Dis. rate where Arp
=
NPD Et PABY
B
=
Y
=
~
integrated area under the photopeak, counts per second D = dilution factor Et = total absolute detection efficiency for source detector geometry used =
(4)
P = appropriate value for the peak-to-total ratio ( 4 , 9 )
A = correction factor for absorption in source and any beta absorber used in the measurement. Tables for absorption coefficients are in (4)
correction for branching ratio and internal conversion of gamma measured chemical yield
LITERATURE CITED
(1) Bell, P. R., “Scintillation Method,” in “Beta- and Gamma-Ray Spectroscopy,” ed. by K. Seigbahm, Interscience, New York, 1955. (2) Bell, P. R., Davis, R. C., Lazar, N. H., Oak Ridge Natl. Lab., Rept. 72 (1957’1. (3) B&&d, A. J., Jr., Chemist Analyst 44, 104 (1955). (4)De La Rubin, P. J., Blasco, L. R. F., Ibid., 44, 58 (1955). (.5 ,) Finston. H. L.. Brookhaven National Laboratofy, private communication.
(6) Glass, G. H., Chemist Analyst 42, 50 (1954). (7) Glass, G. H., Olson, B., Ibid., 43, 70 (1954). \ - - - - I
(8) Glendenin, L. E., Nelson, C. M., National Energy Series Div. IV, 9, Paper 283, McGraw-Hih, Tern York, 1951. (9) L.. Atomic E n e r u Comm. . Research , Heath. R. and Development Kept., I D 0 16408 (July 1, 1957). (10) Kahn, B., Lyon, W. S., Szicleonics 11, S o . 11, 61 (1953). (11) O’Kelley, G. D., Oak Ridge National Laboratory, private communication. (12) Olsen, J. D., O’Kelley, G. D., Phys. Rev. 9 5 , 1539 (1954). (13) Wendlandt, W. LT‘., .\SAL. CHEM. 28, 1001 (1956). RECEIVEDfor review June 11, 1958. Accepted October 13, 1958.
Strontium-90 by an Ion Exchange Method E. A. BRYANT, J. E. SATTIZAHN, and BUDDY WARREN University of California, Los Alamos Scientific Laboratory, Los Alamos, N. M.
b A procedure is described for the radiochemical determination of strontium-90 in fission-product samples which have decayed a t least 10 days. Strontium and barium are adsorbed on a cation-resin column, and after a suitable growth period, yttrium-90, the daughter of strontium-90, is selectively eluted. The yttrium-90 is then adsorbed on and eluted from a second cation-resin column and counted. The radiochemical yield is greater than 97%; gravimetric measurement of the recovery of strontium and yttrium carriers is not required. The method, with modifications, is applicable to samples that contain 100 mg. of iron or uranium.
A
PROCEDURE has been developed for the radiochemical determination of strontium-90 in fission-product samples which have decayed at least 10 days. Such samples contain two radioactive isotopes of strontium, strontium-89, with a half life of 51 days, and strontium-90, with a half life of 27.7 years. Strontium-91, with a half life of 9.7 hours, has decayed to an insignificant level in 10 days. Determination of strontium-90 in the presence of strontium-89 is based on separation and measurement of the radioactive yttrium-90 which is produced by decay of the strontium-90. A problem in the analysis of fission products for strontium-90 (1-3, 7 ) is interference from the high-yield fissionproduct pair barium-140 and its daughter lanthanum-140, which have
334 *
ANALYTICAL CHEMISTRY
chemical properties similar to those of strontium-90 and its daughter yttrium90. A typical procedure ( 2 ) for the determination of strontium-90 in fission products involves precipitation of strontium and barium as the mixed nitrates from a fuming nitric acid solution, followed by removal of barium by precipitation as barium chromate and separation of yttrium from strontium by precipitation of yttrium hydroxide. Each step must be repeated several times to attain sufficient decontamination for the analysis of fresh fission-product samples, and radiochemical yield must be measured for both the strontium intermediate product and the yttrium final product. The procedure described employs a single separation of yttrium from strontium, barium, and lanthanum instead of the two types of separations required in the conventional procedure outlined above. This single separation is accomplished by elution of yttrium from a cation-resin column with a highly selective eluting reagent (6). The use of this reagent and of an evaporative mounting technique makes possible a relatively simple procedure with a radiochemical yield greater than 9770. The high yield kliminates the need for measurement of recovery of strontium and yttrium. There are four stages in the determination of strontium-90 by this method. The most persistent contaminants-zirconium-95, ruthenium-103, and iodine131-are eliminated by preliminary treatment of the sample. The strontium, barium, and other cations are adsorbed on a cation-resin column (6) and
yttrium, lanthanum, and other rare earths are stripped from the resin. Time is allowed for the growth of yttrium-SO, which is then selectively eluted. The yttrium-90 is further purified by adsorption on and elution from a second cation-resin column and is collected for counting by evaporation of the effluent on a counting plate. APPARATUS AND REAGENTS
