphorus-32 (14 days), sulfur-35 (87 days), chlorine36 (2 X 106 years), and many others. It is clear that most of the elements of interest in organic chemistry and biology are included. The method has been in steady use in the laboratories a t Chicago for several years with most gratifying results. EVIDENCE OF EXPONENTIAL CHARACTER OF BETA RAY ABSORPTION FOR SIMPLE BETA R.4Y EMITTERS
The apparat,us used to t,est the applicability of the exponential nbsorption law to beta ray8 in genera! consists of a Geiger counter around which the sample is dispofed cylindrically, either in intimate contact with t h e absorber and t,he counter wall, or with R. distance of about 1 cm. between the inner surface of the sample and the outer surface of the counter wall, and the absorber d i p posed in contact with the sample surface between the samplc and the counter.wal1. These conditions are known and shown on the accompanying curves as “contact” and “distant,” respectively. They were obtained by the use of a screen-wall counter (9, fO), in which the sample is placed on the inner surface of the sample cylinder free to slide inside of an outside containing case. The counter is defined by a gauze or screen cylinder placed along the asis of the cylindrical c o n t h i n g case and in the middle third of its lengt,h. The sample cylinder has a length twice that of the gauze or screen counter and the snniple is disposed on half of this surface in general, though in some of the experiments here a smaller area of sample was used so that the G factor t o be used in Equations 1 and 1’ was somewhat smaller than would be the case if the whole half of the sample rylinder were covered with the sample. Under conditions of “drag-in,” the sample cylinder is maintained a t a negatiw potentip1 with reepect to the w r e n . This is t h e condition labeled “contact” in the figures. As has been shown (9, 10) under these conditions the counter consists of the volume described by the sample itself. Under “drag-out” conditions, the sample is outside the counting volume, and the space between the sample cylinder and the counter wall is inseriritive to radiation, only the volume enclosed by t h e screen itself being sensitive. This is the condition labeled “I cm. distant” on the figures. I n this way absorption curves were run under both drag-in and drag-out conditions with aluminum foils placed over the sxmples. Though the data given here were obtained by the use of the ,screen-wall counter, it is known that similar results are obtained with ordinary counters, both for n.all and end-window placement of the samples and absorbers.
AI DRAG IN DRAG OUT I Cu DRAG IN
0
20c3
0 AI
2000
;RAG 0
IN AI
G R G OUT AI
I CRAG IN C u
100:
-” E
h
60(
-5
IO00
2
800 700
a
50C
Ez=
p
2
600
40C 300
4c
w
0
0
*
80C 701
..
A
DRAG
OUT
Cu
509 400
z 3 0 0
?C0
200 200
100 50
100
150
200
250
300
ABSORBER THICKNESS ( r n g j c r n ? )
IO0
50
100 I50 200 250 ABSORBER THICKNESS (mg/cm.2)
300
Figure 1. Absorption curves of phosphorus-32 as ammonium dihydrogen phosphate in copper and aluminum
Figure 2. iibsorption curves of phosphorus-32 as potassium dihydrogen phosphate in copper and aluminum
Contact (drag-in) and 1 cm. distant (drag-out)
Contact (drapin) and 1 rm. distant (drag-out)
V O L U M E 27, NO. 6, J U N E 1 9 5 5
923
The d a h obtained are displayed 111 Figures 1 through 15. The absorption curves under “contact” and “distant” conditions were drawn to have a common intercept. It is clear from these data that only in the case of rubidium-87 is there any serious evidence of nonlinearity in the plot of the logaiithm of the count rate versus absorption thickness of aluminnni. It is clear from the results in Figures 1 to 7 that there is a difference in the absorption coefficient of aluminum and copper. This effect has been well known for many years and has recently been treated in some detail by Lerch ( 7 ) ,a ho comments that if one considers the mean atomic weight of the absorber as Al?, then the actual absorption coefficient may be written as
(!), x Vf
=
(J)7 x M
= O (1
+$)
Seglwting rubidium-87 for the moment, it can be said that the methodology is apparently applicable to all of these diversified beta emitters from tritium to naturally active potassium, all of M hivh incidentally are known to be simple in the sense of being tr:rnsitions between two single levels and not to involve beta transitions between two or more different levels. Rubidiuni87 ni:by he open to question on this point. 1 EST OF DETERMINATIOIV OF ABSOLUTE SPECIFIC R iDIOACTIVITY WITH GAS-COUNTED RADIOPHOSPHORUS
In order to test the method of determining the specific activity of solids, it was decided to assay rndiophosphorua (phosphorus-32) by gas-counting convert it to solid phosphates, and then to compare a w ~ baqed v on the exponential laiv.
