Determination of 

Radium in Water

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1696-B
Determination of 

ladium in Water

; F. B. BARKER and J. 0. JOHNSON

.ADIOCHEMICAL ANALYSIS OF WATER

EOLOGICAL SURVEY WATER-SUPPLY PAPER 1696-B

'econd of a series of reports describing 

lethods used by the U.S. Geological 

'urvey for measuring radioactivity 

nd radionuclides in water

NITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1964
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402
ILLUSTRATIONS

CONTENTS

Abstract_____________----__-____-___________________ Bl

Introduction-____________________________________________ 1

Methods for determining radium_________________________ ______ 2

Single-carrier-precipitation method._______________________ ____ 3

Principle of the method__________________________________ 3

Apparatus_______________________________________________ 4

Reagents._______________________ 7

Procedure._______________________________________________ 7

Techniques for handling difficult samples _____________________ 8

Calculation of results____________________________________ 8

Errors and precision________________________-__-__-__-_____ 9

Isotope-identification method.________________________ ______ 9

Principle of the method_____-_________-___-______________ 9

Apparatus. ___________________________ -___ 11

Reagents-___________________________-_______--__-_-----_- 11

Procedure. _____________.___________________________ 12

Calculation of results-_____---____- ______________________ 13

Errors and precision_______________________________________ 21

Preparation of radium standard-stock solution._______________________ 21

Derivation of equation for calculating results of isotope-identification

method_______________________________________ 22

References cited_____________________________________ 29

Page 

FiOUBE 1. Filtration assembly for membrane filters__________________ B5

2. Ring and disk sample mounts, assembled and exploded views.- 5

3. Alpha-counting equipment for automatic and for manual

operation_____________________________________________ 6

4. Form used to tabulate data and calculate results of isotopeidentification method__________________________________ 14

5. Plot of the function G(t, At) for different values of t and A<_ _ _ 16

6. Plot of function p(t) as a function of time since purification. __ 17

7. Weighting factors for the individual measurements. _________ 18

8. Growth and decay of alpha activity in mixtures of radium-224

and radium-226_________________________ 20

TABLE

TABLE 1. Short-lived alpha-emitting daughters of the radium isotopes. ___ B22

m

RADIOCHEMICAL ANALYSIS OF WATER

DETERMINATION OF RADIUM IN WATER

By F. B. BAEKEE and J. O. JOHNSON

ABSTRACT

Radium isotopes are common radioactive constituents of natural waters. 

The concentration of radium-226 in potable water is of particular significance 

because this isotope is generally considered the most hazardous of all radionuelides 

with respect to ingestion.

The approximate concentration of radium-226 is determined after coprecipitating radium with barium sulfate. The short-lived daughters of radium are 

allowed to grow for 10-12 days, then the alpha activity of the precipitate is 

measured and compared with that of a precipitate containing a known amount 

of radium-226. Concentrations of the individual alpha-emitting isotopes of 

radium-223, radium-224, and radium-226, are determined by coprecipitating 

radium first with lead sulfate, then with barium chloride, and finally with 

barium sulfate. This final precipitate is initially free of other alpha-emitting 

nuclides, thus permitting the isotopic composition to be determined by measuring 

the growth and decay of the alpha activity of the precipitate.

INTRODUCTION

This paper describes the methods in current use at the Denver 

research laboratory of the Water Resources Division, U.S. Geological 

Survey, for the determination of the concentrations of radium in 

natural water. These methods, although not necessarily the most 

sensitive or precise are usually rapid and inexpensive.

This is the second of a series of reports describing the analytical 

methods used in the Denver laboratory for determining the concentrations of various radionuclides in natural waters. The first paper 

of the series (Water-Supply Paper 1696-A) contains a general introduction to the series; discussions of the sources of radioactivity in 

water, the collection and preservation of samples of water, and the 

measurement of radioactivity; and a description of a method for 

determining gross beta activity in water. Additional papers are 

planned to describe other methods used by the U.S. Geological 

Survey for radiochemical analysis of water, including those for 

uranium, radiostrontium, radon, radiocesium, and alpha activity.

Radium is a naturally radioactive element that is widely disseminated in minute quantities throughout the crust of the earth. Four 

isotopes of radium, members of the natural radioactive series (Barker

Bl
B2 RADIOCHEMICAL ANALYSIS OF WATER

and Robinson, 1963, p. 2-5), occur in nature: radium-226, a member of 

the uranium series; radium-224 and radium-228, members of the 

thorium series; and radium-223, a member of the actinium series. 

The relative abundances of these isotopes vary widely in nature, 

depending on the relative amounts of thorium and uranium in the 

particular geologic system and on complex geochemical processes 

that may upset the radioactive equilibrium at several points in the 

decay chains. Several other isotopes of radium have been produced 

artificially, but these seldom would be found in natural water and 

will not be discussed in this paper.

Radium-228 decays by beta emission; the other three natural 

isotopes decay by alpha emission. The following table shows the 

half lives and specific activities of the natural radium isotopes:

Specific activity

(curies per 

Isotope Half life gram)

Radium-223..__..____.______________ 11.2 days_-------_---_- 5.3 X 10<

Radium-224_________________________ 3.64 days_--__-_-_--__- 1.6 X 10s

Radium-226--._-________________ 1,620 years._________ 1.0

Radium-228.______________________ 6.7 years.-.----.-___ 2.4 X 10 2

Water from all types of geologic terranes is apt to contain radium 

because of the wide distribution of its parent elements, uranium and 

thorium. Concentrations of radium in fresh ground water (no more 

than 3,000 ppm dissolved solids) generally are less than a few picocuries per liter (pc per 1; 1 pc=2.22 disintegrations per minute). 

However, water from highly-mineralized zones or from certain 

geologic formations sometimes contains high concentrations of radium. 

Concentrations of radium in Cambrian and Ordovician limestone 

aquifers in the north-central United States commonly exceed 3 pc per 1. 

Wastes from uranium mining and milling operations are usually very 

high in radium and can be sources of water contamination. Millpond wastes may exceed 1,000 pc per 1 of radium, a large amount of 

which is usually attributable to the 11-day radium-223 isotope.

