Measurement of Radioactive Tracers Particularly CI4, S3’, T, and Other Longer-Lived’Low-Energy Activities W. F. LIBBY, Institute for Nuclear Studies and Department of Chemistry, University of Chicago, Chicago, 111.
The importance to the chemist of the detection of soft beta-radiation is pointed out-the useful longerlived beta-radioactive isotopes all have soft radiations. A n empirical treatment of the absorption of soft beta-radiation is given leading to the range energy relation lo =
1 g o E 5 / 3where 10 is the range
intensity with no absorber, a is the absorption coefficient, and d is the absorber thickness in milligrams per square centimeter. An empirical expression for cy is a = 5/10. This allows a generalized treatment of the problems of absorption and the intensities of radiation from sample layers of various thicknesses. On the basis of this formulation of the problem the relative sensitivities of various counters are discussed, in particular the popular “end window” type, the screen-wall type, and the gas counter.
of
the most energetic beta-rays in milligrams of aluminum per sq. cm., and E is the upper energy limit in kilovolt units. The absorption a t thicknesses less than l o is assumed according to experiment to be exponential in character: I = lae-md, where ZO is the
T
Figures 1 and 2 show the range energy relation for beta-particles. The data are from experiments with monochromatic electron beams as performed by Schonland, Varder, Ellis, and others ( I I ) , and described most carefully by Rutherford, Chad-
HERE is a conspiracy in nature against the chemist, in the form of a relation between the rate and energy of radioactive transformations-the longer lived, the softer the radiations. The radioactivities of lives greater than a few weeks almost without exception possess radiations so soft as to require special detection procedures. Table I contains a list of the more useful light chemical tracers with their half-lives and energies and ranges of their radiations in aluminum listed. It is perfectly obvious from this compilation that the average measuring instrument-counter or electroscope-with wall thickness of a t least 100 mg. per sq. cm. (0.015 inch of aluminum) will be unsuitable for three of the most useful isotopes in Table I, T(H3), CY4, and W.
1000
!
EMPIRICAL TREATMENT OF BETA RAY ABSORPTION
Beta-particles lose energy to absorbers by ionization, and except for the tremendous scattering effects would proceed as alphaparticles do to a rather definite range. The great scattering tendency means that for many experimental arrangements the loss by scattering is a t least as large as that due to true absorption. In other words, though a range energy relation exists, the diminution in intensity caused by interposition of a foil of less than the range in, say, a monochromatic electron beam is much greater than it would be for alpha-particles-olying to the larger scattering effect.
(SPECIAL INSTRUMENTS NECESSARY)
FIGURE I 0’
$1
1
MAXIMUM RANGE vs. ENERGY FOR
BETA PARTICLES
u 4
3
Table I. Isotope
Particularly Useful Radioactive Tracers
Half-life 31 years 2 0 . 5 minutes 4700 years (IO) 112 minutes 3 . 0 ears 14.8 $ours 170 minutes 14.3 days 87 days
Maximum Energy of BetaRadiation Kv. 9.5 950 140
700
580
1400 1800 1690 107
A1 Range cm. 0.23 390
.Mg./sp.
20
260 215 620 860 800 13.5
Haifthickness ,lig./sg. cm.
0.03 54 2.8 36
2-
30 86
120 110 1.9
0.1
2
,
,
I
I
I
I
I
I
I
I
I
t
V O L U M E 19, NO. 1, J A N U A R Y 1 9 4 7 Table 11. Directly Measured Range Soft Betas Activity
Energy (Magnetic) Kv .
DS.
3
Energy Points for
Range
Reference
. l f g . / s q . cm.
I = Ioe-ad
(2)
Henriques, Kistiakowsky, Margnetti, and Schneider (3) give a = 0.32 for Sa5. Calling the maximum range, , ,Z we then can write as a good approximation for sources of soft betas up to E values of 200 kv. L’S 1 3 cd/a
60
F
/
FIGURE 2
= 5
=CY-
(3)
150
This equation rvill serve to correlate upper energy limits and absorption coefficients (usually taken with essentially flat geometry and close proximity of source and detector to absorber). On this basis v x proceed to analyze the problem of detection of betaactivities.
