Properties and Measurement of Carbon 14 ALLEN F. REID1, ADELE S. WEIL, AND J. R. DUXNING Columbia University, Pupin Physics Laboratories, New York, N . Y . This paper lists the properties of C" important to measurement and gives a detailed outline and examples of procedures and techniques for effective C14 analysis using a thin-windowed Geiger counter. j3-Ray absorption effects are discussed, as well as the systematic calibrations which must be made when a counter system is used for detection.
I
N 1940, Ruben and Kamen (4) reported the existence of a long-lived, weak @-emitting isotope of carbon, C14, which
with a maximum range of 25 mg. per sq. cm. of cellophane (0.14 m.e.v., 6). A typical set of measurements with aluminum absorbers is plotted in Figure 1. In cellophane the absorption coefficient was 282 sq. cm. per gram.
could be produced by a number of nuclear reactions:
C'3
+
72 --f C'1+ y
(1)
C13+H2+C14+H1
(3)
N14++nC11+H1
:
0 o O
MEASUREMENTS
(2)
' 800
Either an ionization chamber connected with a suitable electrometer system or a G-hl counter can be used for effective measurements of Cll (as demonstrated, for example, by Henriques and Margnetti, 2 ) . In the case of the former, greater difficulties may be experienced in correcting accurately for self-absorption where small samples must be used. Using counters where carbon dioxide gas is introduced directly into the counter tube, difficulty is experienced in obtaining reproducibility. The techniques given here are for the measurement of C14 samples outside a thin micawindowed Geiger counter of the type shown in Figure 2 (window thickness, 2 to 6 mg. per sq. cm). The cylindrical thin glasswalled counter tube commonly used for radioactive phosphorus measurements cannot be used in this case, since the wall thickness is too great for penetration by the low-energy C14@-ray. Thin mica window counters employed were developed by Wu, hleaker, and Glassford under the auspices of the Manhattan District, Contract W7405-Eng-50. Papers covering their design are now in process of publication. Mica windows are permanently sealed by a mica glass bond and have proved rugged and reliable over an indefinite period. They eliminate many of the difficulties associated k i t h thin-windowed counters. Similar counters are now being manufactured by Technical Associates, Inc., 3730 San Fernando Road, Glendale 4, Calif. COUNTER MEASUREMENT STANDARDIZATION
4
8
bleasurements should be taken with the source of radiation a t a standard position relative to the counter and should be corrected for instrument and sample variations before any attempt is made a t interpretation. The corrections to be made appear in this order:
I2
Figure 1. Measured Activity from C14us. Thickness of Aluminum Absorber
1. 2. 3. 4.
I t s value as a tracer was recognized immediately, but because of the low energy of the @-rayand its long half-life (4700 years, 3) its1utility was contingent on the development of a sensitive and quantitative measurement technique.
Resolving time Background Efficiency changes with time Geometry and absorption corrections
PROPERTIES
In 1941, Ruben and Kamen (5) measured the range of the @particle to be 19 * 2 mg. per sq. cm. of aluminum, corresponding to an energy of 0.145 m.e.v. This value is in fair agreement with results obtained in these laboratories using more intense sources of C'4. Aluminum absorption films were introduced between a source and a mica-window counter of known window thickness, and corrections were made, as indicated below, for obliquity of the paths traversed by the particles through the filters. A mean absorption Coefficient of 247 sq. cm. per gram of aluminum over the useful measurement range was determined, 1
somple position
i/
_I
* t m . c 7
I Figure 2. Thin-Windowed Bell G-M Counter
Present address, Sun Oil Co , Marcus Hook, Pa.
824
N O V E M B E R 1947
C-ACTilAL
I1.000
'
825
NUMBER OF COUNTS PER
O
,025
,050
5To
.4fter both are corrected for resolving time and background, the ratio of sample counts to standard counts is a distinct measure of strength for a calibrated system. Uranium or radium sources are frequently used for standards. 4. Geometry and Absorption Corrections. The corrections to be applied for geometry, and absorption characteristics of the 0-ray, depend on the purpose for which the measurements are made, the 0-ray energy distribution, and the sizes of samples to be used. As such they are classified in three sections in the succeeding discussion, and any of these treatments may be used independently of the others.