The concentrations of radium-226 in potable water supplies are of 

particular significance because this isotope is generally considered the 

most hazardous of all radionuclices with respect to ingestion. There 

is not complete agreement concerning the permissible concentrations 

of radium-226 in safe drinking water. Commonly used criteria 

range from 3 pc per 1, the drinking-water standard recommended 

by the U.S. Public Health Service (1962), through 10 pc per 1, the 

maximum permissible concentration (MFC) recommended by the 

National Committee on Radiation Protection (1959).

METHODS FOR DETERMINING RADIUM

Several methods are available for determining radium-isotopes concentrations of less than 10 pc per 1. These methods can be divided
DETERMINATION OF RADIUM IN WATER B3

into two general classifications: emanation methods and carrierprecipitation methods. Under ideal conditions, the minimum detection limit of either method is somewhat less than 0.01 pc per 1; however, 

the practical limit for most investigations is about 0.01-0.1 pc per 1.

Emanation methods involve the measurement of the radioactivity 

of the inert gases radon-222 and radon-220 (Evans, 1935; Hursh, 1954; 

Bate and others, 1953). Concentrations of radium-224 and radium-226 

can be determined by measuring the activity of the radon daughter 

nuclides in equilibrium with the radium parents. Under some 

conditions radium-223 might be determined from radon-219; however, 

this generally would be limited to samples of high concentration 

because of the short half life (3.92 sec) of radon-219.

The U.S. Geological Survey sometimes uses an emanation method 

for determining radium-226 in water. This use is incidental to the 

measurement of radon-222, however, and the method will be described 

in a subsequent report on radon in water.

In the carrier-precipitation methods, radium is removed from 

solution by physical or chemical attachment to an insoluble salt 

(carrier) that is precipitated from the solution. Salts that remove 

radium from solution efficiently include barium sulfate, lead sulfate, 

and barium chloride. Radium can be separated from other radioactive 

substances by additional chemical separations using one or more 

carriers. The final precipitate is collected on a suitable filter or 

planchet, and radium is determined by measuring the amount of 

radioactivity. Before measuring the radioactivity, the precipitate 

can be aged to permit the growth of short-lived daughter nuclides, 

thus increasing the activity of the precipitate. Individual radium 

isotopes can be determined from the growth and decay of radioactivity 

in the sample (Stehney, 1955) or by separating specific daughter nuclides and measuring their radioactivities at predetermined times 

(Petrow, and others, 1960; Baratta and Herrington, 1960).

This report describes two carrier-precipitation methods for determining radium in water. One of these involves a single precipitation of the barium sulfate carrier, permitting only the determination 

of the total activity of the alpha-emitting radium isotopes (Barker and 

Thatcher, 1957). The other method, adapted from one used by 

Ames and others (1949) and modified by Russell and others (1950), 

utilizes three carrier precipitations. This method, referred to as the 

isotope-identification method, permits radium-226 and the short-lived 

isotopes radium-223 and radium-224 to be determined individually.

SINGLE-CARRIER-PRECIPITATION METHOD

PRINCIPLE OF THE METHOD

Barium and radium form an isomorphous series of crystalline sulfates in which barium and radium ions are interchangeable in the
B4 RADIOCHEMICAL ANALYSIS OF WATER

cationic positions of the crystal lattice. Therefore, when barium sul 

fate having a slight excess of sulfate ions is precipitated, radium i 

removed quantitatively from solution by isomorphous replacement 

even though the solubility product of radium sulfate has not beei 

exceeded. The alpha activity of such a precipitate can be measurec 

and compared with that of another precipitate consisting of the sam< 

amount of barium sulfate carrying a known amount of radium-226 

Thus, the quantity of alpha-emitting radium isotopes present can b< 

reported in terms of radium-226.

The specific procedure used is based on one coprecipitation of radiun 

by isomorphous replacement in barium sulfate. The single-carrier 

precipitation method is simple and rapid and requires a nominal in 

vestment in equipment. The method is suitable for most purposes 

where radium need not be determined with high precision and when 

the activity from radium-224 and radium-226 need not be differen 

tiated. The method is adequate for many geochemical investigations 

Also, it is usually satisfactory for monitoring potable water for conformance to health standards, even though the reported result maj 

be somewhat greater than the actual radium-226 content because oj 

the presence of radium-224 and other interfering alpha-emitting 

nuclides.

This method is sufficiently accurate and specific for most hydrologic

investigations of radium in ground water and surface water, at least

in the initial phases. A study of the variations of radium and uranium 

contents in a major aquifer (Barker and Scott, 1958) and an evaluation 

of the natural levels of radioelements in ground water (Scott and 

Barker, 1959 and 1962) are examples of such investigations.

APPARATUS

Much of the equipment used in radium determination is of a general 

nature and is available in a typical analytical laboratory. Special 

equipment and supplies needed include:

2-liter beakers

2-liter or larger filter flasks

Molecular membrane filters, 0.45-micron pore-size, black, 45-mm 

diameter

Filtration assemblies for membrane filters, including ~a clamp, 

funnel, and base (fig. 1)

Ring-and-disk sample mounts (fig. 2)

Alpha-counting equipment, consisting of a windowless alphascintillation detector mounted in a suitable sample changer, a 

regulated high-voltage power supply, and a sealer (the last 

two items generally are combined in one instrument). Typical 

assemblies are shown in figure 3.
DETERMINATION OF RADIUM IN WATER B5

I! jt,*

rj"^*?**-^.

FIGUBE 1. Filtration assembly for membrane filters.

FIGUBE 2. Ring and disk sample mounts, assembled and exploded views.
B6 RADIOCHEMICAL ANALYSIS OF T/ATER

FIGURE 3. Alpha-counting equipment for automatic (above) and manual (below) operation.
DETERMINATION OF RADIUM IN WATER B7 

REAGENTS

Ammonium sulfate solution. Dissolve 400 g of reagent-grade ammonium sulfate in 1 liter of hot distilled water, cool to room temperature, and filter.

Barium carrier solution (1.4 mg Ba+2 per ml). Dissolve 2.5 g of 

reagent-grade barium chloride dehydrate in distilled water and dilute 

to 1 liter.

Radium standard solution (1 pc Ra226 per ml). Dilute 10 ml 

radium standard-stock solution (see p. 21) and 10 ml of concentrated (36-38 percent HC1) reagent-grade hydrochloric acid to 500 

ml by adding distilled water.