RANGE vs. ENERGY
ETIPIRICAL THEORY OF S O F T BETA DETECTION
FOR BETA RAYS
Intensity from I n h i t e l y Thick Layer. Suppose a plane surface to be covered to a depth large with respect to the range, lo with a beta-emitting material, which has a specific activity of u (microcuries per gram). The curie is taken as 3.7 X 10’” disintegrations per second, so the microcurie is 2.22 X loe disintegrations per minute. What will be the count rate i f an area A of this solid be put in a counter with no intervening window? From a layer of depth 1 (mg. per sq. cm.) the yield will be (if we neglect back reflection, so only half of the radiation is considered)
ELECTRON BEAMS. 0 BETAS, MAGNETIC DEFLECTION VS. ABSORPTION. EMPIRICAL CURVE
20
or
0
50
I
I
I
I
100
I50
200
250
ENERGY (KV)
wick, and Ellis (11). A few data are given for soft natural betaemitters, for which the energy limits have been measured magnetically and the absorption limit determined. These fall on the same curve. rhese points are given in Table 11. The electron beam work showed relatively little dependence on atomic number, so the range values are quoted purely in milligrams of weight per square centimeter, whenever possible aluminum absorbers or substances of similar atomic number being used. T h e error even with gold is not large, however. It appears that siattering somehow compensates for change in energy loss per centimeter of true path. Figure 2 shows an empirical range energy curve given by Range, lo =
E613
~ o . 4 1 0 ~ 0= UALX
where x / x o is the dilution ratio.
(5)
Therefore
[E(kv.)l5I3 150
This may be expected to hold only for energies up to 200 kv. Wilson ( I d ) noted early that whereas the absorption of a monochromatic electron beam was far from exponential in character, a typical beta-ray emitter was rather accurately exponential as far as about 90yo loss of beam intensity, and he correctly ascribed this paradox to the existence of a range of velocities in betaemitters, the superposition of such a spectrum of energy values resulting in an approximately exponential absorption curve. It is of real importance that we be able to predict the absorption coefficient from the upper energy limit (the quantity usually available for beta-emitters) . I n order to do this we shall assume that the shape of the betaspectrum is essentially the same for all activities, in so far as it affects the ratio of the absorption coefficient and the range. Then we \Till expect the absorption coefficient to vary inversely with the range as given by Figures 1 and 2. I n other words, if I is the beta-ray intensity where d is the absorber thickncss (in mg. per sq. cm.) and is the absorption coefficient, (Y
Therefore the count will be 10% of the total disintegrations from a layer of a depth at least equal to the range, lo or - in 150 milligrams per square centimeter. Self-Absorption Curve. Consider a given number of millicuries of a soft beta-activity successively diluted with inert material making a thicker layer, always of the same area, A. What will be the count rate without an intervening window for each of the various dilutions? State all thicknesses in terms of lo as unit. Then the initial thickness xg contained Aloxo grams a t activity U O , so
and if I , represents the value as 2 0 --f 0
I =--1 - e+
I,
(z
5X
s
1)
(7)
which is a self-absorption curve of general applicability. This is shown in Figure 3, together with important values. This Equation 7 obviously should not apply beyond x = 1 because the exponential cannot apply then. The new form then will be /I = -
I,
1 5,
*ictually, Equations 7 and 7‘ differ so little that Equation 7 can be used throughout. Window or Foil Absorption. If a foil or window has thickness n (in terms of the range, l o )
I
Ioe-aalo =
1~~--6q
(8)
ANALYTICAL CHEMISTRY
4
" Saturation" Curve. Consider the activity from a layer of sample of uniform specific activity, u, of various thickness, x, i n terms of the range, Io. Its activity will be
FIGURE 3 GFNFRAL SEI F-ARSORPTION CURVE FOR SOFT BFTAS
if / 50
-
or
'
0
~
~
5
~
"
1
10
'
' (UNIT
~
P.,
1 5'
1
~
= 0.139 lo
(91
I n other words, the inasirriu~iirange will be expcctcd to be 7.2 times the half-thickness. Figure 4 gives the gencral absorption curve, together with the lo values for T, S3j,and C".
FIGURE 4
GENERAL ABSORPTION CURVE FOR SOFT BETAS
1
'
n.he1.c I, is thc activity for an nfinitely thick layer. The general "saturation" curve for soft betas is given in Figure 5 .