Apparatus. Aluminum counting inches. plates, 31/4.x 21/2 X Double-sided Scotch tape. Mylar film, 1.7 mg. per sq. cm. Fritted-glass pressure filter, with a 25- t o 30-ml. reserroir and a drip tip, fine fritted disk. Beta proportional counter, methaneflow, 2 inches in diameter, 4.8 mg. per sq. em. aluminum windor. ION EXCHANGE COLVMSS. Three types of columns are used. The first cation column is prepared by sealing a 12-cm. length of glass tubing 18 mm. in inside diameter to a 9-em. length of tubing 6 mm. in inside diameter, fitted with a drip tip. The second cation column is prepared in a similar manner from a 9-em. length of tubing 5 mm. in inside diameter and a 15-nil. centrifuge cone. The anion column is prepared by sealing a 40-ml. centrifuge cone to a 10-em. length of tubing 10 mm. in inside diameter fitted with a drip tip. Reagents. Sea sand, n-ashed with concentrated hydrochloric acid and rinsed with water. Ammonium hydroxide solution, approximately 0.6F “,OH, prepared by saturating water with ammonia gas and diluting the saturated solution 1 to 25 with water. ELUTING REAGENTS.-4 solution of 0.5F a-hydroxyisobutyric acid (Fair-
mount Chemical Co.) made up to pH 3.55 with concentrated ammonium hydroxide. A solution of 0.5F a-hvdroxvisobutyric acid made up to pH 6withconcentrated ammonium hydroxide. BARIUM, LASTHANUM,STRONTIUhI, AND ZIRCONIU&l CARRIER SOLUTION, 2 mg. of barium, 1 mg. of lanthanum, 4 mg. of strontium. 1 mg. of zirconium per ml. as nitrates in 1F nitric acid. LANTHASUM CARRIER SOLUTIOK, 0.3 mg. of lanthanum per ml. added as nitrate to a 0.4F hydrochloric acid solution. STRONTIUM CARRIER SOLUTIOK, 4 mg. of strontium per ml. as nitrate in water. BARIUbr, LANTHANUM, AND ZIRCONIUhl CARRIERSOLUTION, 2 mg. of barium, 1 mg. of lanthanum, 1 mg. of zirconium per ml. as nitrates in I F nitric acid. EXCHANGE RESINS. AG 50 X-4, cation resin, 200 to 400 mesh, processed from Dowex 50 X-4 by Bio-Rad Laboratories, 32nd and Griffin Ave., Richmond, Calif., converted to the ammonium form by treatment with 6 F ammonium hydroxide, and washed with water. AG 1 X-8, anion resin, 100 to 200 mesh, chloride form, processed from Dowex 1 X-8 by Bio-Rad Laboratories. Preparation of Resin Columns. The tip of a column is plugged with glass wool and a slurry of the resin is added. The resin, when settled, should extend to within about 2 em. of the shoulder. One to 2 em. of sand is added to prevent agitation of the resin. Just before use, the cation columns are washed with water and the anion column is washed with concentrated hydrochloric acid. RECOMMENDED PROCEDURES
The basic procedure can be applied t o samples n hich contain not more than about 1 mg. of iron, 10 mg. of uranium. or 10 mg. of calcium. A supplementary procedure is used for removal of 100-mg. amounts of iron and uranium. Basic Procedure. STEP 1. Add the sample t o a 40-ml. centrifuge cone which contains 1 ml. of concentrated perchloric acid and 1 ml. of the barium, lanthanum, strontium, and zirconium carrier solution. Evaporate the solution to concentrated perchloric acid on a steam bath and add about 20 ml. of water (the evaporation to perchloric acid ensures removal of iodine131). Bubble in ammonia gas until a flocculent precipitate forms, and continue bubbling for about 10 seconds. Digest the mixture on a steam bath for about 5 minutes. STEP 2A. For samples that contain less than about 1 mg. of iron, 3 mg. of uranium, or 10 mg. of lanthanum. Transfer the contents of the centrifuge cone to a fritted-glass filter placed in position above the first cation-resin column. Apply air pressure to force the liquid through the filter into the reservoir of the column. Rinse the centrifuge cone with 3 ml. of the 0.6F ammonium hydroxide solution and transfer to the filter. Use the liquid to wash the walls of the filter and then force the
liquid through the filter. Repeat the wash a t least once. STEP2B. For samples that contain about 1 mg. of iron, 3 to 10 mg. of uranium, or 10 to 100 mg. of lanthanum. Centrifuge the contents of the cone and decant the supernatant solution into a fritted-glass filter placed in position above the first cation-resin column. Apply air pressure to force the liquid through the filter into the reservoir of the column. Dissolve the precipitate in the centrifuge cone with a minimum amount of perchloric acid, add 1 ml. of the strontium carrier solution, and add water until the volume of the solution is about 10 ml. Reprecipitate the hydroxides n ith ammonia gas as described in Step 1. Transfer the contents of the centrifuge cone t o the filter and force the liquid through the filter into the reservoir of the column. STEP3. Remove the filter and apply air pressure to