Sulfuric acid wash solution. Dilute 5 ml of concentrated sulfuric 

acid to 1 liter by adding distilled water and then add 10 ml of saturated 

Aerosol OT solution.

PROCEDURE

1. Measure 1 liter of the sample, previously filtered if necessary, 

into a 2-liter beaker. If the sample contains more than 350 ppm 

(parts per million) calcium, take a smaller volume and dilute to 1 

liter, so that the solution contains less than 350 ppm of calcium. If 

a sample is believed to contain sufficient quantities of barium, strontium, or other dissolved or suspended material to add more than 1 or 

2 mg to the weight of the precipitate, a "spiking" technique should be 

used. This technique is described in a later section on procedures for 

handling difficult samples.

2. Prepare duplicate standard solutions, each consisting of 25 ml of 

radium standard solution (1 ml=l pc radium-226) diluted to 1 liter 

by adding distilled water and a blank solution consisting of 1 liter of 

distilled water.

3. Heat blank solution, samples, and standard solutions to incipient 

boiling point and adjust the pH to approximately 3.5 by adding concentrated hydrochloric acid and using several drops of methyl orange 

as the indicator.

4. Add 3 ml of the barium carrier solution to each beaker and stir 

vigorously. While stirring, add 15 ml of saturated ammonium sulfate solution; continue stirring intermittently for several minutes.

5. Allow the precipitate to digest at room temperature for 4 hours 

or longer, then collect the precipitate on molecular membrane filters. 

Wash with small volumes of the sulfuric acid-aerosol wash solution. 

The barium sulfate precipitate should be evenly distributed to minimize self-absorption losses for alpha particles. A fine jet of the wash 

solution can be used to redistribute the precipitate on the filter, the 

filter permitting the analyst to determine when an even distribution 

is obtained.
B8 RADIOCHEMICAL ANALYSIS OF WATER

6. When the membrane filter is practically dry, mount it in the 

ring-and-disc holders. (The nutrient pads, supplied with certain 

niters or other flat stiff disks of proper diameter, can be used as sample 

mounts when manual sample changers are jused. The membrane 

filter can be conveniently attached .to such disks by using doublesurfaced cellophane tape.)

7. Determine the alpha activity of the precipitate after allowing 

a period of 10-12 days for the growth of the short-lived daughter 

nuclides. Typical counting times are 15 minutes each for standard 

solutions, and 1 hour each for blank solutions and samples.

TECHNIQUES FOR HANDLING DIFFICULT SAMPLES

Special techniques are necessary for analyzing many brines or other 

unusual waters that may contain large concentrations of barium or 

strontium, and for analyzing samples that contain colloidal or suspended material. Samples containing large amounts of suspended 

material should be filtered; both the nitrate and residue can be analyzed for radium if desired. If the residue is to be analyzed, it should 

be leached with dilute nitric acid (approximately 6 N), and the analysis should be performed on the clear leachate by the usual procedure. 

Brines and other samples containing only small amounts of suspended 

material often can be analyzed by diluting the sample.

A "spiking technique" (use of internal standard solutions) sometimes must be used, particularly if the sample is suspected to contain 

significant amounts of barium. This technique requires two parts of 

the sample. A known amount of radium is added to one part and 

both are analyzed in the usual manner. Comparison of the counting 

rates of the "spiked" and "unspiked" parts permits evaluation of the 

increased self-absorption and calculation of the concentration or 

radium in the sample.

CALCULATION OF RESULTS

Gross radium activity is calculated by means of the formula

ft SRX H&~VBS

where

Ra=total radium, hi pc per 1 expressed as radium-226 activity 

V= volume of sample, in liters 

S= amount of radium-226, in picocuries, in each standard

solution

Rs= average net counting rate of the two standard solutions 

Rx=neit counting rate of the sample.
DETERMINATION OF RADIUM IN WATER B9

When an internal standard solution or "spike" is used, gross 

radium activity is calculated by the following formula:

Ra= SEx

where

Rx=net counting rate of the "unspiked" sample

-Bg=net counting rate of the sample containing the radium-226

"spike" 

S= amount of radium-226, in picocuries, used for "spike."

ERRORS AND PRECISION

The single-carrier precipitation method is not specific for radium 

because significant amounts of other elements such as thorium, 

bismuth, lead, and polonium may be carried in the barium sulfate 

precipitate. Any alpha-emitting isotopes carried in the barium sulfate 

precipitate are counted as radium, and other alpha-emitting isotopes 

or descendants of these elements are found in nature. However, 

study of the uranium and thorium series indicates that the only nuclides 

producing significant interference probably would be thorium-228, 

-230, and -232 and polonium-210. Fortunately, the thorium isotopes 

and polonium-210 do not usually occur in natural waters in detectable 

amounts. The elements, if present in significant quantities, would 

be detected as radium. After the prescribed aging period for the 

barium-sulfate precipitate (11 days), 1 pc each of the aforementioned 

nuclides would be reported as the following estimated amounts of 

radium: Thorium-232, 0.15-0.2 pc; thorium-228, about 0.2 pc; 

thorium-230, 0.15-0.2 pc; and polonium-210, about 0.2 pc.

The practical minimum detection limit for radium in the singlecarrier precipitation method is about 0.1 pc per 1. The precision of 

the reported result is somewhat difficult to define, partly because of 

the lack of specificity for radium-226 and partly because of those 

factors relating to the measurement of radioactivity that were discussed in chapter A of this series. The two-standard-deviation level 

is probably about ±0.1 pc for samples containing 0.1-0.5 pc per 1 of 

radium and about 20 percent for samples containing more than 0.5 

pc per 1 of radium.

ISOTOPE-IDENTIFICATION METHOD

PRINCIPLE OF THE METHOD

Ames and others (1949) found radium coprecipitated with barium 

chloride to be almost entirely free of interfering alpha activities. 