absolute carefully methods, the solid
liters of phosphorus t i ~ h ~ o m i dneel e added to dissolve thc phosphorus and a deficiency of bromine was then added to convert most of the phosphorus to phosphorus tribromide. The solution was refluxed for 10 minutes to give a homogeneous solution. Zinc fluoride was prepared by treating zinc oxide with excess hydrofluoric acid, and evaporating. The phoqphorus trifluoride then was prepared by gently warming phociphorus tribromide Rith excess zinc fluoride. Phosphorus trifluoride, a colorless gas boiling a t - 151’ C., is bubbled through water to remove phosphorus pentafluoride, phosphorus oxyfluoride, and phosphorus tribromide, which may be present, and is then passed 1hrough two sulfuric acid drying towers and finally through a bath of freezing 2-propanol to remove any traces of impurities which may remain. Phoqphorus trifluoride is condensed in liquid nitrogen, and transferred to the vacuum line. It is freed of dissolved gascs by repeated fuqion under vacuum. Vapor density determinations indicated n purity greater than 99%. The radioactive phosphorus ti ifluoride !vas measured in a flatended Geiger counter a t a carefully measured pressure of about 1 mm of mercury in the presence of 15 cm. of argon and 1.5 em. of ethylene. The counters, after thorough miuing, were counted on standard waling circuits to 1% statistical error. The background rates were determined before and after each phosphorus frifluoridc measurement. It was found that no appreciable inciease in background occurred. The end and wall corrections necessary to calculate the absolute activity of the phosphorus trifluoride, as measured in the flat-ended Geiger counters, are giLcn by Engelkemeir, Hamill, Inghram, and Libby ( 1 ) and Engrlkemeir and Libby ( 2 ) . The counters ueed were of four sizes 2 inches in diameter by 18 inches in length which had an end loss correction of 3.54% and a wall loss correction of 3.2%; 2 by 24 inches m-ith corrections of 2.48 and 3.2%; 3 by 18 inches tlith corrections of 5.02 and 2.1%; and 3 by 24 inches with corrections of 3.87 and 2.1%. Using these counters the specific radioactivity of the radiophosphorus, corrected to a standard time for decay, was 3 95 i 0.02 X disintegration per minute per microgram of phosphorus trifluoride. The data on the gas counting of the phosphorus trifluoride sample are contained in Table I. The errors given are the sta-
Technical red phosphorus, Mallinckrodt, was used to prcpai e radioictive phosphorus-32. The solid phosphorus was carefully packed on a milled copper target, covered with a 1-mil aluminum foil, and bombarded with 8,000,000 volt deuterons in the 36-inch cyclotron a t the University of Chicago [supported by AEC Contract No. AT(11-1)-86]. The phosphorus was scraped from the target after the bombardment in an inert atmosphere of carbon dioxide and transferred directly to a 200-cc. round-bottomed flask. It was attached to a reflux condenser. Twentyfive niilli-
6 00
-5
d c3 z I-
300 200
z
I-
3
2
100
F z =
80 60 40 30 20
800 700
4 00
< m
e AI DRAG IN I Cu DRAG IN
E, 1000
s
W
8
2000
c7.
A I DRAG IN 0 AI DRAG O U T I C u DRAG I N A C u DRAG OUT 0
1000 800
3000
600 500 400
0 V
---
300
-\
200
IO0
IO
50
100
150
200
250
300
ABSORBER THICKNESS (mg./cm?)
20 40 60 80 100 140 180 ABSORBER THICKNESS (mg./cm?)