the cation column to force the liquid through the resin a t about 1 ml. per minute. Wash the resin with two 5-ml. portions of water. The cation resins are never blovin dry; remove pressure when the liquid surface reaches the sand. STEP 4. Wash the resin Iyith 10 ml. of 0.2F perchloric acid. The acid is necessary for conversion of yttrium and lanthanide hydroxides on the resin column to a form in which they can be eluted. STEP5. Force tivo 5-ml. portions of the pH 6 ammonium a-hydroxyisobutyrate solution through the resin column a t about 1 ml. per minute. This solution strips yttrium, lanthanum, and other rare earth ions from the resin. STEP 6. Wash the resin immediately with 5 ml. of water and record the time as the beginning of the growth period for yttrium-90. Cover the tip of the column with a rubber policeman, add about 1 ml. of water to the reservoir, stopper the column, and set it aside. STEP 7. After 2 or more days remove the policeman and the stopper and allow the water in the reservoir to flow through the resin. Place the second cation column, n i t h a policeman covering the tip, in position under the first column. Put 3 ml. of the lanthanum carrier solution in the reservoir of the second column (the hydrochloric acid in the lanthanum carrier solution is necessary to break up the yttrium ahydroxyisobutyrate complex ion). Add 5 ml. of the p H 3.55 a-hydroxyisobutyric acid solution to the reservoir of the first column. Force the a-hydroxyisobutyric acid solution through the resin a t about 1 ml. per minute and collect the effluent in the reservoir of the second column. Record, as the end of the gron-th period and the beginning of the decay period for yttrium-90, the time a t which the elution is complete. The first column may be discarded a t this point. (If desired, a second sample of yttrium-90 may be obtained from this column. Wash the column with water and proceed as in Step 6.) STEP 8. Stir the mixture in the reservoir of the second column, remove the policeman, and force the solution
through the resin. Wash the column with 5 ml. of water. STEP9. Force 10 ml. of 0.5F ammonium perchlorate through the second column and test the last few drops of effluent with p H paper to determine whether the column has been completely converted to the ammonium form. If conversion is complete, the pH will be that of 0.5F ammonium perchlorate (about 5) ; if incomplete, less than about 3. When the conversion is complete, wash the column nith 5 ml. of water. STEP 10. Prepare a counting plate for sample collection by sticking a 4.25em. disk of KO. 2 Whatman filter paper to an aluminum counting plate with double-sided Scotch tape. Place the counting plate on a hot plate and position the second column so that its tip is about 0.5 inch above the center of the paper. Add 4 ml. of the p H 3.55 a-hydroxyisobutyric acid solution t o the reservoir of the column and allow the liquid to pass through the resin onto the paper by force of gravity (about 2 drops per minute). Adjust the temperature of the hot plate so that evaporation takes place smoothly (about 250" C.). The Scotch tape and the filter paper will usually turn brown in the hour required for elution and evaporation. STEP 11. When the elution is comalete. remove the aluminum d a t e . allow it .. to. cool, .. and cover the filterpaper with Mylar film. Suuolementarv Procedure for Removii'of Iron 0; Uranium. STEP 1. Add the sample to a 40-ml. centrifuge cone which contains 1 ml. of the strontium carrier solution and 1 ml. of concentrated perchloric acid. Evaporate to concentrated perchloric acid on the steam bath. Add 10 nil. of concentrated hydrochloric acid and transfer the solution to the reservoir of the anion-resin column. Allow the solution to flow through the resin and drip into a receiver. Rinse the centrifuge cone and the sides of the reservoir with three 5-nil. portions of concentrated hydrochloric acid. Allow each rinse to flow through the resin. Force the last drops of the final rinse from the resin with air pressure. If the sample contains more than about 100 mg. of iron or uranium, a larger anion-resin column and more hydrochloric acid are necessary. STEP2. Add to the collected effluent 1 ml. of the barium, lanthanum, and zirconium carrier solution. Evaporate to concentrated perchloric acid and proceed as in Step 1 of the basic procedure. Calculations. Calculate the strontium-90 disintegration rate in the original sample by the formula, D(Sr90) = .4(Y90)(eY)-l d t ( l -
e-XT)-1
where D(Srg0) is the disintegration rate of strontium-90, A (Y90) is the measured activity of yttrium-90 a t time t after separation of the yttrium from the strontium (Step 7), T is the time allowed for growth of the yttrium-90 (Steps 6 and 7 ) , A is the decay constant for yttrium-90 [half life 64.03 hours ( 4 ) ] , VOL. 31, NO. 3, MARCH 1959
0
335
Table I.
