Measurement of Specific Disintegration Rates by Internal Gas Counting Radiocarbon MAXWELL LEIGH EIDINOFF Queens College, Flushing, N . Y . , and Sloan-Kettering Institute for Cancer Rooearch, Y e w York,N . Y. Although the commonly used technique of counting solid samples containing radiocarbon furnishes useful relative activities, i t is not satisfactory for absolute disintegration rate measurements unless special precautions are taken. The method used in this study eliminates the important difficulties of the solid-counting procedures. The use of a glass shield, the position of which can be varied along the central anode wire, eliminates counting corrections a t the counter ends. The specific disintegration rate can be determined by plotting observed counting rate as a function of the position of the movable shield and by taking into account the cross-sectional area and the pressure and temperature of the gas. The efficiency in the Geiger-MGller region of the counting gas mixture containing carbon dioxide admixed with carbon disulfide was studied. The counting rate for unit
A
LTHOUGH the measurement of the relative activity of solid samples containing weak beta-particle emitters ie usually made using a thin-window bell-type counter, the measurement of specific disintegration rates (disintegrations per minute pes gram) by this method involves a number of experimental difficulties. These include the change of apparent sensitive volume with beta-particle energy (8), precise determination of the geometry, and, of particular concern, the nature of the aelf-scattering and back-scattering corrections. For this reason, the development of internal gas counting methods is of importance in the case of radioelements that can be conveniently handled in the form of gaseous compounds. Theoretical considerations indicate that a favorable gas mixture should possess, in the sensitive volume, a counting efficiency for weak beta-particles that is close to 100%. The number of atoms of the element per unit volume, in the effectiveregion of the counter, is calculated from the pressure and temperature of the filling gas. Counter-tube fillings consisting of radiocarbon dioxide admixed with carbon disulfide vapor are satisfactory for precise measurements of relative activities (1, 4, 6, 16). The utilization of this procedure and counter-tube filling as a primary method for the measurement of specific disintegration rates of samples containing carbon 14 involves two additional considerations. The first is concerned with the decrease in counting efficiency in the end portions of the counter tube. Engelkemeir and Libby investigated end effects in counter tubes made from brass cylinders with flat Lucite ends filled with an argon-alcohol vapor mixture (6, 7 ) . Hawkings, Hunter, Mann, and Parkinson (12, 14) evaluated end corrections in carbon dioxide-carbon disulfide mixtures using a pair of counters having the eame cross-sectional area. The counter described below makes it possible to eliminate end corrections by utilizing only one cylindrical cathode and a movable glass shield. The second consideration of importance in the measurenient of specific disintegration rates is the demonstration that the counting efficiency of the carbon dioxide-carbon disulfide filling for the beta-particles from carbon 14 is close to 100% throughout
quantity of a radioactive sample in the middle portion of the counter was shown to be independent of the cross-sectional area in the range 2.0 to 6.6 sq. em. An external source furnished equal counting rates for argon-alcohol and carbon dioxidecarbon disulfide gas mixtures. The counting rate for a given pressure of radiocarbon dioxide is the same in the higher gain portion of the proportional region and in the Geiger-Miiller region. These results lead to the conclusion that the efficiency of the carbon dioxidecarbon disulfide mixture for beta particles from carbon 14 is close to 100% and that the effective counting cross-sectional area is equal to the area defined by the cathode cylinder. These experiments support the use of internal gas counting as a satisfactory method for the measurement of specific disintegration rates of radiocarbon samples.
the entire volume in the effective length of the tube. According to commonly accepted mechanisms of counter action in the Geiger-Muller region, the formation of one electron in the effective volume by the passage of an ionizing particle leads, by an avalanche process, to a recorded pulse (IS). This affords a basis for the estimat,ion of the efficiency of a counting mixture by calculating the probability, P , of production of an ion pair.