For solutions containing appreciable sulfate ions, a preliminary separation is necessary to prevent precipitation of barium sulfate. Lead

723-108 O - 64 - 2
BIO RADIOCHEMICAL ANALYSIS OF WATER

sulfate coprecipitates radium quantitatively and, unlike barium sulfate, 

can be dissolved readily. The combination of a lead sulfate precipitation 

followed by a barium chloride precipitation, therefore, permits quantitative separation of radium from almost all other naturally occurring 

alpha-emitting nuclides. Slight interference may be found as a result 

of actinium-227 and bismuth-210 which are carried into the final 

precipitate (see discussion of errors and precision of this method). 

This method was used by Ames and others to determine uranium in 

process waters and was adapted by Russell and others (1950) and used 

to determine radium in urine and other biological materials. In the 

absence of interfering alpha emitters, the amounts of the individual 

radium isotopes in the sample can be determined by measuring the 

growth and decay of the radioactivity. Steh'ney (1955) used this 

technique and a similar method to measure radium-224 and radium-226 

in water.

The isotope-identification method used by the U.S. Geological 

Survey was evolved from these procedures. The water sample is 

evaporated to dryness, and the carbonates are destroyed by adding 

nitric acid. The soluble part of the residue is dissolved in dilute nitric 

acid, and the radium is coprecipitated with lead sulfate. The lead 

sulfate then is dissolved in a hydrochloric acid-ether solution, and the 

radium is coprecipitated with barium chloride. Finally, the barium 

chloride is dissolved in dilute nitric acid, and the radium is coprecipitated with barium sulfate, which is collected on a membrane filter and 

mounted for counting. The radium isotopes are determined by 

measuring the growth and decay of alpha activity in the barium 

sulfate precipitate and fitting the data to the appropriate equations 

by a suitable method.

If the concentration of radium-223 is small compared to the concentrations of radium-224 and radium-226, it can be ignored, and the 

data can be put into a form amenable to treatment by the method of 

least squares for a straight line. A discussion of this treatment and of 

the derivation of the necessary equations is given on pages B15-B19. 

Even if the concentration of radium-223 is not negligible, the straightline equations are reasonably valid. However, the result for 

radium-226 will be too high by an amount equal to 40 percent of the 

radium-223, and the result for radium-224 will include all the radium223. Although it is possible to estimate the concentration of radium223 and correct the results accordingly, the precision with which the 

concentrations of radium-223 and radium-224 can be reported is poor, 

so that it is generally better to report the sum of the two as the 

concentration of the short-lived isotopes. This topic is discussed in 

more detail in the section on errors and precision of this method.
DETERMINATION OF RADIUM IN WATER Bll

The least-squares equation for a multiple linear regression (a plane) 

could also be used to estimate the concentrations of the three isotopes. 

However, the small improvements in the precision of the results for 

radium-223 and radium-224 are somewhat offset by a decrease in the 

precision of the results for radium-226 and the total short-lived 

isotopes. Therefore, the more tedious calculation involved in this 

procedure is not considered justified for any slight advantage that 

might be gained when working with natural, unpolluted water.

APPARATUS

Much of the apparatus needed is commonly found in a chemical

laboratory and will not be listed. Special items are listed below:

Centrifuge, size 1, preferably refrigerated. An unrefrigerated

centrifuge can be used if it includes large cups that can be

packed with ice so that 50-ml centrifuge tubes can be chilled

during the centrifugation. 

Molecular membrane filters, 0.45-micron pore size, black, 45-mm

diameter

Filtration assemblies for membrane filters (fig. 1) 

Ring-and-disk sample mounts (fig. 2) 

Alpha-counting equipment as described on page B4 (fig. 3)

REAGENTS

Ammonium hydroxide, concentrated. reagent-grade, 28-30 percent 

NH3 .

Ammonium sulfate solution. Dissolve 400 g of reagent-grade 

ammonium sulfate in 1 liter of hot distilled water; cool and filter the 

solution.

Barium carrier solution (8 mg Ba+* per ml). Dissolve 1.5 g of 

reagent-grade barium nitrate in distilled water and dilute to 100 ml.

Hydrochloric acid-ether reagent. Mix six parts, by volume, of 

concentrated (36-38 percent HC1), reagent-grade hydrochloric acid 

with one part of reagent-grade ethyl ether.

Lead carrier solution (100 mg Pb+2 per ml). Dissolve 15.5 g of 

reagent-grade lead nitrate in distilled water and dilute to 100 ml.

Nitric acid, concentrated. reagent grade, 69-71 percent HNO3 .

Nitric acid, 0.1 normal. Dilute 6.5 ml concentrated nitric acid 

to 1 liter by adding distilled water.

Radium standard solution (1 pc Ra226 per ml). Dilute 10 ml 

radium standard-stock solution (p. 21) and 10 ml concentrated 

(36-38 percent HC1) hydrohcloric acid to 500 ml by adding distilled 

water.

Sodium sulfate solution. Dissolve 10 g of reagent-grade sodium 

sulfate in distilled water and dilute to 100 ml.
B12 RADIOCHEMICAL ANALYSIS OF WATER

Sulfuric acid, concentrated. reagent-grade, 95-98 percent H2SO4 .

Sulfuric acid wash solution. Dilute 5 ml of concentrated sulfuric 

acid to 1 liter by adding distilled water and add 10 ml of saturated 

Aerosol OT solution.

PROCEDURE

1. Select a volume of sample containing no more than 350 mg of 

calcium, and filter if necessary. Add 5 ml of concentrated nitric 

acid and evaporate to dryness in a 400 ml beaker on a steam table. 

If the volume of sample exceeds about 300 ml, the evaporation must 

be performed stepwise; however, the beaker should not be allowed 

to become dry before adding the next part.

2. Prepare two standard solutions, each consisting of 25 ml of 

radium standard solution (25 pc) and 1 ml of sodium sulfate solution, 

and a blank solution consisting of 1 ml of sodium sulfate solution. 

Dilute by adding distilled water to about 100 ml, add 5 ml of concentrated nitric acid, and evaporate to dryness in the same manner 

as the samples.

3. Wash each beaker with 0.1 N nitric acid, policing thoroughly, 

and transfer each residue to a 50 ml centrifuge tube. Centrifuge at 

about 500 gravities for 5-10 minutes.

4. Transfer the supernatant liquid to a 250 ml centrifuge bottle. 

Wash the precipitate thoroughly with 30-40 ml of 0.1 N nitric acid. 