Figure 3. Absorption curves of potassium-40 and potassium dihydrogen phosphate in aluminum and copper
Figure 4. Absorption curves of potassium-40 as KHFz in aluminum and copper
Contact (drag-in) and 1 c m . distant (drag-out)
Contact (drag-in)
ANALYTICAL CHEMISTRY
924
tistical counting errors, except in the case of the grand average in which the deviations of the averages for the individual runs are used. After the gas counter assay the phosphorus trifluoride was converted to sodium dihydrogen phosphate by hydrolysis. Approximately 0.5 gram of gas was introduced into a weighing bulb and accurately weighed. It was then distilled under vacuum onto a 50% solution of sodium hydroxide a t liquid nitrogen temperatures. After t h e phosphorus trifluoride was quantitatively transferred the system was closed off and warmed t o 50' C. to effect a complete hydrolysis. The solution then was quantitatively transferred t o a I-liter round-bottomed flask and trentetl with concentrated nitric acid to oxidize phofiphite t o phoqphtjte. A solution of 85% phosphoric acid was added, and the temperature \vas raised to 160" C. to expel hydrofluoric acid
Table I.
Phosphorus Trifluoride Gas Counting Data
Counter 3 x 3 X 2 X 2 X
2 1 (vol. 2555 18 (vol. 1903 24 (vol. 1088 18 (vol. 807
cc.) cc.)
cc.) cc.)
Net Rate above Background Corrected for E n d and Wall Losses, C.P.1\1. Run I (0 time) 1840 i 17 1309 zt 13 806 i 8 GO1 i 6
Average R u n I1 (15 hours later) 2280 i 20 1650 i 15 921 i 10
3 X 24 3 x 18 2 x 24 2 X 18
728
f
7
ALerage Average corrected t o 0 time R u n 111 (20 hours later) 2570 i 20
x 24 3 X 18 2 x 24 2 x 18 3
1840 =t15
1089 I 10 749 f 7
Average Average corrected t o 0 time Grand average for runs I , 11, and 111
and nitric acid. Sodium hydroxide solution then was added until the total acidity was reduced t o the sodium dihydrogen phosphate equivalent point. The soldtion was evaporated to dryness under vacuum and heated t o 110" C. for 1 hour, and weighed. Two batches of sodium dihydrogen phosphate were prepared and two similar batches of potassium salts were made by using potasfiium hydroxide instead of sodium hydroxide. A determination of equivalent weight indicated the material was approximately 99% pure. I n order to obtain a mass of fine crystals which could be mounted conveniently in the counter, the salts were dissolved in a minimum quantity of water, and absolute alcohol was added. This preripitated the salts as a very fine powder. The sample then was mounted in a well-defined area on the sample cylinder under conditions such t h a t t h e counting geometry factor, G, in Equation 1 would be neal.ly 2 under drag-in conditions. After the sample had been mounted, t h e counter was pumped carefully and filled Tvith a mixture of 1.5 cm. of mercury pressures of eflir 1ene and I 5 em. of argon. The data obtained are given in Table 11.
Specific Activity, D.P.nI./-y P F I 3 . 7 9 zt 0 . 0 4 3 . 6 3 i. 0.04 3.90 0.04 3 . 9 2 i0.02 3 . 8 1 zt 0 . 0 2
*
3 3 3 3 3 4
94 83 75 99 88 00
10-2 10-2 10-2 10-2 10-2
i 0 01 x 10-2 i 0 04 X 10-2
x 10-2 *i00.04 04 x 10-2
i 0 02 X 10-2 i 0 02 X 10-2
z!= 0 04 i 0 04 zt 0 04 5 0 04 z!= 0.02 4.04 zt 0.02 3 . 9 5 i 0.07 3 95 3 80 3 92 3 88 3.88
X X X X X
x
10-2 10-2 10-2 X 10-2 X 10-2 X 10-2 X 10-2
x x
3000 t
2000
AI DRAG IN Cu DRAG IN
40
EO
120
160
200
240
ABSORBER THICKNESS (rng./cm2)
Figure 6. Absorption curves of potassiuni-40 as potassium bromide in aluminum and copper Contact (drag-in)
1000
E,
s w I-
2 o z 2 3
ou
800 700
I
600
400
-
3 00
2: c
200
z!3
500
5
1000 100
0'
500
< a
' 300 0
8
100
40 80 120 160 ABSORBER THICKNESS (mg./cm. 2)
200
200
100 ABSORBER THICKNESS (m&/,/em2)
Figure 5 . lbsorption curves of potassium-40 as potassium chloride in aluminum and copper
Figure 1. Absorption curves of potassium-40 as potassium iodide in aluminum and copper
Contact (drag-in)
Contact (drag-in)
V O L U M E 27, N O . 6, J U N E 1 9 5 5
925
aluminum, the absorption coefficient for which was used in the calculations.
