A. W. Fairhall
University of Washington Seattle
Dating of Uranium Minerals by the Specific Radioactivity of Lead
This paper discusses a method for estimating the age of a uranium mineral without recourse to elaborate mass-spectrometric techniques.' The method is admittedly a very crnde one; however, its purpose is not intended to be an alternative to the more accurate dating methods based on lead isotope ratios. Instead it serves as the basis for a few simple radiochemical manipulations, which are instrnctive in themselves, and as an illustration of the principle of age determination of a mineral via radioactivity. The required manipulations are fundamental to radiochemistry and at the same time so simple that the outlined experiments are suitable for use at the undergraduate or senior high school level. Only very rudimentary equipment is required, consisting of a Geiger counter, a set of aluminum absorbers, and a few elementary pieces of chemical apparatus. The raw material for the experiment, pitchblende ore, is readily
their &fications.
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obtainable from mineral specimen supply houses and only a small quantity is required per student. Reagent grade uranyl nitrate, available from a number of chemical supply houses, is the only other special chemical which is needed. As outlined in detail below, the experiment is carried out in two parts, each of which may be completed in a 4-hour laboratory period. The second part is optional and the teacher may instead provide the students with the information (the counting efficiency of the counter) afforded by doing this part of the experiment. It is suggested that the students work in pairs. In addition to the regular laboratory period it will generally be advantageous if the students can have access to the counting equipment for about 3 ta 4 weeks in order to measure periodically the radioactivity in the samples; however, only one measurement can suffice for the first experiment provided it comes at least 5 days after the chemical separation. The teacher will recognize that in addition to the two experiments outlined below there are other experiments which the student may perform using the same
radioactive samples. These include (a) studies of backscattering of fl radiation by various thicknesses and various kinds of material, (b) the determination of a decay curve, (c) determination of the complete absorption curve of a sample for an estimation of the range of a given fl emitter, ( d ) separation of Biz" from PbZIQby a variety of techniques. The pitchblende ore is a rich source of other radioelements which the student can isolate, for example, radium and polonium, and it can serve as the starting point for other radiochemicalexperiments. The dating method has been tested on a few minerals which have been accurately dated by mass-spectrometric techniques.% These specimens were furnished through the courtesy of Professor Wallace R. Broecker and Mr. Ian G. Swainbank of the Lamont Geophysical Observatory. Samples of these minerals were given to a class of 12 students in the author's senior-level laboratory course in radiochemistry. The results are tabulated in Table 1. It is seen that rather good agreement between this method and the known age of the minerals was achieved in a few instances, and even in the poorest cases the results are "in the right ball park." Table I.
Results Using Mineral Specimens of Known Age
Student group
Sample no."
1 2 3 4 5 6
K 6 K 1!l IC105 K105 K120 K120
Age of mineral (in ym) 6 X 8 X 3.4 X 3.4 X 1.6 X 1.6 x
10' 108 lo8 loa 10)
lo9
Age, this method (in yrs) 14 X 1 0 " 6 . 9 X 10' 3 . 8 X 108 2 . 9 X 108 1 . 7 X 10e 1 . 2 X 10"
Sample designations ae given in footnote 2. "his specimen is pnrtieularly young and contamination by non-radiogenic lead is relatively severe, amounting to 72% of the lead content. Allowing for this fact, the spperent age which is outained is close to the value to be expected by the present method. Isolation of Radiogenic Lead and Measurement of Its Beta Activily
Consider a uranium mineral, such as pitchblende (U308)for example, which a t some time, t, in the past has crystallized or otherwise been deposited in solid form. If a t the time of deposition a fractionation occurred such that the uranium-bearing mineral was formed free of lead, either "ordinary" lead or lead which had formed prior to t through radioactive decay of uranium, then decay of the uranium subsequent to time t will result in an accumulation of lead in the uranium mineral. Radioactive decay of uranium produces lead through two long sequences of u and @ decays. A few key steps in these sequences are as f0llou.s :
UPa6
40's
lives (UZ", 4.51 X lo8 yrs; P5 7.1 X lo8 yrs) their relative numbers of atoms change with time. If we consider 100 n uranium atoms now, where n is some unspecified but very large number, then we have 99.28 n atoms of UZa8and 0.72 n atoms of UZa5. ACcording to the laws of radioactive decay, t years ago there were 99.28 n dz3"atoms of U238and 0.72 n eUas1 atoms of W5. Here X refers to the decay constant of the radionuclide in question and is numerically equal to 0.693/half life. Since the total weight of each uranium isotope is proportional to the number of atoms and their atomic weights, the proportionality constant being the reciprocal of Avogadro's number N, we can write n Wt Us" (t) = 99.28 - ,238 ehzs1g N