Centrifuge, and add the wash solution to the supernatant liquid in 

the centrifuge bottle. Repeat the washing step, adding the second 

wash solution to the centrifuge bottle. Discard the residue.

5. Add 2 ml of concentrated sulfuric acid to the combined solutions 

and mix well. While stirring vigorously, add 1 ml of lead carrier 

solution (100 mg of lead). Continue stirring for 10 minutes.

6. Place the centrifuge bottle in an ice bath and continue stirring 

for at least another 15 minutes. Centrifuge and discard the supernatant liquid.

7. Dissolve the precipitate in 20 ml of hydrochloric acid-ether 

reagent and transfer to a 40-50 ml centrifuge tube. Wash the centrifuge bottle with 5 ml of hydrochloric acid-ether reagent, and add 

to the centrifuge tube.

8. Cool the solution in an ice bath. While stirring, add 0.50 ml 

of barium carrier solution (4 mg of barium). Continue stirring for 

at least 5 minutes. Note: steps 8, 9, 10, and 11 should be performed 

as rapidly as practicable; avoid unnecessary delays.

9. Centrifuge in a refrigerated centrifuge at about 500 gravities for 

10 minutes. (An ordinary centrifuge may be used, but the centrifuge 

tubes must be placed in ice-packed cups.) Discard the supernatant 

liquid.
DETERMINATION OF RADIUM IN WATER B13

10. Dissolve the precipitate in 25 ml of 0.1 N nitric acid, warming 

if necessary, and transfer the solution to a 250 ml beaker. Wash the 

centrifuge tube several times with 0.1 N nitric acid, adding the 

washings to the beaker.

11. Dilute to about 150 ml by adding distilled water, add a few 

drops of methyl-orange indicator, and adjust to the yellow end point 

by adding ammonium hydroxide. Add a few drops of concentrated 

nitric acid to restore the red color. Heat to incipient boiling point and 

add 10 ml of ammonium sulf ate solution (4 g of ammonium sulf ate) ; stir 

until the precipitate forms. (Note and record the time of precipitation as the time of separation of radium from its daughter nuclides.)

12. Allow the solution to digest at room temperature for at least 

4 hours, then collect and mount the precipitate in the manner described for the single-carrier-precipitation method.

13. Determine the alpha activities of the precipitates at six times 

by alpha-counting. A near-optimum schedule for the counting, 

measured from the time of separation of radium from its daughter 

nuclides, is: 1st day, 2nd day, 3rd day, 5th day, 13th-15th day, and 

30th-40th day. One-hour counts are recommended for each precipitate including the standard solutions and the reagent blank solution. 

If no correction is to be made for radium-223, measurements need not 

be made after the 15th day. Tabulate the data in a form such as 

that shown in figure 4.

CAIX3ULATION OF RESULTS

The complete derivation of the equations used in the isotopeidentification method are found starting on page B22.

If the results are not to be corrected for any radium-223 present,

the concentrations of radium-224 and radium-226 are found as follows :

1. Calculate the average, net counting-rate of the standard solutions

for each set of measurements (through the 15th day) by the

equation

and calculate the net counting-rates of the samples for the same 

sets by the equation

TX

where

Rs average net counting-rate of standard solutions 

JBa;=net counting-rate of sample
RADIUM ISOTOPE IDENTIFICATION METHOD

Sample Description 

Final Separation: Date. Time: Volume ml: Stand

Date 

counted Item

Std. A

Std. B

Same.

Std. A

Std. B

Samp.

Std. A

Std.B

Samo.

Std. A

Std.B

Samo.

Std. A

Std.B

Samp.

Std. A

Std. B

Samp.

Time

Total 

count

At 

(min)

Blank 

(cpm)

Net Rate 

(cpm)

t 

(hrs) G(t,M)

Relative 

activity

(Y) 

Totals 1 

Ra___Assumed negligible 

Ra226 __________±_ 

Ra 224 __________±_

pc/1

PC/1

FIOTTBE 4. Form used to tabulate data and calculate results of isot
DETERMINATION OF RADIUM IN WATER B15

Nit N2 , and Nx= total counts observed for the two standard solutions and the sample, respectively

TI, T2 , and TX= counting times for the two standard solutions and the sample, respectively

B= average counting-rate of the blank solution.

Determine the value of the function G(t, Atf) from the graph in 

figure 5, where t is the time elapsed between the separation of 

radium from its daughter nuclides and the measurement of the 

alpha activity, and Atf is the difference between the time when the 

sample was counted and the time when the standard solutions 

were counted. G(t, A£) is a function to relate standard-solution 

and sample counts to the same time base.

Calculate the value of the function Y for each set of measurements, 

using the equation

 

' R,G(tit A*)

where

S=the amount of radium in each standard solution,

generally 25 pc

Fi=the activity of the sample compared to the standard 

solution at any time it.

Determine the values of the function <p(t) from the graph in figure 

6 and estimate the weighting factors, Wi} from the graph in 

figure 7. <p(ti) is the ratio of the alpha activity of radium-224 

compared to radium-226 at any time tt. Values of <p(tt) are the 

x values of the least-square equations. The function <p(tt) is 

described more fully on pages 23-25.

Calculate the concentrations of the radium isotopes from the leastsquare equations

DV 

and

DV 

where

V= volume of sample, in millimeters.
1.140

1.120 -

1.100 -

1.080 -

1.060

1.040 -

1.020 -

1.000

0.980

0.960

0.940

0.920

0.900

0.880

0.860

10 20 30 40 50 60 70 80 90 100 110 120 130 140 

TIME SINCE PURIFICATION (t), IN 

FIGURE 6. Plot of the function 0(t, AQ for differen
DETERMINATION OF RADIUM IN WATER B17

I
B18

1000 

100

S '°

£ 

3

I

J 

J

Jj

5 1.0

0.1 

n m

RADIOCHEMICAL ANALYSIS

s.I-X

\

N

^ ^^

"^-

Pa ran

Backg 

_ Stand 

Count

\

\

X

^

RS --

leter 

roun 

ard s 

ingt

\ 

\

\

N

bS

d

olu 

me

\

^s

S

S

S^

S

s

X,

S

s

s

s,

\,

s ^

\

S

]

s

tions___.

s

\

\

s

s

10

^ ^

\

s\

\\

Vzo^1

X

v 

X\

\

0.06 cp 

25 pc 

SOmin

^\

V\

>

v

\

m

)

\

SN\

N

\

\

\\S

\

S

sN

\

S

^

N

v

\

\

\^

s

V

OF WATER

iv-w 

s \\

, v\

\ \\v Yv\^

\

!\

NS

\

S

^vn-SS

^ ^

A

^. ^

\

V

s^V

\s 

s

0.1 1.0 10 

RELATIVE ACTIVITY OF THE SAMPLE (Y)

100

FIGTJEE 7. Weighting factors for the individual measurements.
DETERMINATION OF RADIUM IN WATER B19

The relative counting rates of various mixtures of radium-226

and radium-224 are plotted against time in figure 8. This graph

is useful in estimating the relative amounts of the isotopes and

checking the accuracy of the calculated results.