Table 11. Test of Method of Determination of Absolute Specific Radioactivity in Solids with Radiophosphorus (PS2) Abs. Specific Count R a t e Activity of Salt Observed from Gas Counting, from Salt, C.P.M./Sq. Cm. D.P.hI./Gram
PF8, Gram
I t is therefore recommended that assays of simple beta emitters be made by use of Equation 1 or Equation 1' as outlined in the previous section, providing G be not much larger than 3.
Calcd. Abs. Specific Activity of Salt ( R G / A = 122 hfg. per Sq. Cm.; G = 2)
Salt Prepared Grains XaHzPO4 316 3 19.6 0.2 322 0.633 80 189.7 2 11.9 0.423 NaHzPOa 89.6 195 10.2 0.'3 158.3 1.6 KHzPOdn 100.3 167 0.400 13.9 0.4 208 2 I C H Z P O ~ ~ 91.1 228 0.478 Potassium backgrounds were obtained by mounting ordinary potassium containing no radioactive phosphorus and determining rate with it-i.e., t o correct for natural potassium-40 count rate.
GENERAL METHODOLOGY AND TESTS FOR ENERGY AND SPECIFIC ACTIVITY DETERMINATIONS FROM SOLIDS
The data given in Figures 1 through The agreement between the absolute assay determined by as accurate a method as exists-namely, gas counting-given in columns 4 and 5 of Table 11, and that by the method discussed in this paper given in columns 6 and 7, is within 10% and is particularly good when the atomic number of the salt is close to
-
___
10000 v8000
DRAG I N BaC03
I
D R A G OUT E a C 0 3
Table 111. Values of Aluminum Absorption Coefficient, Half-Thickness, Range (6) and Ratio of Range to HalfThickness for Yarious Simple Beta Emitters Epmax,
6000 5000
'
Isotope
T
0 DRAG IN Na2C03
\\
4000
3000
0
15 are summarized in Table 111.
A DRAG OUT Na,CO,
2000
-.
6 2. w
+
1000
2
800
0
600 500 400
5
2
"
Halfthickness,
2I.e.v. 0.0189
.\Ig./Sq. Cm.
0.060 0.0785 0.155 0,270 0.296 0.319 0.63 0.762 1 36 1.708
0.38 0.63 1.93
0.050
4.85
6.09 6.30 16.0 20.6 67.0 84.3
Range, Mg./Sq. Cm. 0.70 5.0 8.7 30.0 63.6 76.5 83.5 212.0 283.0 605,O 801.0
Ratio of Range t o Half-Thickness 13.0 14.3 13.8 15.5 13.1 12.0 13 3 13 2 13.7
9.1 9.5
300 200
IO 000
100
80
7000
60
5000
50
2
4
6
8
IO
12
3000
ABSORBER THICKNESS (m$.Al/cm?)
Figure 8. Absorption curves of carbon-I4 as barium and sodium carbonate in aluminum
P.
8
Contact (drag-in) and 1 cm. distant (drag-out)
v
w I
I
2000
E
t CT
1000 700
r3
500
%
300
z
3
200 100
70
0
z
F
30
50
3 Z
u 0
30
20
20 IO
IO
0.2
0.4
0.6
0.8
1.0
1.2
1.4
ABSORBER THICKNESS (rng.A/crn2)
0.2 0.4 0.6 0.8 ABSORBER THICKNESS (mg.A / c ~ ? J
Figure 9. Gas absorption curve of zirconium-97 as ZrOn and Fez03 in argon and helium
Figure 10. Gas absorption curve of tritium-3 as an acroflavin dye in argon and helium
1 c m . distant (drag-out)
1 om. distant (drag-out)
ANALYTICAL CHEMISTRY
926 The results summarized in Table 111 show that there is a relationship between the range (or the energy) and the half-thickness of the beta radiation under the close geometry conditions where exponential absorption obtains. Therefore the absorption coefficient or its reciprocal, A, can be used to obtain a measure for the energy of the beta rays of simple beta emitters. If the data in column 5 of Table 111are plotted against energy, a curve is obtained which can be used to predict the ratio between range and half-thickness for any given energy or range or halfthickness. If the absolute specific activity of a solid containing a radioactive material such as carbon-14, of known energy, is desired, the literature is consulted to find that carbon14 has the 155-kv. energy and it is noted that a single transition is involved. Then it is observed that according to the data in Table 111, the ratio of range to half-thickness will be about 14. Using the Katz and Penfold range-energy relation (6) it is observed that its range should be 30 mg. per sq. cm. of aluminum. Dividing by 14 the predictions of the half-thickness and the reciprocal of the absorption coefficient, A, are made. These are used in Equation 1 to calculate the absolute specific activity, u, from the observed count rate, R, under the geometry conditions, G , for an area of sample, A . Therefore it is possible, by the use
< W
400
3 W I-
a
z
Iz 2 V 0
2000
c
,
e IO00
A-
8 00 DRAG IN
\e
600
300
w
c
ZOO
OUT
I DRAG
500
v
t I
DRAG IN I DRAG
-
OUT
-
300 200
Using the methods outlined, measurements were made on five Dotassium salts. and the data obtained are shown in Table IV .