p = 1 -
e-zPi
(1)
where 1 is the path length in centimeters, p is the pressure of gas in atmospheres, and i, the specific ionization, is the number of ions produced per centimeter length per atmosphere pressure ( 2 ) . Using i = 300 for the carbon 14 beta-particle of average energy (d), the path lengths required to yield a P equal to 0.99 are 0.12, 0.06, and 0.03 cm. at a carbon dioxide pressure of 10, 20, arid 40 cm. .4t the latt,er pressure and in a counter tube of 1-cm. radius, less than 2YGof the path lengths arc smaller than that rvquircd for P = 0.99. These general considcratioris would i~idicate that the counting efficiency, f, in Equation 2 can be Inittie close to unity. A particular gas mixture would not, however, be suitablr for specific disintegration rate iiieasurements if there occurrcd a significant decrease in efficiency as a result of negative-ion formation by electron attachment, or an apparent increase in efficiency from spurious pulses arising as the positive-ion sheath is collected a t the cathode. A search was made for effects of this kind in carbon dioxide-carbon d i d f i d e mixtures by evaluating the effect of varying cross-sectiorial area, by comparison with a gas filling, the efficiency of which had been measured, and by comparison with counting in the proportional region. The elimination of end corrections was achieved by incorporuting inside the Geiger-Muller counter tube shown in Figure 1 a movable glass shield, C, surrounding the central wire anode, IA 180 volts; slope 0.5 to 1% per 100 volts. ApJ proximately 30,000 counts were taken for each of Figitre 1. Counter Tube for Measurement of Specific Disintegration Rates the experimental points in Figure 2. The probable .4. Cold finger for condensation of carG. Millimeter s c d e error in the counting rate that results from stabon dioxide H. Precision-ground stopcock tistical variation is less than 0.4%. The numbers B. Fixed glass shields J. Cathode lead wire C. .Movable glass shield along the abscissa are relative to the fixed scale Tungsten Standard taper anode joint, wire oil (4 mil) -PPI L. K. --. D,E. Silver cathode surface covered with thin laver of colloidal graphite .M. Anode lead wire mounted on the tube. The actual distance beF. Glass point iridicator tween the fixed and movable glass shields varies from approximately 65 to 138 mm. The background The counting in t,he proportional region was carried out using counts for these distances are 14 and 30 counts per minute, rean amplifier plus scale of 128 scalar (Model 162, Nuclear Instruapectively, when inside a 1-inch lead housing. .4t a distance of ment and Chemical Co., Chicago, Ill,), and an electronically 135 mm., the end of the movable shield is still more than 2 cm. stabilized voltage supply extending up to 5000 volts (Model 1090, inside the silvered surface. The counting rate is corrected for Suclear Instrument and Chemical Co.). I n order to increase the stability of the circuit and reduce the incidence of spurious background and resolving time. The straight-line fit of the expulses, the proportional scalar was modified by introducing a oneperimental points shows that each increment of cathode length, stroke multivibrator to replace the amplifier stage preceding obtained by displacing the movable shield across the interval the Higinbotham scaling circuit. plotted in Figure 2, represents an increment of constant counting The discriminator dial was set to permit pulses greater than 1 mv. to be counted. Under these conditions, good shielding of efficiency. Each increment of cathode length is, therefore, in the the lead wires is necessary in order to prevent the pickup of “effective middle” of the counter tube. Slopes were obtained in spurious pulses. The counter tube was completely surrounded a similar manner for the measurements reported in Tables by a brass cylinder with hinged door ends directly attached to the scaling circuit ground, eliminating cable leads. The anode lead I and 11. wire, the insulator, and the portion of the counter tube containEstimate of Effective Length. The slope, S, needed for the ing the leads were dried in a warm air stream for several minutes measurement of specific disintegration rates using Equation 2 prior t o counting. Three counter tubes having cross-sectional areas of 2.006, 3.782, and 6.562 sq. em. were constructed with does not require a measurement of the actual distances between movable shields. The glass tubing was selected on the basis the k e d and movable shields. These distances were measured, of agreement in inside diameter of the ends and checked for however, with an error of less than 1 mm., and were used in uniformity of cross-sectional area by measuring the rise in the
L T p : V5 -_-~
ANALYTICAL CHEMISTRY
634 Table I. Extrapolation of Counting Rates Using Counters with Movable Shields (Maximum effective cathode length, 150 mm.) Inside Diam. of Counter Intercept of Extrapolated Tube, Cm. Line on Abscissa. 311n. l.5YE - 4 , -3, -2" 2.185 - 2 , - 3 , -2" 2,890
-1
Counting in proportional region: filling inixtiire: 3 CIl4: discriminator setting: 1 m y . "
CO2 p l u s 62 e m .
tin.
Figure 3 (solid line). Extrapolation of the solid line to zero counting rate furnished an intercept along the X axis of - 4 * 1 mm. The extrapolated portion (broken line) has the slope corresponding to the uniformly effective middle portion of the tube. The counting rate for a distance d mm. between the glass Ehield ends may thus be int,erpreted as the counting rate for an idealized tube for which the effective counting length is d 4 mm. The results of three series of measurements for tubes 1 and 2 and one series for tube 3 are given in Table I. The intercept of the extrapolated line nith thr abscissa is g j v ~ nin the wcond column of this t,able.