Determination of Yield
Yield, Y ,
Y X D(SrW)6, D.P.M./hIg. 1802b
Sample
% 98.9 98 8
18Olb
1810b 99 _ _ 318066 99.1 1799" 98.7 1803" 99.0 1802c 98.9 AV. 1803 990A1 a Y X D(Srso) calculated from measured yttrium-90 activity, A( YsO),for each sample. Basic procedure, Step 2A. Supplementary procedure.
Table II.
Table 111.
Anion" Concn., Jloles/Liter 0.1
0.4 0.6 0.8 1.1 1.2 1.8 2.4
Effect of Anions on Yield
SrsoRetained on Resin, %
PerChloride Nitrate chlorate , . . 100 100 ... 100 ... 100' 100 ... ,.. 96.8 72.3 ... ... 56.2 100' ... ... 91.3 ... ... 79 2
Total volume of solution, 20 ml. Nitrate and perchlorate solutions, O.1M in chloride ion.
Effects of Cations on Yield
Yield, % Weight of Cation, Rig. 1 5
10 20 30 40
50 60 70
80 100 a
Ca(I1) ... ...
99.1 97.7 91.4 68.2
...
... ... ... ...
Basic Procedure" Fe(II1) La(II1) 96.6 99.4 92.6 98.7 86.9 98.8 72.3 97.3 ... ... ... 96.6 58.7 ... ... 97.8 ... ... ... 97.3 15.5 97.6
Step 2.4.
E is the detection efficiency for yttrium90, and Y is the radiochemical yield of the procedure.
RESULTS AND DISCUSSION
Mounting Technique. When yttrium-90 samples are mounted by evaporation of the column effluent as described, t h e yttrium activity migrates t o t h e periphery of a circular area about 1 inch in diameter. Measurement of the activity in such a deposit requires a beta counter with a window about 2 inches in diameter. When samples are to be counted on the more conventional 1-inch window counters, the diameter of the deposit must be reduced accordingly. A deposit satisfactory for a 1-inch counter may be produced by reduction of the flow rate and total volume of the effluent.
Trial samples were mounted by evaporation of the effluent from a second cation-resin column 2 mm. in diameter and 6 em. long. The yttrium-90 effluent from the first column was collected in the reservoir of the second resin column as usual and the mixture of the lanthanum carrier solution with the effluent from the first column was stirred. The solution was passed through the second column and the resin was washed and converted to the ammonium form. The yttrium-90 \vas eluted with 1 ml. 336
ANALYTICAL CHEMISTRY
U(V1) 97.8 97.9 95.9 93.6
Supplementary Procedure U(V1) Fe(II1) ...
...
... ... ... 97.1
... ... ... ...
98.3 ... 98.0
... ...
Av.
...
...
97.1 97.6
...
...
... ... 97.9
... ...
98.5 98.7 , . .
98.3 98.4
Table IV. Strontium-90 and Molybdenum-99 in Fission Products
Weight of UraniumIrradi235, Mg./ ation No. Sample 1 9
Time of SrQO
Detn.. Days after Irrad. 76 76 70 42 20 20
D(Sr")/
A(Mo99)"
x 104 6 . 05b 9 6.09O 2 100 6 . 0gc 3 100 6 . 18c 4 4 5.98b 8 5.990 11 6 08" 5 6 Av. 6 08 Each value of D(SrSo)/A(hloQQ) is average of duplicate determinations. A(Moeg) is activity of molybdenum-99, measured shortly after irradiation and corrected for decay. * Basic procedure, Ste 2B. Supplementary procefure. of the p H 3.55 a-hydroxyisobutyric acid solution a t a rate of 1 drop every 45 seconds. The elution required about 2 hours and produced a deposit about 0.5 inch in diameter.