M A X RAKE)
The half-value absorber thickness is gircn directly by Equation 8 as ti:
I 2 0'
T H E O R Y OF DETECTION BI- COUNTERS
GESZRALTRE.xTJrExT. In order to facilitste the discussion, we shall adopt a definition of sensitivity. TTe shall define the sensitivity, S,as that limiting dilution of the sample (in grams per microcurie) which will just allow the sample to be measured to 10% (standard deviation) in 10 minutes. As the counter background will be of the order of the crosssectional area in square centimeters (measuring count rate in minutes-'), n-e are free to calculate t,he sample count rate which will ensure 10% accuracy in 10 minutes by using the Poisson sta(cm.). tistics and the counter length L (em.) and diameter L / o ~ The background is proportional to L 2 / a (counts per minute) and the total with sample L 2 / a E , where E is the sample's count rate. Then the error in E nil1 be
+
($ e-5x X=x) 1 WHERE
50
['F
where it has been assumed that equal intervals of 5 minutes be spent with and without the sample. (This approximation has been made t o facilitate the calculations and is accurate for the counters of highest sensitivity.) Setting AE equal to E/10 and solving for E , we obtain
1
FIGURE 5 GENERAL "SATURATION" CURVE
FOR SOFT BETA EMITTING SOLIDS 0
I
I
1
I
I
I
0.5
SAMPLE THICKNESS
(X=
-&),
I
I 1.0
as the general expression for the miriimum count from the sample foi, 10% accuracy in 10 minutes' measurement. Figures 6 and 7 present this limiting sample count us. the background and the background tis. counter dimensions, respect ively . ESD WIXDOIVCOUSTER. This popular type of counter is a short, large diameter (small L and a ) counter with LL thin n?-indowa t one end, the plane of the window being perpendicular to the axis of the cylinder. It is described by Yanknich, Rollefson, and Korris ( I S ) , and by Henriques, Kistiakowsky, Margnetti, and Schneider (3). Figure 8
5
V O L U M E 1 9 , N O . 1, J A N U A R Y 1 9 4 7 shows the general features of this instrument as described by these authors.
_
_ (grams per ~microcurie) (14)
2 LZ
If u is the specific activity of the sample in microcuries per gram lo, the range (mg. per sq. em.) PO, the window thickness thcn the expected count rate (counts per minute) is
Eqwting this to Equation 12, we solve for the limiting value of
1 , u bvhich we liave dcfincd as thc sensitivity, S.
J
N
Similarly, the minimum weight of sample to give an infinitely thick layer is TY in
Figure 0 presents S os. W values for counters ranging from 1 to 100 cni. in length, and 01 values of 5 to 10. The t,op curve is for and the second is for Sa5. T c:innot he detected \\.it11 these instruments. SCREEX WALL COUXTKR.Tliis initlument ( 6 , 8) I ) o w w w two ndvantages in sensitivity over the end Tvirrdoii- tlt-iyii : CIA
fl
z
400-
1
FIGURE 6 LIMITING SAMPLE COUNTS vs. BACKGROUND COUNT
\
t
z
$
300-
&
0 100
-
STOPCOCK FOR-
FOR
t
/ METAL I
I
I
I
I
!
1
500 BACKGROUND COUNT
I
I
I
I
I
I
1000 (COUNTS/MIN.)
? /
,
I
FIGURE 7
/
/
THIN WINDOW W I T H OR WITHOUT
MAY b E AS THIN L C R E E N SUPPORT. i.5 3MG./CM? WINDOW WAXED IN POSITION
Figure 8.
End Window Counter
BACKGROUND COUN; COUNTER (d
vs,
DIMENSIONS
IS RATIO OF LENGTH T O DIAMETER
/
I I
I
FIGURE 9 SENSITIVITY vs SAMPLE W T
I
//I
SENSITIVITY DEFINED A5 LIMITING DILUTION TO WVE 10% ACCURACY IN 10 MINS. P- GAS PRESSURE OF ACTIVE GAS
V = NO. MOLES ACTIVE GAS PER GM.
6
ANALYTICAL CHEMISTRY moles of this gas produced by 1 gram of sample, then the basic equations are
METAL CYLINDER
KHOTINSKY WAY
,f /
rMETAL
SAMPLE CYLINDER CONNECTION TO SCREEN
and
TT’ = 3.17 x 10-5
Figure 10.