+
I500
t c
L
5
/
,/
M E NO. I FlLLlNO NO. 1
500
0
,/
I ,
0
I
I
,++\
EXTRAPOLlTED
I
/
I
so
I
l
I
l
I
100
I
I I50
DISTANCE BETWEEN FIXED AND MOVABLE GLASS SHIELD (millimeters)
Figure 3. Counting Rate as Function of Distance between Fixed and Movable Glass Shield
This t.able shows that the idealized effective lengths of these counter tubes are within several per cent of the actual distance between the glass shield ends when working a t a cathode length of about, 15 cm. Consequently, when approximate estimates of specific disintegration rates are needed ( * 5 % , ) , it is possible to use the simpler fixed-shield counter tube described in (4). The contributions to the effective vdume by perturbing effects a t t.he electrode ends are complex, and act in opposing directions. The degeneration of the electric field intensity a t the ends arts to decrease the counting efficiency in this region. Howevrr, ionization produced by beta-particles originating outside the cylindrical volume defined by the glass shield ends will initiate the discharge pulse and result in a count. This effect thus acts to augment the effective volume a t the cathode ends. The resultant of these effects has been observed experimentally in Figure 3 and Table I. These end effects can be expected to vary a-it'h counter-tube area (6, 7 ) . The experiments reported herein did not extend beyond a counter-tube inside diameter of 2.9 em. Effect of Varying Counter Tube Area. The use of counters for which end corrections can be eliminated (Figure 1) makes it pnpsible to study the effect, of varying the cross-sectional area
of the counter. In a satisfactory count,ing gas mixture for the. measurement of specific disintegration ratrs, a given volunic e k ~ ment should make the samra contribution to the counting ratti, regardless of its radial location. This can he checked dit by comparing the counting rates per centimeter effective length, S , for two counters of different area and filled with r a d i o a d v e carbon dioxide a t the same pressure and temperature. The results of three such measurements are shown in Table 11. Each counter tube in a pair was opened to the active gas sample a t the same time, so that the pressures in each tube would lie exactly equal (column 2). The ratios of the counting rates per unit length, S , are given in column 3, while the ratios of the crosssectional areas are given in column 4. The deviations between columns 4 and 5 are not considered significant. The results in Tahle I1 show that the counting rate per unit quantity of radioactive sample is independent of the' crosssectional area of the counter tube over the range studied. Comparison with Argon-Alcohol Counting Gas Mixture. Greisen and Kereson (11) concluded from coincidence measurements that counters of I-cm. diameter and 20-cm. length and filled with argon and alcohol vapor a t Orcssures of 9.1 and 0.9 cm., respectively, were more than 99% efficient. I n order to obtain a direct comparison of the carbon dioxide-carbon disulfide m d argon-alcohol counting gases, a small external sodium 22 source was securely attached near the middle of a 15.~-niiil. internal-diameter counter tube (.$) having a cathode length of approsimately 17 cm. When an inactive carbon dioxide ~ I L I P carbon disulfide filling vias used at partial pressures of 40 and 2 cm., respectively, the counting rate IWP 828 =t5 counts per minute. \Then this filling was pumped out. and replaced by argon and alcohol a t 9.5 and 1.3 cni., respectively, the counting rate was 824 * 5 counts per minute. The argon-alcohol filling had a counting threshold of 900 volts, and a plateau of 100 volt,s with a slope less than O.iyoper hundred volts. The carbon dioxide-carbon disulfide filling had a threshold of 3500 volts and a plateau of 300 volts with a slope less t,han 0.5% per hundred volts. Comparison of the above countmirigrates for each filling shows that the count.ing efficiency of the carbon dioside-c:irl)on disulfide mixture is, within the error of thew measurpinrtitF, caqual to thxt for the highly efficient argon-:ticoho1 filling.