SECOND
,075 l
.IO0 ,
Figure 3. Resolving-Time Correction Curve 1 1. Resolving-Time Correction. The G-11 counter registers the passage of individual primary and secondary energetic electrons and positrons through the tube, but there is a short interval following each registered count (resolving interval) when it is not able to register such emissions. That time varies from system to system and somewhat within the system. A fairly precise correction may be made assuming a constant resolving time, T d , for a system. There are two limiting cases of counter mechanism (1) which determine the resolution effect mathematically. The "true" counting rate, Ca, for a recorded counting rate, C, is limited by
CO= C eCoTd
(Curve -4, Figure 3)
A. The case in which only relative measurements are desired and where plenty of the sample material is available. This is usually true for biological and biochemical investigations. B. The case in which only relative measurements are wanted and where only limited sample material is available. This is the case for certain sDecial mob= LJ lems in tracer work. C. The case in which absolute measurements of sample activity are desired. This is normally the case only when production or other assay measurements are being made and has little application in actual tracer work. CASEA. If a sample is so thick that none of the 0-rays emitted from the furthest removed layer are counted, a comparison of the counting rates a t a standard position of samples (corrected for resolving time and background) gives a direct measure of the relative activities. It is only necessary that the samples be well mixed and their top surfaces be geometrically identical. The thickness of. sample required is determined by the range of the @-particles. However, the intensity transmitted may fall off rapidly enough from absorption so that for all practical purposes a much thinner layer of material can be used. I n the case of the weak-energy CI4 @-particles,about 16 mg. of sample per sq. em. of sample area are generally sufficient. .I
(4)
and
co
L
=
md(Curve B, Figure 3)
(5)
Normally the correction lies somen-here between the two; however, a t comparatively slow counting rates there is little difference. For high precision, counting speeds should be kept low in the solid-line region of Figure 3. The value of the resolving time for a system may be quickly determined by the use of two sources giving approximately equal recorded counting rates, C1 and C?. If C I is ~ the counting rate recorded with both sources present, Td is found from (see Figure 4)
2
Td
=
c 1
+
0" +-
.
2
.05-
c 2
111 c , * c 1 2
I
or
/
0
Since the determination of the resolving time depends on small differences between quantities, the individual measurements must be made to extremely high precision to get fair accuracy in resolving time. I n a typical case a t least 106 pulses must be recorded for each rate to get 5% precision in Td. Changes in resolution of an unchanged system with time are normally slight, but it has been found to be a good policy to check resolving times a t regular intervals. 2. Background Correction. After the resolving correction has been made, the background rate should be subtracted. This rate should be measured under the exact conditions of the other measurements, without the source. 3. Efficiency Changes with Time. These may be easily normalized by counting a standard long-lived source regularly.
,025
,050
075
,100
Figure 4. Resolving-Time Correction Curve 2
CASEB. Where only limited amounts of sample material are available, self-absorption correction factors may be established empirically by measuring samples of graduated thicknesses and standard strength. Such calibration is straightforward, sound, and of easy application t o analvsis results. However, if desired, some of the principles out1ined"in Case C may be applied. Figure 5 gives a calibration curve for C14 active samples for which a bell-shaped counter was used, with about 20% of the radiation from the standard source position being incident on its window. CASEC. Geometry Corrections. Where measurements of absolute activity are desired, the effective geometrical efficiency, 7, of the counter must first be determined. This may be done by using a source of known @-particleemission strength with a
V O L U M E 19, NO. 1 1
826
low absorption coefficient, p. Knowing this, qualitative corrections can be made for the amount of p r a y absorption within the counter window, and an approximate q determined. Using this approximate value, absorption corrections can be made as indicated below and the effective q determined. For cases in which a source of known @-particleemission is not available, q can be calculated geometrically as shown in Figure 2. Where 5 is the cosine of the angle (from the source) subtended by a base radius of the counter cathode. toalcd. =
0.5 (1 -
(8)
5)
paper. The use of a sample support in the low atomic number range will reduce back-scattering errors.) As indicated before, the absorption of @-raysfrom a given disintegration is approximately exponential within its range with a definite coefficient,
I -lo =
pdlIz =
In 2
(11)
Given, then, the effective thickness it has to penetrate to be counted, the efficiency of a particular @-raycan be easily calculated (Figure 7). Although generally measured in terms of aluminum, p and R (in mass units) change little from substance to substance. PRECISION OF MEASUREMENTS
The precision of all measurements is limited bj the statistical accuracy of counting. To review the calculations: Where random events are being counted the error involved in using the average rate observed is proportional to the square root of the total number of events observed. The “probable error” is often used as a measure of the precision of a value; it is mathematically equal to 0.6745 times the square root of the number of events observed. The probability of occurrence and magnitude of error one may expect are given in Table I. From Table I we see, for example, that if a value of 100.0 is given us with a probable error of 1.0 (often written as 100.0 * l.O), the chances are even that the true value is between 99.0 and 101.0-and there is only one chance in 1000 of its not being between 95.12 and 104.88.