6. Calculate the variances of the concentrations from the equations

The precisions of the concentrations are best expressed as

standard deviations (o-), probable errors (0.675o-), or 95-percentconfidence limits (2o-). The U.S. Geological Survey uses the 2oindex to indicate the precision of radiochemical analyses.

If the results are to be corrected for radium-223, proceed as follows:

1. Determine the least-squares constants from the first five sets of 

data as described above. These constants are denoted as A 

(instead of Ra226) and E (instead of Ra224).

2. Calculate the value of the quantity Z from the sixth set of data 

using the equation

7_WWSRt 

VRS

and determine the value of the function \f/(t) for the time the 

sample was counted. $(f) is the ratio of the growth-decay 

equation for radium-223 to that of radium-226 and is equal to

40-0.00258*_ e\. 1520*

4.001 3.010e-°- TO755 '+0.021e-1 - 652' 0.012<r2- m'

A graph similar to figure 6 (<pt versus t) can easily be prepared 

for (\l/t versus t) to facilitate computation.

3. Calculate the concentrations of the isotopes by the equations

0.40-^(0

Ra223=^4~Z

Ra224+Ra223 =£
B20 RADIOCHEMICAL ANALYSIS OF WATER

100 200 300 400 500 

TIME SINCE PURIFICATION (t), IN HOURS

600 700

FIGURE 8. Growth and decay of alpha activity In mixtures of radium-224 and radium-226.

4. Calculate the variances of the concentrations by the equations

<r2 Ra228=^

[0.40-tff 

<r2 Ra224+Ra223=<r2#

a2 Ra223 =

"[0.40-^(0?
DETERMINATION OF RADIUM IN WATER B21

The precision of the results may be expressed in any convenient 

form as discussed previously.

The calculations described above may be carried out most easily 

by using a suitable form for tabulating the various quantities and 

results of the intermediate calculations. A worksheet that is convenient for this purpose is shown in figure 4.

ERRORS AND PRECISION

Although the isotope-identification method is much more specific 

for the radium isotopes than is the single-carrier-precipitation method, 

some other radioactive substances may interfere. Small fractions 

(not exceeding 10 percent) of any actinium and bismuth present are 

carried in the precipitate. The only natural isotopes of these elements that can have a significant effect on the results, when the prescribed schedule for counting is followed, are actinium-227 and 

bismuth-210. Actinium-227 interferes owing to the growth of thorium-227 and other alpha-emitting daughter nuclides. The overall 

effect is that about 9 percent of any actinium-227 is reported as 

radium-226 and about 0.2 percent of any bismuth-210 is reported as 

radium-226 and radium-224. These radionuclides generally may be 

neglected because of the low efficiency and their small natural abundances in most waters; however, some waters polluted by uraniummill wastes might contain sufficient actinium-227 to cause a significant 

error in the analysis.

Error also occurs when the isotope radium-223 is not or cannot be 

measured separately. Under these conditions the value reported for 

radium-226 will be too large by an amount equal to 40 percent of the 

radium-223 actually present.

The random errors that determine the precision of the method result mainly from the randomness of the radioactive-decay process 

and the nonuniformity of the deposit of barium sulfate on the filter. 

The precision is a function of the ratios of the amounts of the isotopes 

present, each isotope being determined most precisely when the 

amounts of the others are small. The precision with which the isotopes radium-223 and radium-224 can be reported individually is 

always rather poor; however, the precision of the sum of the two is 

comparable to the precision of the radium-226 value.

PREPARATION OF RADIUM STANDARD-STOCK SOLUTION

A radium standard-stock solution containing 50 pc of radium per 

milliliter is prepared from a National Bureau of Standards radium-226 

gamma-ray standard solution containing 0.1 ng (microgram) of radium226. The standard solution, as received, consists of about 3 ml of 

solution in a glass vial. Although the activity is low, care should be
B22 RADIOCHEMICAL ANALYSIS OF WATER

taken to prevent ingestion of the solution or contact of the solution 

with an open wound; therefore, it is advisable to wear rubber gloves 

when handling the standard solution and making the initial dilution. 

Drop the vial into a clean 1-gallon pyrex bottle fitted with a sarancovered rubber stopper. Break the vial by shaking vigorously, then 

add approximately 1 liter of distilled water. Shake thoroughly, then 

let the solution remain in contact with the broken vial for 1-2 hours. 

Transfer the solution to a 2-liter volumetric flask, leaving the vial in 

the bottle. Add 50 ml of concentrated hydrochloric acid (36-38 

percent HC1) to the bottle, and let the acid remain in contact with the 

broken vial for at least 12 hours. Transfer the acid to the volumetric 

flask containing the raduim solution, rinsing the bottle several times 

with small amounts of distilled water which are also added to the 

volumetric flask. Dilute the solution to 2 liters by adding distilled 

water and mix thoroughly.

DERIVATION OF EQUATION FOR CALCULATING RESULTS 

OF ISOTOPE-IDENTIFICATION METHOD

When natural radium is freshly purified, the only alpha activity 

is that due to the isotopes radium-223, radium-224, and radium-226. 