Tahle 11. Comparison of Counting Rates per Cnit Effectile Cathode Length for Ttthes of Different Cross-Sectional 4 rea Cross Sectional Area, Sq. Cm. 2.006 3.752 2.006
3,752 3,752 6 562
Partial Ratio of Counting Pressure C-';O? Sample a t 20 C., Rates per Cm. Hg Cm. 1.22 1.89 + 0.02 1.22 1.44 1.44 *pprox'
0.6
0 02
1 86
+
1 78
*0
02
Ratio of CrossSectional Area
%
Difference (Column 4 Column 3)
I E70
-- 1 . 1
1 E70
t o 5
1 749
-1
7
Comparison with Proportional Counting. Sweral nieasurcments were made in which counting rates \wre obtained in the proportional region for the gas misturr inside the counter tube. -4gas mixture consisting of :I radioactive carhon dioxide sample and methane at, a pressure of about 5 and ti0 cm., respectively, was satisfactory. When a counter t,ulje with :in inside diameter of 16 mm. and a silvered-cathode length of 15 em. is used with a discriminator (set, to allow pulses larger than 1 mv. to be, amplified) and a counter, the counting threshold is approximately 2600 volts. The threshold region is followed, after a sharplv rising region of about 900 volts, by a counting plateau of abut 600 volts nith a slope of less than 0.3y0per hundred volts. T h r long, flat plateau s h o w that practicdly a11 the pulses were h i i i g counted a t thr start of this level rcgion of the charactcribtic
V O L U M E 23, NO. 4 , A P R I L 1 9 5 1 curve; an increase in positive potential of 600 volts, with a consequent large increase in the gas amplification factor, does not appreciably increase the measured counting rate a t fixed scalar sensitivity. h comparison was made of the observed counting rates for the same quantity of radioactive carbon dioxide inside the counter tube under trvo sets of conditions: (a)admixed with carlion tliwlfide and measured in the Geiger-Miiller region as described herein anti as previously descrihed (41, and (0) admixed with methane and measured in the proportionul region. I n ( a ) the gas mixture contained 3.29 cm. of the radioactive carbon dioside standard, admixed with 37 rm. of inactive carbon dioxide and 2.0-em. pressure of carbon disulfide. The o l ~ s ~ r v tcomting d rate \\-as 3.27 * 0.03 X lo3 counts per minute. 111(6) the gas niiyt:ire contained 3.29 cm. of t'ica r:idiouctive carbon dioxide st,and:ud and 62 em. of methane gas;. The oherved counting rate \vas 3.29 * 0.03 X lo3. This value was obtained by det,ermining characterist,ic curves over a range of discriminator settings and extrapolating t.he counting rate for n fixed voltage on the plateau portion to zero discriminator setting. The magnitude of the ext,rapolation from the measured value a t the 1-mv. setting was 0.6%. This agreement in counting rate is consistent with an equality of the counting efficiency fnct,or, .f, for each method. Further, the long plateau in the proportional region is consistent with the conclusion that almoit all the pulses are being counted. This comparison offers strong evidence for the absence of any significant number of spurious pulses arising from the emission of electrons or photons a t t,he cathode during the collection of the positive-ion sheath in the Geiger-~liillerregion. This effect would be far less probable in the proportional region for which the gas amplification factor is relatively sniall. DISCUSSlON
1Iann and Parkinson ( 1 4 ) and Hawkings, Hunter, and Mann ( 1 2 ) utilized a pair of counters of different length but having the same cross section. The cathode ends were fabricated in as similar a manner as possible in order to be able to eliminate end effects by subtracting the counting rates and dividing by the difference in the cathode lengths. This corresponds to two points on a plot such as Figure 2. The counter with the movable ~ h i e l ddescribed herein is a single tube with one end fixed. T h e straight-line fit of points in a plot such as Figure 2 demonstrates that the increase in cathode length resulting from the displacement of the movable shield has occurred in the uniformlj. efficient middle portion of the counter tube. Hawkings, Hunter, and l l a n n ( 12 ) calculated end corrections by comparing counting rates for the long and short counters in a pair. For counters of 0.7-cm. radius and 15-em. length, the end correction was only 0.2%. However, the correction for large counters having a radius and length of 3.5 and 16 cm., respectively, was about 12%. These results show that for tubes with a radius less t,han 1.5 cm. and at least 15 cm. long, the idealized effective length is within several per cent of the actual distance hetween the glass shields. Engelkemeir, Libby, Hamill, and Inghram ( 6 , Y), showed that end losses in flat end-brass wall count,ers were