(1)
Evidently the difference between the weights of uranium isotopes at time t given by these expressions and the corresponding weights of uranium isotopes present now, 99.28.n/N.238 g and 0.72.nlN.235 g, respectively, represents the weight of the uranium isotopes which have disintegrated in the intervening t years. Thus Wt UPa8 disintegrated
- 1)g = 0.72m/N.235 (eh2J5'- 1)g
=
Wt Uassdisintegrated
99.28.n/N.238(e"'"
(3) (4)
According to the decay sequence of the radioactive species, each 238 grams of U2" which disintegrate gives 206 grams of PbZo6,the remaining mass being that of the a particles which were emitted. Likewise each 235 grams of U235gives 207 grams of Pb*. Thus we can write for the weight of accumulated lead isotoves in the mineral Wt Pbm'accumulated = 99.28.n/N .238(ehZsL- 1) 206 238 207 Wt Pbm7accumulated = 0.72,n/N .235(e"'"' - 1) 235
The ratio of equation (5) to equation (6) is seen to he a function of t, and hence the ratio PbZo6/PbZo7 is a sensitive measure of the age of the mineral. However the determination of this ratio requires massspectrometric techniques. The present simplified method is based on the sum of equations (5) and (6) : Total wt Pb accumulated =
n
199.28 X 206(ehl"' - 1 )
+ 0.72 X 207(e"P" - I)]
The weight of accumulated lead in comparison with the weight of uranium remaining in the mineral may be expressed as the ratio: Ph201(stable)
At the present time uranium is made up of 99.28 atom per cent U2" and 0.72 atom per cent UZS6. Because these two isotopes of uranium have different half %ECKELMANN, W. R., AND KULP,J. L., Bull. Geol. Soe. Am.,
w t accumulated Pb =
wt of U remaining n -
N
+ 1.49 X 1O1(ehXw5' - I)] ,-n [99.28 X 238 + 0.72 X 2351
[2.05 X 10'(ehzm'- 1)
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This ratio is plotted in Figure 1 for various values of the time t. It will be seen from this figure that for minerals less than about 70 X 106 years old the radiogenic lead is less than ly0 by weight of the uranium present. Such young minerals are more difficult to date by the present simplified method, requiring somewhat larger samples in order to have sufficient recoverable lead; and the results are more sensitive to traces of non-radiogenic lead in the miueral.
.
-
a
LL 3
-.
0
a
-
-
.
-
where T refers to time after chemical isolation of : from the mineral in the laboratory. Therefore total radioactivity of the lead isolated from the min is
I n both of the expressions (10) and (11) we considering times T of the order of one month, wl is short relative to the half life of Pb210 (19.4 That is, for a time short relative to the half lift PbZlothe change in the disintegration rate of PI and hence in the equilibrium value of BiZ'O, insignificant. Let us now consider the specific activity of the lated lead fraction. Specific activity is defined as number of radioactive disintegrations per unit t per unit weight of a substance. In our present exan this is given by the ratio of equation (11) to equal
(7): Specific activity of lead = hs8 X 99.28 X n(2 - e-hBiPloT) n - P.05 X 104(eua" - 1) 1.49 X 102(e"zssL N
-
+
-
. .
a '
10'
10'
AGE OF MINERAL
10'
(YEARS)
Figure 1. Ratio of the weight of accumulated lead tothe weight of uranium remaining as a functionof the age of the mineral.
I n equation (7) we have neglected the weight of Pb'" formed as an intermediate because it is present in exceedingly small amount, by weight. I n terms of its radioactivity, however, it gives the same number of disintegrations per unit time as does the U238in the specimen, the reason being that the decay sequence is in a state of secular equilibrium. This means that for each of the species in the sequence the rate of formation is equal to the rate of decay, and a steady state exists. In the example which we are considering, namely 99.28.n atoms of UZa8 present now, the decay rate of Ph210in the sequence is equal to the decay rate of U2", which in turn is given by decay rate UzJ' = hpagX 99.28-n atoms dis per see.
(9)
This is also the disintegration rate of Biz", the species formed by decay of Pb210. Suppose, however, that we now make a chemical separation of lead from the mineral, leaving behind all other elements, radioactive or otherwise. Approximately three hours after the chemical separation, the radioactivity in the purified lead is just that of Pb210.J However, the decay of Pb210produces fresh Bizlowhich soon accumulates in sufficient amount to contribute its own radioactivity to that of the Ph210;after a few weeks the Bi2'O and Pb2I0have come into secular equilibrium with each other and both have the same decay rate. The equation which gives the growth of Bizloactivity with time is given by the expression d/see Biz10 = d/sec Pb2" (1 - e-ABifloT) (10) =At the time of the chemical separation there is present also 26.8 m Pb2", the antecedent of Pb2'0. This activity and its immediate decay products soon decay completely to Pbz'o.