The maximum variation in activity, measured with a I-inch counter, Eas 3% for six trial samples and the average value differed by less than 1% from the expected value.
Determination of Yield. 1 radiochemical yield, Y , of 99 & 1% was established by a series of analyses on samples from a carrier-free strontium90 solution. The results of t h e analysis of three samples by the basic procedure and of the analysis of four samples by the supplementary procedure are shown in Table I. The strontium-90 solution Tvas standardized by counting samples in a 4 - ~ geometry, methane-floir-, beta proportional counter. The average strontium-90 disintegration rate, D(SrgO),for seven samples was 1822 & 14 d.p.m. per mg. of solution. The average detection efficiency, for six samples from a carrier-free yttrium-90 solution was (51.76 =k 0.14%). The detection efficiency is the fraction of yttrium-90 disintegrations nhich is detected when a sample is mounted and counted as described in this procedure. The disintegration rate of the yttrium-90 solution was established by counting samples in the 4-A counter. Effects of Cations on Yield. Analyses &-ere performed on strontium-90 samples which contained u p t o 100 mg. of calcium, iron, lanthanum, or uranium. The effects on the radiochemical yield of various amounts of these cations are summarized in Table 11. As much as 10 mg. of calcium can be tolerated when a cation column of the prescribed size is used. The cationresin column is about 127, loaded lyhen 10 mg. of calcium, 4 mg. of strontium (carrier), and 2 mg. of barium (carrier) are adsorbed on it. Use of a larger resin column Tyould permit the analysis of a sample containing a proportionately larger quantity of calcium. The loss of yield encountered in the analysis of samples which contain iron, lanthanum, or uranium occurs during the hydroxide precipitation. The basic procedure can be applied to samples which contain 1 or 2 mg. of iron, 1 to 10 mg. of uranium, or 10 to 100 mg. of lanthanum, if the hydroxide precipitate is dissolved and reprecipitated in the presence of additional strontium carrier. Larger amounts of iron or uranium should be removed by adsorption on an anion-resin column. Effect of Anions on Yield. The effects of chloride, nitrate, and perchlorate ions on the retention of strontium-90 by t h e cation-resin column are shown in Table 111. The individual data were obtained by application of the basic procedure to a series of samples containing 2 ml. of a 1 F hydrochloric acid solution of strontium-90 to which various amounts of the acids of these anions had been added. The addition and evaporation to perchloric acid (Step 1) were omitted. The loss of strontium-90 mas measured by beta-counting aliquots from each of the effluents from
the first column. The retention of strontium-90 was calculated from the yttrium-90 measured in the final product. The sum of the two quantities of strontium40 agreed, for each sample, with the known quantity of this activity introduced a t the start of the analysis. It may be seen from Table I11 that there is no loss of strontium-90, if the solution passed through the resin column is less than about 0.5V in chloride or nitrate ion or 1.OJf in perchlorate ion. Radiochemical Punty of Product. The radiochemical purity of t h e y t t r i u m 4 0 from analyses of fissionproduct samples Ivas determined by ?-ray spectruni analysis and study of t’he decay rate of the samples. Samples obtained froiii an analysis of 11-day-old fission products showed no signs of foreign activity. However, during development of the procedure, a number of contaminants \yere observed in the vttriuni-90 activity. An attempt to shorten the procedure by elimination of the hydroside step resulted in contamination of the product by about 0.01% each of the zirconium-95 and ruthenium103 actiJ.it#iesn.hich were present in the
sample at the time of analysis. Failure to evaporate the sample to perchloric acid resulted in contamination of the product by about 0.01% of the possible iodine-131 activity. On several occasions about 1% of the product activity was due to iodine-132 which had appaiently grown in from tellurium-132 adsorbed on the cation resin. The short half life (2.3 hours) of iodine-132 renders this contaminant harmless, if sample is not counted earlier than about 12 hours after separation. Analysis of Fission Products. The precision and accuracy of t h e strontium-90 procedure were tested by analyses for strontium-90 and molybdenum-99 performed on a series of samples of uranium-235 which had been irradiated with thermal neutrons. The results (Table IV) indicate that the procedure is suitable for the determination of strontium-90 in fission products. The value of 6.08 X for D(SrgO)/A(Mogg) is in reasonable agreement with the value 6.26 X 10-4 obtained previously by a conventional strontium-90 procedure ( 2 ) . The corresponding values for the fission yield of