approximately the same for internal gas fillings and C14, and were related to the lengthcontaining A3', &a5, diameter ratio. I n the counters used in this investigation and hy Hawkings, Hunter, and Llann ( 1 2 ) , the contribution t o the effective length by beta-particles originating outside the cathode length proper acts in a direction opposed to the inhomogeneity of field effect a t the cathode ends. I t is for this reason that a counter tube of suitable dimensions can have an idealized length very close t o the act,ual cathode length ( 1 2 ) . The results of this investigation using carbon dioxide-carbon disulfide fillings and silvered cathodes coated with colloidal carbon are in agreement with those for copper-tube cathodes reported hy Hawkings, Hunter, and Mann ( 1 2 ) , who found no
635
significant change in counts per unit volume at, a definite pressure and temperature for tubes of radii 0.58, 0.70, and 3.50 cin. If the effective counting region were localized in the high intensity field near the anode wire, observed counting rates per unit volume would be dependent on the cross-sectional area. .I striking dependence of efficiency on radial distance f r o m t h r central wire was found by Friedinan and Birks ( 9 , 1 0 1 for :i filling mixt,ure containing argon and methylene bromide '~"ipor, using a collimated beam technique. Carver and iyhite (Y) 01)served a similar effect and ascribed it to the formation. h y VI(+ tron at,tachment,,of negat,ive ions in methylene bromidc. [-sing a similar technique, Hawkings, Hunter, :md 1Iann ( 1 2 )concludcd that t.he counting efficiencies for counter tubes of dianietcsr.- i . 0 and 1.2 cm. are 98 and 97%, respectively. A counting pa: mixture that had a poor efficienc t points removed from the central wire ( 9 , 1 0 ) would be expected to furnish relatively poor counting characteristics and a marked dependence of counting rate on electric field intensity. The author ( 4 ) found that the observed counting rate of a tube 15.5 nun. in diameter filled with carbon dioxide admixed with carbon disulfide was constant over a carbon dioxide pressure range of 20 to 155 cm. (corresponding to an approximately 2.5-fold increase in the electric field intensity) and over a sixfold range of the relative pressures of carbon dioxide and carbon disulfide. The plateau lengths nere in the range 150 to 400 volts with slopes less than 1.3% per 100 volts. These results indicate t,hat the counting rate does not depend, t o any significant extent, on the electric field intensity over this range. The results of these experiments and those reported by Hawki n g ~Hunter, , and l l a n n ( 1 2 ) sho\v that the internal gas counting of a radiocarbon sample-for es:iinple, carbon dioxide admixed with carbon disulfide vapor-iP Iwtisfactory method for t lie nieasurement of specific disintrgrstion rates. ACKNOWLkXG\lE:NT
This investigation mas jointly supported by t,he Office of Sitval Research, Contract SC-ori-99, T.O.1, and the Atomic Energy Commission. A portion of the equipment was purchased as a result of a Frederick Gardner Cottrell grant-in-aid by the llesearch Carp. to Queens College. The author acknowledges his obligation to Edward J. Kuchiriskas and Albert Roberts for assistance in the counting measurements, to Mones Berman for assistance in electronic design and construction, and to Harold Beyer and Kendell C. Peacock for helpful discussions. LITER4TURE CITED
(1) Brown, S. C., and Miller, W.W., Re~c~. Sci. Instrumenla. 18, 496 (1947). (2) Calvin, M . , et al., "Isotopic Carbou," Xew York. John iTileg- 6 Sons, 1949. (3) Carver, J . H., and White, G. K., .Vnture. 163, 526 (1949). (4) Eidinoff. hf. L., -4x.k~.CHEM.,22, 529 (1950). 15) Eidinoff. hl. L.. Science. 108. 535 il948). (6j Engelkemeir, G., Hamili. W.'H., Inghram, >I., and Libby, IT. F., P h y s . Rcc., 75, 1825 (1949). ( 7 ) Engelkemeir, A. G., and Libby, IT. 17.. Rer. Sci. Inutruma~tfr.21 550 (1950). (8) Engelkenieir, D. IT., Rubinsori. JV. K., and Elliot, N.,Atonii(. Energy Commission, Rept. CC-851 (August 1943). (9) Friedman, H., Proc. I.R.E., 37, 791 (1949). (10) Friedman, H.. and Birks, L. S.. Reo. Bci. Instruments, 19, 323 (1948). (11) Greisen, K., and Sereson, K., Piij/s. Reu., 62, 316 (1942). (12) Hawkings, R. C., Hunter. R. F.,and Mann, W.B., Can. J . X I . search, Sect. B, 27, 555 (1949). (13) Korff, S. A., "Electron and Suclear Counters," New York. L). Van Nostrand Co., 194G. (14) Rlann, W.B., and Parkinson. G. R . , Rcc, Sci.1nstrument.s. 20, 417 (1949). (15) hliller, TT. IT., JSciincc, 105, 123 (1947). (16) Reid, A. F.. TTeil. .-i. S., and Dunning, ,J. R., A N A L .C H E M . .19, 824 (1947).
d.
R E C E I V E JDu l y 2 6 , 1950