0'
I
T
APPLICATION TO NATURALLY R4DIOACTIVE POTASS1U.M
B
e
800 700 600 500
observed count rate, calculate the specific activity, u. If an unknown beta radioactivity is being investigated its aluminum absorption coefficient under close geometry condition (G 2 or a little larger) is observed and the half-thickness as taken from the absorption curve can be compared Kith the data in column 5 of Table 111, and column 3 of Table 111, to predict the range and so from the Katz-Penfold range-energy relation (6) obtain the energy.
400
2000 -1
1000
of standard references, t o predict the count rate that will be observed for a given specific activity, u j or vice versa, from the
2o
-
t 2
4
6
8
12
IO
16
14
18
20
22
24
26
ABSORBER THICKNESS (mg.Al/cm?)
Figure 12. Absorption curves of rubidium-87 as rubidium in aluminum
100
2
6
4
8
ABSORBER THICKNESS (mg.Al/cm.
Contact (drag-in) and 1 cm. distant (drag-out)
12
IO
2
)
Figure 11. Absorption curves of rubidium-87 as rubidium chloride in aluminum
e io00
Contact (drag-in) and 1 cm. distant (drag-out)
Table IV. Potassium-40 Beta Disintegration Hate from Absorption Measurements and Equation 1 Salt KHzPOI KHFr KC1 KBr KI
Count Rate, C.P.S./Sq. Cni. 0.42 i0.06 0 75 * o . 1 0 0.678 0.10 0 . 4 7 8 3= 0.006
+
0 . 3 2 6 i. 0 . 0 5
Half-Thickness of Aluminum. Mg./Sq. Cm. 68 1.2
* *
66 1.2 66 =t 1 . 2 A7 1.2 68 Z t 1 . 2
Specific Activity, D.P.S./Grani of K 29.5 i 1 . 8 3 1 . 1 i- 1..5 2 6 . 8 =t 1 . 5 2 9 . 8 I1.6 2 7 . 8 i- 1.:
Table V. Potassium-40 Beta Disintegration Hate from Phosphorus-32 Standardization by Gas Counting Salt KHIPOI
Observed Count Rate Drag-in Drag-out conditions conditions 27.26 i 0 2 18 89 i- 0 . 2
2
_ _
6
8
IO
12
14
Figure 13. Absorption curves of rubidium-87 as rubidium
3 0 7 fl ' 285 i l Average 29 6 f 0 7
____
4
ABSORBER THICKNESS (mg.Al/cm?)