strontium-90 are 5.45% and 5.61%, respectively. LITERATURE CITED
(1) Glendenin, L. E. Paper 236, Sational Nuclear Energy deries, Div. IV, Vol. 9, hlcGraw-Hill, New York, 1951. (2) Kleinberg, Jacob, et al., U’. S. Atomic Energy Comm.,. ReDt. - LA-1721,2nd ed. (August 1958). (3) Martell, E. A., “Chicago Sunshine Method. Absolute Assav of Srwin Biological Materials, Soils,“ Waters, and Air Filters,” Enrico Fermi Institute for Nuclear Studies, University of Chicago, May 1956. (4) Salutsky, M. L., Kirby, H. IT., ANAL. CHERT. 27, 567 (1955). (5) Smith, H. L., Hoffman, D. C., J . Inorg. and Nuclear Chem. 3, 243 (1956). (6) Stanley, C. TT., Kruger, P., “Determination of SrgOActivity in Katers with Ion Exchange Concentration,” Pittsburgh Conference on Analytical Chemistry, Pittsburgh, Pa., Feb. 29, 1956. ( 7 ) Sunderman, D. S . , Rleinke, IT. W., ANAL.CHEM.29, 1578 (1957). RECEIVEDfor review May 31, 1998. Accepted December 15, 1958. Division of Analytical Chemistry, Symposium on Radiochemical Analysis, 133rd Meeting, ACS, San Francisco, Calif., April 1958. Work done under the auspices of the U.S. Atomic Energy Commission.
Particle Size Analysis by Gamma-Ray Absorption CHARLES
P. ROSS
Savannah River Laboratory, E. I. du Pont d e Nemours & ,Accurate particle size analyses of uranium oxide were obtained by a y-ray absorption method. As particles settled from a uniform suspension, their concentration a t a fixed depth was continually determined by measuring the transmittance of yrays from an americium-241 source. The data were readily converted to a standard curve of particle fractions under a certain size vs. the diameter obtained from Stokes’ law. For the uranium oxide particles that were tested, the absorption of y-rays depended only on the mass of suspended material. The fraction undersize was determined with a 95% confidence limit of about A 0 . 0 4 , and the average diameter according to Stokes’ law was determined to about A0.3 micron. The method can b e used for any subsieve particles having an absorption coefficient significantly different from that of the suspending liquid.
M
practical methods of particle size analysis depend on the fact that the size and density of particles govern the settling velocity in a fluid. Many methods have been described (1, 2, 5 , 7 ) . One of the most accurate
Co., Inc.,
Aiken, S. C.
consists of drying and weighing samples that are drawn from a certain distance below the surface at various times after settling begins from a uniform suspension. If the sampling procedure r e r e replaced by a method of continuous measurement which would not disturb the suspension, the speed and accuracy of the particle size analysis mould be vastly improved. Such a method, based on the attenuation of an x-ray beam by the suspended particles, was briefly described in 1954 ( 1 ) . S o data were given, b u t because the method appeared to be fast and reliable, i t was investigated a t the Savannah River Laboratory for the particle size analysis of high density material. -4y-ray source was substituted for an x-ray tube, because a source is more compact and it is stable over longer periods of time. The attenuation of gamma radiation has previously been used to determine the concentration of heavy metals in solution and in suspension (3,8 ) .
as expressed by the following equation
( 4 ): where
Zro
=
Z
=
p/p =
C
=
2
=
The fraction of the particles that are of a size that will not settle from the surface to the depth of the beam in time t is gil en by
where
Ct
=
C,
=
OST
THEORY
The absorption of a monoenergetic gamma beam by a suspension of particles of a given chemical composition in a cell should obey the Beer-Lambert law
intensity of gamma beam emerging from cell with no particles in suspension intensity of gamma beam emerging from cell with particles in suspension mass absorption coefficient of particles for the energy of the beam, sq. em. per gram concentration of particles, gram per cc. path length of cell, cm.
concentration of particles a t time t , gram per cc. concentration of particles in initial uniform suspension, gram per cc.
Expressed in terms of gamma ray absorption, this fraction becomes VOL. 31, NO. 3, MARCH 1959
337