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Journal of Chemical Education
Note that in this expression the quantity n cancelled from numerator and denominator. Si this quantity represented essentially the amount uranium being considered in our example, its can lation from the equation means that the specific acfi of lead given by equation (12) i s independent of amount of uranium under consideration. It is I independent of the efficiency with which the lead he recovered from the mineral. The specific a c t i ~ of lead isolated from a uranium mineral depends o on the time, t, since the mineral was deposited lead-! in nature and the time T following the chem isolation of lead from the mineral in the laboratc Curve A of Figure 2 is a graph showing the spec
OF
LEADDUETO
OF
LEAD DUE TO
VI
m (r
a
Figure 2. Specific activity of lead reporated from a uranium mineral I function of time after the reparotion. Curve A refers to the totol radic tivity in the lead,cvrve Btothe radioactivity dueto Bi"oonly. Secular e librium is attained after .bout 1 month.
,ctivity of the lead as a function of T. The secular quilibrium value is reached after about one month. In practice, the observable specific activity of lead 3olated from a uranium mineral is due soley to the 3i21° daughter of PbZIO. The reason is that the radiaions emitted by Ph210are so low in energy that esentially none of them penetrate the usual type of letectors used to measure the radioactivity. On the ~therhand, the radiations of Bi210 are sufficiently )euetrating that practically all of them are detectable. rherefore, the observed specific activity of purified lead ollows curve B in Figure 2 rather than curve A, and ~t secular equilibrium the observable specific activity s one-half of that given by equation (12) : Ihserved specific activity of lead ttt equilibrium
lead present. A more sophisticated technique involving mass spectrometric analysis of the isolated lead is required for accurate dating of uranium minerals contaminated with ordinary lead. Figure 4 is a graph showing the apparent age versus the true age of a uranium mineral for various proportions by weight of radiogenic lead and contaminating lead in the specimen. Of course if the mineral incorporated some of its previously-formed radiogenic lead during recrystallization there is no way to determine whether this type of contamination has indeed occurred and an older apparent age will result. Experiment Dating Uraninite Minerals
Place a small quantity (about 100 mg) of the mineral in a 1 5 4 centrifuge tube. Add 10 drops each of 2.05 X 104(e"23B' - 1) + 1.49 X lO2(ehPZ6'- 1) conc. HiYOa and H2S01and heat to boiling (caution!) glead (I3) over a burner. The U8O8will dissolve readily in this The observable smcific activity of chemicallv mixture at a rate denendent unon . . . narticle size. As the in Figure 3 as solated lead, due only to B P , is acid boils away replenish with more conc. HN08. L function of the uranium mineral formation time, t, When most of the mineral appears to have dissolved, 'or various times T after the isolation of lead. By evaporate off most of the excess acid, cool, and dilute ;he use of this graph the age of a uranium mineral the mixture to 5 ml with H90. Warm the mixture and nay be determined by observation of the radioactivity add 1 drop satd. Ba(NO& solution (Note 1). Keep mociated with lead isolated from the mineral. the solution hot for a few minutes, then centrifuge the In all of the preceding it has been assumed that the mixture. Decant and discard the aqueous phase. iranium mineral was initially lead-free. If some lead Wash the residue with 2-3 ml of warm H,O containing :ontaminated the uranium mineral when i t was formed, a drop of dilute (1 :10) HeSO4. Centrifuge and dis;hen the observed specific activity will be less and the card the washings. tpparent age of the mineral will be older than it TO the residue in the centrifuge tube add 1 ml 6 AP ,thenvise would be if there were no contaminating NaOH. Disperse the solid with a stirring rod and warm the mixture in a boiling water bath. Dilute to 5 ml nith water (stir the mix1 ture) and centrifuge. With an eye dropper pipet transfer the aqueous phase to a clean - centrifuge tube. To the solution add a drop of methyl orange indicator. Acidify the solution by - dropwise addition of HNOs until the indicator turns from yellow to red (Note 2). Use a stirring rod to mix the solution 1 thoroughly during acidification. Add 1 -- ml of 0.5 A l Na2SOa solution. Warm the - solution in a boiling water bath for a few '0 - minutes, stirring frequently. Cool under running tap water. Centrifuge the precipitate of PbSOd, discarding the aqueous phase. Redissolve the precipitate of PbSO, in 1 ml 6 M NaOH and dilute the solution to 5 ml with water. Stir the solution in the test tube and add 1 drop of 10 mg/ ml Fe(II1) carrier. Stir vigorously so as to disperse the precipitated Fe(OH)3. Centrifuge the precipitated Fe(OH)s, decanting the solution into a clean centrifuge tube. I I I I I , I , I I I I 1 I l l I Acidify cautiously with HNOJ using lo7 loB lo9 methyl orange indicator in the same manner AGE OF MINERAL (YEARS) as before. Add 1 ml of 0.5 M N&Oa Figure 3. Speriflc ~ O i v i t yof lead i d a t e d from a uranium minerol or a functionof the age warm the mixture to coawlate solutiol,, of the mineral for measurements made otrarious times T after the time o f separation of lead frorn the mineral. the precipitate of PhSO+ Using a filter=
x2*.N .99.28
.