I
>
t8 2
!-
u a
96 (r
Iw
v,
2.4 .2 0
With the above in mind, an estimation of the practical strength of a radioactive material for a given purpose m i y be made. Suppose a probable &-or of not greater than 5 % is desired. A counting time of 30 minutes for each sample and 60 minutes for background is to be allotted. The counter background normally runs about 20 counts per minute, so in 60 minutes the back-
Figure 5. Measured Actikity from C14 us. Thickness of Sample of Uniform Concentration
However, the effective volume is somewhat less than the calculated volume, because of the degeneration of the electric field a t the outer periphery of the cathode. This effect is approximately equivalent t o the effect that would be produced by shortening the cathode and may be taken into account on that basis. Absorption Corrections. For most cases it is permissible to assume exponential absorption for @-raysfor most of their range. The absorption coefficient, p, often characterized by the halfequivalent absorptive thickness, dllz (the mass per unit area to reduce the intensity of radiation to one half), is measured as above. This is necessary so that a correction may be made for the absorption of the counter windov, other absorbing layers, ttnd the self-absorption of the source itself. Account must be taken first of the self-absorption of source material. In the case of a flat source of thickness t , with the radiation uniformly distributed, the mean absorbing thickness perpendicular to the surface is t In 2
1
Table I.
Statistical .kccuracy of Mean Probability of Occurrence 1,000 0.500 0.177 0.0430 0.00100 0.0100
Error Greater Than: 0
Probable error 2 . 0 0 X probable error 3 . 0 0 X probable error 3 . 8 2 X probable error 4 . 8 8 X probable error
(9)
Where a source parallels the counter window, this mean thickness is calculated with 1, the effective thickness, indicated below. If the actual absorbing thicknesses are known, corrections should be made for the effective thicknesses involved, as only a small proportion of the particles go through the shortest thicknesses, most of them taking an oblique path. For a bell-shaped counter with a round, flat window and the source effectively on the counter window axis,
where z is the z of Equation 8. This relationship of effective thickness to efficiency is plot,ted in Figure 6. The approximate strength of a sample may INTERPRETATION. be established, then, by taking the counting rate (corrected for resolving time and background), dividing by the geometrical efficiency, and then correcting for the absorption using the effective thicknesses. (Because of such factors as back-scattering of the @-raysand slight variations from exponential absorption, absolute values require treatment beyond the scope of this
0
.IO
.20
.30
40
Figure 6. Effective Counter-Wall Thickness VI. Geometric Efficiency, q, for Flat-Windowed &Ray Tube
N O V E M B E R 1947
827 - -
100
80
I
Table 111. Activity
60
Corrected activity h l g . per sq. cm. of sample Thick sample factor Thick sample count Activity relative to standard
40
Sample I 50.6 1,65 1/0.425 119.1 0.964
Standard 123.4 >20 1.000 123.4 1.000
D t = HALF-EQUIVALENT
20
Sample I1 3.17 2.45 1/0.557 5.69 0.0461
--
Table IV. Approximate Absolute Activity IO
Thick sample activity, counts per minute Activity at 1 mg. per sq. cm. a t 0 mg. per sq. cm. thickness (Figure 5) Area of sample, sq. cm. Activity per mg. at 0 thickness, counts per minute Windor thickness mg. per sq. cm. Air thickness (see’Figure 2), mg. per sq. cm. Effective thickness Actual thickness Effective thickness
-
>
diiz
I. .8
Absorption correction factor Geometrical correction factor Activity per mg. of BaCOn, disintegrationp per minute Activity per mg. of carbon
6
Figure 7. Exponential Absorption Curve a
123.4 X 32
x
0.335
r
123.4 X 32 X 0 . 3 3 5 lr
421
4.; 1.0 1.27 1.27 X 5 . 6 = 2,73 2.6 22.73 = 6 . 6 3 5.0 5 . 0 X 6 . 6 3 X 421 = 13,900
19127.4 = 2 . 2 9 X 106 disintegrations per minute or 0 . 1 0 p curies= per mg. of carbon 1 microcurie = 3.7 X 104 disintegrations per second. X
Table 11. Disposition of C14 Labeled Group 16-minute register Counts per minute Reaolvina time correction Background correction Corrected activity Activity relative t o standard Probable error (statistical)
Standard 1824.0 1 2 1 . 6 X 32 + 2 . 4 X 32 - 0 . 6 X 32 1 2 3 . 4 X 32 (1.000)
.......