Screen Wall C o u n t e r
L2 T L 2 1. Sample area is r- vs. - CY 4 a2 2. S o window between sample and counter. ( I t is recommended that the instrument be operated with “drag in” voltage-i.e., &amber wall negative with respect t o screen for maximum sensitivity) It has the disadvantage that about 20 minutes are required normally to mount and change samples, in contrast to 2 or 3 minutes for the end window design. Figure 10 presents its essential features.
f
P L3
-v CY2
(19)
These are illustrated in Figure 9 for counters of sizes from 1 to 100 cm. in length and C( values of 5 to 10. The principal disadvantage of these counters is the requirement that the gas sample not too seriously damage the counting properties. At pressures of 3 or 4 mm. of mercury this is not a serious restriction, but a t the higher pressures required for the maximum S value it is a serious For T, hydrogen gas serves. This can be used easily to Pressures of 4 or 5 em. if several centimeters of A be added together
THICK -WALLED CAPILLARY GLASS /DE
’
ENDS KHOTINSKY WAX
CYLINDER OF DESIRED SIZE CLEANED IN ACID AND DRIED IRON WIRE-POLISHED CLEAN EMERY BEFORE USING
The equations for this counter are
per microcurie)
T L ~ IY = - 10 X 01
(16)
‘\,
(grams)
’ I
LWAX
iCROSS
BAR TO HOLD WIRE
(17)
They are derived as for the end window type, and are illustrated in Figure 9 for all sizes up to L values of 100 cm. and a: values of 5 to 10. The superior sensitivity of the instrument is obvious from this comparison. GAS-FILLED COUNTERS. One of the most sensitive uses of a counter is the direct introduction of the sample into the counter gas when possible. This, also, is a direct way of obtaining an absolute measure of the radioactivity. The counter can be standardized for absolute sensitivity with the sample filling (or the control dummy filling of the same composition chemically), and the observed sample rate converted directly to curies of activity. The sensitivity is independent of the type and energy of the radiation, providing it produces a few ion pairs per centimeter of path at atmospheric pressure, and providing the physical and chemical characteristics of the gas are such as to make a good counter. In the use of gas-filled counters it is necessary, of course, to work with a vacuum rack. The pressures of the gas must be measured with due regard to its linear effect on accuracy, and su5cient cognizance must be given to adsorption of absorbable gases on the counter walls, etc. A convenient construction is shown in Figure 11. It is well to have a plentiful supply of cylinders and glass ends to fit. The construction of a counter takes about 15 minutes if these standard materials are available.
If P be the pressure in atmospheres t o which the counter
can be filled with the gas being measured, and v the number of
WIRE CONNECTION RUBBER BAND TO KEEP WIRE T I G H T
Figure 11. Gas-Filled C o u n t e r
with a few millimeters of ethanol. For CA4,the alcohols are excellent, of course. Methane is good, as are other hydrocarbons. There seems to be some hope for carbon dioxide. No sulfur gas has been reported yet. LITERATURE CITED
(1)
Alvarez, L. W., and Cornog, Robert, Phys. Rev.,56, 613 (1939); 58, 197 (1940).
Brown, S. C.,Ibid.,59, 954 (1940). (3) Henriques, F. C., Jr., Kistiakowsky, G. B., Margnetti, Charles, and Schneider, W. G., IND.ENG.CHEM.,ANAL.ED., 18, 349 (2)
(1946). (4) Hull, D. E., Latimer, W.M., and Libby, W. F., J . Am. Chem. SOC.,57, 593 (1935). (5) Kamen, M.D., Phys. Rev.,60, 537 (1941). (6) Lee, D. D., and Libby, W. F., Ibid.,55, 245 (1939). (7) Ibid.,p. 252. ( 8 ) Libby, W.F., Ibid.,46, 196 (1934). (9) Ibid., 56, 21 (1939). (10) Reid, A. F., Dunning, J. R., Weinhouse, S., and Grosse, A. V., Ibid., 70, 431 (1946). (11) Schonland, Varder, Eddy, et al., as described in Chap. XIV of
Rutherford, Chadwick, and Ellis, “Radiations from Radioactive Substances”, London, Cambridge University Press, 1930.
(12) (13)
Wilson, W., Proc. R o y . Soc., 982, 612 (1909) Yankwich, P. E., Rollefson, G. K., and Norris, T. H., J . Chem. Phys., 14, 131 (1946).
PRESENTED before the Division of Physical and Inorganic Chemistry a t t h e 110th Meeting of the AJIERICAX CHEMICAL SOCIETY, Chicago, Ill.
