Lecture 10: Geochronology VI: U-Th decay series dating

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Geol. 655 Isotope GeochemistryLecture 10 Spring 2003where the superscript naughtdenotes the initial activity (attime t = 0). We can also write:( 234 U) uo= ( 234 U) o – ( 234 U) s10.7which just says that the initialunsupported activity of 234 U isequal to the total initial activityof 234 U less the (initial) supportedactivity of 234 U. Since to a verygood approximation the activityof the parent, 238 U, does not changeover times on the order of thehalf-life of 234 U or even ten halflivesof 234 U, the present 238 Uactivity is equal to the activity att = 0 (we make the usual assumptionthat the system is closed).And by definition the supportedactivity of 234 U is equal to the activityof 238 U, both now and at t =0. Hence, 10.5 can be expressed as:( 234 U) = ( 238 U) + ( 234 U) u10.8and 10.7 becomes( 234 U) o u = (234 U) o – ( 238 U)10.9Substituting 10.9 into 10.6 yields:234 234( U )u = ( U )° – (238 U)e–l 234tSubstituting 10.10 into 10.8, we have:234( U ) = (238 U)+ (234 U)°– (238 U)e–l 234t10.1010.11Just as for other isotope systems, it is generally most convenient to deal with ratios rather than absoluteactivities (among other things, this allows us to ignore detector efficiency provided the detectoris equally efficient at all energies of interest ‡ ), hence we divide by the activity of 238 U:234U= 1 + ( 234 U )° – (238 U)e –l 234 t 10.12238238or since 238 U = 238 U°:UU234= 1 +234U238Uo– 1 e –l 234 t 10.13238UUThus the present activity ratio can be expressed in term of the initial activity ratio, the decay constantof 234 U, and time. For material such as a coral, in (isotopic) equilibrium with seawater at sometime t = 0, we know the initial activity ratio was 1.14. Carbonates, for example, concentrate U. If wemeasure the ( 234 U/ 238 U) ratio of an ancient coral, and can assume that the seawater in which thatcoral grew had a ( 234 U/ 238 U) the same as modern seawater (1.14), the age of the coral can be obtainedby solving equation 10.13 for t. The age determined is the time since the material last reached isotopicequilibrium with seawater.(a)(c)Figure 10.2. Hypothetical ( 230 Th/ 232 Th) as a function of depth in acore. (a) is normal, constant sedimentation rate, (b) reflects achange in sedimentation rate, (c) reflects bioturbation mixing thesediment at the top of the core, (d) is a case of dominance by U-supported 230 Th. From Faure (1986).(b)(d)‡ In the case of 238 U and 234 U the a energies are quite similar (4.2 and 4.7 MeV). Interestingly, the energies of a particlesare approximately inversely proportional to half-life. From our discussion of a decay, you should be able to surmisewhy.63 February 12, 2003
Geol. 655 Isotope GeochemistryLecture 10 Spring 2003The application of 234 U/ 238 U has been largely restricted to corals. It is not generally useful forfreshwater carbonates because of uncertainty in the initial activity ratio. Mollusk shells and pelagicbiogenic carbonate (e.g., foraminiferal ooze) often take up U after initial deposition of the carbonateand death of the organism, thus violating our closed system assumption. The technique is typicallyuseful up to about 4 times the half-life of 234 U when alpha spectrometry is the analytical method, butcan be applied to longer times with mass spectrometry because of higher precision.230 Th- 238 U DatingThe 244 U- 238 U technique does not have high temperature applications, because at high temperature,234 U and 238 U do not fractionate as they do at low temperature. The reason is that radiation damage,which is the reason 234 U is removed in weathering more easily than 238 U, anneals quite rapidly athigh temperature. Disequilibrium between 230 Th (the daughter of 234 U) and its U parents can, however,provide useful geochronological and geochemical information in both high- and low-temperaturesystems. We start with an equation analogous to equation 10.6:230Thu = 230Th0u e–l 230t10.14As is the usual practice, we normalize to a non-radiogenic isotope:230Th232Th=u230Th232Th0e–l 230t10.15( 232 Th, although non-radiogenic, isradioactive, of course. However, with ahalf-life of 14Ga, its abundance will notchange on time scales comparable to thehalf-life of 230Th ).In seawater, and in general in itsoxidized state, U is quite soluble. Th,however, is quite insoluble: its seawaterresidence time is 300 years or lesscompared to about 500,000 year for U. (Itshould be noted here that solubility inseawater does not control concentrationsor residence times. Neverthelesssolubility is a good guide to both ofthese.) Once a 234 U atom decays to 230 Th,it is quickly absorbed onto particles thatin turn are quickly incorporated intosediment. As a result, relatively highconcentrations of unsupported 230 Th canbe removed (by leaching) from somesediments (mainly relatively slowly accumulatingones). In cases where theamount of leached 234 U is negligible andwhere the ( 230 Th/ 232 Th) o is known (from,for example, zero-age sediment at theseawater-sediment interface), equation10.14 can be used to determine the age ofthe sediment. If we can't neglect 234 Uthen we can still determine the age bytaking this into account, though themathematics becomes more complex (seeuFigure 10.3. (a) 230 Th— 238 U isochron diagram. The( 238 U/ 232 Th) of the source is given by the intersection of theisochron with the equiline. (b) shows how the slopechanges as a function of time. After Faure (1986).64 February 12, 2003
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Lecture 10: Geochronology VI: U-Th decay series dating

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