Calcd. Absolute Specific Activity of K'0 Using G Calcd. from Pa2 Standardization
carbonate in aluminum ~
-
Contact (drag-in) and 1 cm. distant (drag-out)
V O L U M E 27, N O . 6, JUNE 1955 I
Table VI. Population of Gamma Radiation and Disintegration Rate of Potassium-40
1000 a 800
E DRAG
40
Observed Rate, C.P.M. NazC03 119.5 f 0 . 7 KzCOa (316 9.) 230.0 3z 0 . 6 3318 f 6 NazCOa (wet) (465,000 d.p.m. of C060) Observed gamma efficiency, % 0.322 f 0 , 0 0 3 Calcd. gamma emission rate from ordinary potamium 2 96 & 0.04 per second per g . K Substance Counted
IN
I@ D R A G IN A I
5u‘
u
IO 5
IO
15
20
25
30
ABSORBER THICKNESS (mg.Al/crn2)
Figure 14. Absorption curve of rubidium-8i as rubidium perchlorate in aluminum
2 0
g + z 3
8
600 500
400 300
Contact (drag-in)
200
These results are very close to the generally accepted specific radioactivity of potassium, 30 d.p.s. per gram. I n Table V, the specific radioactivity is calculated more accurately by using the phosphorus-32 calibration by the method of gas counting phosphorus trifluoride-i.e., the phosphorus-32 is used t o obtain a more accurate value of G to be used in Equation 1 and this G is used on the potaspiurn. The data shown are given in Tables I and 11. The disintegration scheme for potassium-40 consists of a branching in which most of the disintegrations occur by means of a simple bet,a ray going to calcium-40, but a few per cent occur by orbital capture to a n excited state of argon-40 which then emits a 1.45-n1.e.v. gamma ray. I n order to determine the total disintegration rate of potassiuni-40-i.e., the half l i f e which is of conyiderable int>erestfor geophysics in the determination of the age of t,he earth and old rocks, an attempt TTas made to measure t,he absolute rate of emission of gamma rays. A thick sample of potassium salt was placed around a n ordinary cylindrical Geiger counter 2 inches in diameter and 12 inches in length. The ~vallwas sufficiently thick so that none of the beta rays from t,he potassium would penetrate and count. To obtain the background, the sample holder was filled with sodium carbonate. The potassium salt used was potassium carbonate. The difference in rate was taken t o correspond to the potassium40 gamma radiation. The counter efficiency was determined by dissolving the sodium carbonate used in the background determination and adding to i t 0.1 cc. of a solution of standard cobalt60. The cobalt-60 gamma ray disintegration involves two gamma rays in series of 1.17 and 1.33 m.e.v. Then the solution of cobalt-60 and sodium carbonate was evaporated to dryness and the salt heated and dried for 12 hours a t 150°C. Over 99% of the sodium carbonate was recovered and replaced in the holder. The increase in counting rate over the background was ascribed to the gammas from the cobalt-60. A standard source very kindly supplied by Arthur Jaffey of the Argonne National Laboratory was used. It had been assayed by the coincidence counting method ( 4 ) to a n accuracy of about 1%. Inasmuch as the disintegration rate of the cobalt-60 sample was known, the efficiency of the counter with respect to the 1.17 and 1.33 m.e.v. gamma rays which are in cascade may be calculated. I n Table VI, the counting rates are given together with the calculation of
100
5
IO
15
20
25
ABSORBER THICKNESS (rng.Al/cm?l Figure 15. Absorption curve of technetium-99 as rubidium perchlorate (TcO;) in aluminum Contact (drag-in)
the final efficiencies and the final specific gamma emission rate of potassium. This final result shows that 10 beta particles are emitted for every gamma ray, or 10 beta particles for every orbital capture, or 10 calcium40’s for every argon-40. This means that t h e over-all half-life calculated from these determinations is 1.25 It 0.04 X lo9 years (this uses t h e value 0.0119~oas the isotopic abundance of potassium-40). The general agreement with t h e previously published values in the literature is satisfactory. LITERATURE CITED
(1) Engelkemeir, A. G., Hamill, W. H., Inghram, AI. G., and Libby, W. F., Phys. Revs.,75, 1825 (1949). (2) Engelkemeir, A. G., and Libby, W. F., Rev. Sci. Instr., 21, 515
(1950). (3) Final Report, Air Force Contract AF 33(038)-18013, Bupplemental Agreement 2(52-385). Dee. 1. 1952. (4) Fried, S., raffey, A. H., Hall; N. F.; a n d Glendenin, L. E.. Phys. Revs.,81, 741 (1961). (5) Johnston, F., and Willard, J. E., Science, 109, 11 (1949). (6) Katz, L., and Penfold, A. S., Revs.Mod. Phys., 24, 28 (1952). (7) Lerch, P., Helv. Phys. Acta, 26, 663 (1953). (8) Libby, W. F., ASAL. CHEM.,19,2 (1947). (9) Libby, W. F., Phys. Revs., 46, 196 (1934). (10) Libby, W. F., and Lee, D. D., Zbid., 55, 245 (1937). (11) Suttle, A. D., Jr., “Method for the Routine Absolute Intensity and Energy Measurements of Beta Radiation,” thesis s u b mitted to University of Chicago, August 1952. RECEIVED for review June 29, 1954. Accepted December 17,1954. Research supported by the United States Air Force under contract monitored by the Office of Scientific Research, Air Research and Development Command.