Sample I 87.53 5 . 8 4 X 32 0 . 0 2 X 32 0 . 6 0 X 32 5 , 2 6 X 32 0.0426
Sample I1 309.0 2 0 . 6 0 X 32 0 . 0 8 X 32 0 . 6 0 X 32 2 0 . 0 6 X 32 0.1625 =t0.0005 .t0.0011
ground is 1200 23.3, or 20 * 0.39 per minute. If the sample itself gives 18 counts per minute, when measuring it the combination of it and background in 30 minutes gives 1140 * 22.8, or 38 * 0.76 counts per minute. The difference, 38 20 = 18 counts per minute, is the measured sample activity. However, the probable error of the sample measurement is augmented by the uncertainty of the background correction: Statistically the combined error is the square root of the sum of the squares of the (0.76)’ = 0.85. The sample individual errors of d ( 0 . 3 9 ) 2 activity is then 18 * 0.85 counts per minute or 18 * 4.770 which is satisfactory for the work.
-
+
PROCEDURES AND APPLICATION
The preparation of a C1* sample for measurement is straightforward-the carbonaceous material is burned to carbon dioxide which is passed into a barium hydroxide solution. Distribution of the baiium carbonate with adequate uniformity for counting may be obtained in several ways-for example; the precipitate may be suction-filtered onto fine filter paper supported on a sintered-glass base. (A guard ring may be used to keep the edges of the paper free from barium carbonate.) Or the barium carbonate may be centrifuged out and suspended in collodion, diluted 10 to 1 with acetone, and the suspension spread on the sample holder to be used. I n either case drying by an overhead infrared lamp is recommended. The use of barium carbonate is not mandatory; in many cases calcium carbonate niay be perferable since the same weight of sample has a higher carbon content. In other cases specific absorbente, or even slices of material, may be used; the only criteria are uniformity of sample thickness and carbon dispersion. I t is good practice to keep samples in an atmosphere of controlled humidity. The following examples may serve to illustrate somewhat the interpretation procedures for C14 measurements as well as to indicate provisions for satisfactory experimentation: Case A. An experiment is carried out tracing the disposition of a C14 labeled group in a compound. Samples containing from
5 to 10 mg. of carbon each are taken, converted to carbon dioxide, precipitated as barium carbonate onto a standard 2-cm. diameter filter, and counted in a standard position. The mechanical register measured every 32nd count. The system’s resolving time is 3.11 X lo-‘ second. Case B. The same type of experiment is carried out except that less than 1 mg. of carbon is available for each sample and the activity is expected to be too small t o make dilution feasible. The thickness-activity calibration is that of Figure 5. Case C. The approximate absolute activity of the standard sample above is desired. The counter geometrical efficiency is determined to be 2075, the window thickness is 4.1 mg. per sq. cm. A tabulation is given in Table IV. An estimate of absolute activities necessary for experimentation may be made from this and the section on precision. DERIVATION OF EQUATIONS
Equation 9. Let a: = specific activity x = activity a t surface Start with a thin surface ( t + 0) and keep piling layers on it: dx = p z d t ordt Integrating:
+
But
_ --
fft
e-rfmean
Thus which is equivalent to Equation 9. Equation 10.
t iJseC-lz =
e - p t #eo
a
sin
cy
a
which gives Equation 10 on integration. LITERATURE CITED
(1) Beers, Y . ,Rev. Sci. Instruments, 13,72 (1942). (2) Henriques, F. C.,and Margnetti, C., IND.ENG.CHEM., ANAL. ED.,18, 417 (1946). (3) Reid, A. F., et aE., P h y s . Rev., 70, 431 (1946). (4) Ruben and Ramen, Ibid., 57, 549 (1940). (5) Ibid., 59, 349 (1941). (6) Schonland, B. F. J., Proc. Roy. Soc. (London), AIOS, 187 (1925). RECEIVED October 12, 1946.