However, other radionuclides, called radioactive daughters begin to 

form immediately as a result of the radioactive disintegration of the 

radium atoms. The radium isotopes decay, and their radioactive 

daughters grow and decay at rates characteristic of their several 

half lives. Some of these daughter nuclides are alpha emitters; thus, 

the alpha activity of an initially pure radium isotope varies with 

time in a manner determined by the half life of that isotope and the 

half lives of its various daughters. The relation between growth 

and decay of radioactivity and the half lives of the parent and daughter 

nuclides is discussed in any standard text on radiochemistry for 

example, Priedlander and Kennedy (1955, p. 127-137).

The alpha-emitting daughter nuclides that grow into a mixture of 

radium isotopes to a significant extent within a few weeks are listed in 

table 1. The half lives of the various radionuclides, the factors that 

control the rates of growth and decay of radioactivity, differ for each 

of the decay chains. Therefore, the growth and decay of alpha 

activity in a mixture of radium isotopes will be a complex function of 

the amount of each isotope present. Figure 8 shows the variation of

TABLE 1. Shortrlived alpha-emitting daughters of the radium isotopes

Parent _______________ Ra223 Ra224 Ra226

Daughter.........._.____ Rn"9 Rn220 Rn222

p0215 p0216 

p0211
DETERMINATION OF RADIUM IN WATER B23

alpha activity with time for certain binary mixtures of radium-224 and 

radium-226. Ternary mixtures, containing radium-223 in addition 

to the other two isotopes, would produce more complex growthand-decay curves.

Radium-223 is generally not a major constituent of natural water 

because it is sparsely abundant in nature less than 5 percent that of 

radium-226, in terms of radioactivity. Natural waters polluted with 

uranium-mill wastes often contain considerable amounts of radium223. Usually, only radium-224 and radium-226 need be considered 

when measuring the alpha activity of purified radium samples derived 

from natural water. The equation which describes the alpha activity 

of such a binary mixture as a function of time is :

 0.012<r 2- m')

- 687 ') (1)

where

A= total activity of radium-226 and radium-224 at any time, t 

Al= activity of radium-226 at t=0 

.^2 activity of radium-224 at t=0 

£=time elapsed, in hours, since separation of the radium isotopes from their parent and daughters 

e=base of natural logarithms.

This equation is only approximate, but it is valid within 0.1 percent 

over the range from 1 hour to 100 days, assuming the decay constants 

are accurate to three significant figures. More complete equations 

for this and other systems involving members of the three natural 

radioactive series were given by Kirby (1953).

Assuming that the alpha counter used is equally sensitive to alpha 

particles from all radium isotopes and their daughters, the following 

equation applies:

Rt(f)=ExA=Ex(A°J(f) +AlF(f)] (2) 

where

counting rate of the sample at tune, t 

Ex= overall efficiency with which the sample is measured. 

This includes chemical yield as well as counting efficiency.

- 552 ' 0.012<r 2- m<

Stehney (1955) determined radium-226 and radium-224 in water 

using a similar equation. Values of Ex (t) and t from two measurements were substituted in the equation, and the resulting simul-
B24 RADIOCHEMICAL ANALYSIS OF WATER

taneous equations were solved for A° and A°2. A third determination 

usually was made as a check.

More precise results can be obtained by counting the sample and 

standard solutions five times during a period of about 15 days from 

the time of purification and fitting the data to the equation by statistical methods. The basic equation can be transformed into one 

amenable to treatment by the method of least squares using the procedure described below.

The net counting rate of the radium-226 standard solution at any 

time, t, is:

R,(t)=E3SJ(t) (3) 

where

Ri(t) = aver age net counting rate of radium-226 standard solution

at time, t

.Es= over all efficiency with which the standard is measured 

S amount of radium-226 in the standard solution, in picocuries.

Then, assuming the efficiencies are equal for both sample and standard 

solution,

SRx (t)_ , , A0 F(t) f .

- l+ * (4)

The standard solution and the sample cannot be counted at the 

same time in the same instrument; thus a correction factor must be 

applied to adjust the measurement of the standard solution to the 

time when the sample was counted. The value of this factor depends 

on the time elapsed since purification of the radium and on the 

difference between the time when the sample was counted and that 

when the standard solution was counted. The equation describing 

the counting rate of the standard solution as a function of time (t) 

can be written in the form

R,=ESf(t+At) (5)

Taking the arbitrary time to be that time at which the sample is 

counted, and combining equations (3) and (5), the net counting rate 

averaged for the two standard solutions is

«) (6) 

where

=
DETERMINATION OF RADIUM IN WATER B25

The function G(t, Af) has been evaluated over the range of interest 

and is shown graphically in figure 5.

By combining equations (4) and (6), the equation for the variation 

of counting rate as a function of both time and the amounts of radium 

isotopes present can be written

where

The values of <p(t} for times from 20 to 500 hours are shown graphically 

in figure 6.

Equation 7 is of the form Y=a-{-bX and can be evaluated by a 

method of least squares for linear regression. The values of <p(f) for 

times from 20 to 500 hours are known very accurately compared with 

values of the quantity on the left-hand side of the equation ; therefore, 

the least-squares equations for the case where only Y is subject to 

error can be applied. This method is described in most texts on statistics or data-handling techniques for example, see Worthing and 

Geffner (1943, p. 238-266). Letting

the appropriate equations are

(ii)

where the subscript i refers to any individual set of measurements and 

wt is a weighting factor which adjusts the contribution of each measurement of Y according to its reliability.

In the absence of conflicting information, weighting factors usually 

are considered to be proportional to the inverse of the variance. 

Thus,

K
B26 RADIOCHEMICAL ANALYSIS OF WATER

where

HC=any arbitrary proportionality constant applied to a set of

data 

a-i2= variance of the ith measurement of Y.

The overall efficiency does not appear in the final equation because 

the efficiencies for the samples and standard solutions were considered 

equal and, therefore, were cancelled. However, there is an uncertainty in this equality owing to variations in the instrument, barium 

sulfate deposits, sample position, and so forth. This uncertainty 

must be considered in calculating the variances and the weighting 

factors for the measurements. The statistics of counting also must 

be considered.

Placing the individual values of the efficiencies into equation 8,

_ 2SEtRx

The net counting rates are obtained by subtracting the counting-rate 

of the blank solution from the observed counting-rates. Thus,

RX=CX -B, (14a) 

and

RS=C,-B (14b) 

where

C= an observed counting-rate 

.B=background counting-rate.

The variance of an observed counting-rate, including background, 

depends only on the total number of counts observed and the counting 

time (provided instrument variations are negligible) according to the 

equation

ff *=N/i* 

where

N= observed number of counts 

T=time interval during which N counts were collected.

Applying the general equation for calculating the variance of an 

indirectly measured quantity to equation 13, and using equations 14a, 

14b, and 15 for substitutions, the variance of Fis found to be
DETERMINATION OF RADIUM IN WATER B27

where

o-«2= variance of counting efficiency of samples and standards 

Afj:=number of sample counts in time, rx 

Nt= number of background counts in time, T6 

Af,= number of sample counts in time, TS .

When Y is equivalent to several picocuries, both standard solutions 

are counted for the same length of time, and At is only a few hours, the 

following approximations and equalities may be used:

E,=E,=E

Nx=Rxrx

ft A*)

The variance of Y then is approximately

2, 'V

, .

Under conditions generally met in the Denver laboratory and for 

samples containing more than about 2 pc of radium, the following figures may be used:

0.0025

t, A£) ~ 15-50 (depending mainly on time after separation) 

J5«0.09 

T6=300

The approximate equation for the variance then can be put in the form

2 _ °-017 °-0012 _

0.058 0.030 - y 0.75 , ,

"'" 1 u ;

The weighting factors, calculated as the reciprocals of the variances 

given by this equation, are shown as functions of Fand ^LtRs G(t, At) 

in figure 7.

Because only the ratios of the weighting factors, not their absolute 

values, are significant, and even these need be only approximate, this
B28 RADIOCHEMICAL ANALYSIS OF WATER

graph can be used in many situations where the numerical values of 

certain parameters are not equal to those used in making the graph. 

If some radium-223 is present in the sample, the above derivation 

is not valid. However, it can be shown that a straight line fit to the 

data will provide consistent results over a wide range of concentrations 

of the radium isotopes. The ternary-mixture equivalent of equation 

7 can be written

(19)

where ^(2) is the ratio of the growth-and-decay equation for radium223 to that for radiuin-226. The least-squares equations for a 

straight line through the values of Y then take the forms

,o 

np_ 2 -

Evaluation of the coefficients of A3 in the above equations, for the 

counting times recommended in this report (1, 2, 3, 5, and 15 days), 

gives values of A and B of

(22)

(23)

The individual isotopes can be evaluated if another measurement 

is available after the radium-224 has decayed to a negligible value, 

say 30 days after purification. The quantity is calculated from this 

measurement by the equation

,~A\ C24)

The value of Z is a function of the amounts of radium-223 and radium224 in the sample:

Z=Ka226+(0 Ka223 (25)
DETERMINATION OF RADIUM IN WATER B29

where (t) is the alpha activity of an originally pure radium-223 

sample t days after purification. Equations 22, 23, and 25 can be 

solved simultaneously to give values for the three isotopes. However, 

the precisions of the individual values are generally rather poor.

REFERENCES CITED

Ames, D. P., Sedlet, J., Anderson, H. H., and Kohman, T. P., 1949, Rapid radiometric assay for radium and application to uranium ore process solutions, 

Paper 22.70, in Seaborg, G. T., Katz, J. J., and Manning, W. M., The transuranium elements: New York, McGraw-Hill Book Co., Nat. Nuclear 

Energy Series, Div. 4, v. 14B, p. 1700-1716.

Baratta, E. J., and Herrington, A. C., 1960, The determination of isotopic radium: 

U.S. Atomic Energy Comm. WIN-118, 27 p.

Barker, F. B., and Robinson, B. P., 1963, Determination of beta activity in water: 

U.S. Geol. Survey Water-Supply Paper 1696-A, 32 p.

Barker, F. B., and Scott, R. C., 1958, Uranium and radium in the ground water of 

the Llano Estacado, Texas and New Mexico: Am. Geophys. Union Trans., 

v. 39, p. 459-466.

Barker, F. B., and Thatcher, L. L., 1957, Modified determination of radium in 

water: Anal. Chemistry, v. 29, p. 1573-1575.

Bate, G. L., Volchock, J. L., and Kulp, J. L., 1953, A low level radon counting 

system: U.S. Atomic Energy Comm. NYO-6202, 21 p.

Evans, R. D., 1935, Apparatus for the determination of minute quantities of 

radium, radon, and thoron in solids, liquids, and gases: Rev. Sci. Instruments, 

v 6, p. 99-112.

Friedlander, Gerhart, and Kennedy, J. W., 1955, Nuclear and radiochemistry: 

New York, John Wiley and Sons, 468 p.

Hursh, J. B., 1954, Radium content of public water supplies: Am. Water Works 

Assoc. Jour., v. 46, p. 43-54.

Kirby, H. W., 1953, Decay and growth tables for the naturally occurring radioactive series: U.S. Atomic Energy Comm. MLM-859, 30 p.

National Committee on Radiation Protection, 1959, Maximum permissible body 

burdens and maximum permissible concentrations of radionuclides in air 

and in water for occupational exposure: U.S. Nat. Bur. Standards Handb. 

69, 95 p.

Petrow, H. G., Nietzel, O. A., and DeSesa, M. A., 1960, Radiochemical determination of radium in uranium process samples: Anal. Chem., v. 32, p. 926.

Russell, E. R., Lesko, R. C., and Shurbert, J., 1950, Determining radium in 

exposed humans: Nucleonics, v. 7, p. 60-64.

Scott, R. C., and Barker, F. B., 1959, Radium and uranium in ground water of the 

United States: United Nations Conf. on the Peaceful Uses of Atomic Energy 

2nd, Geneva 1958, Proceedings, v. 2, p. 154-157.

 1962, Data on uranium and radium in ground water in the United States 

1954 to 1957: U.S. Geol. Survey Prof. Paper 426, 115 p.

Stehney, A. F., 1955, Radium and thorium in some potable waters: Acta Radiologica, v. 43, p. 43-51.

U.S. Public Health Service, 1962, Drinking water standards, 1962: U.S. Public 

Health Service Pub. 956, 61 p.

Worthing, A. G., and Geffner, Joseph, 1943, Treatment of experimental data: 

New York, John Wiley & Sons, 342 p. (sixth printing, 1950).