Decay Series and Radioactive Equilibrium 238 U, 235 U, and 232 Th decay to Pb through a series of α decays (8, 7, and 6, respectively). Since the daughters tend to be neutron-rich, some also β- decay. Most of these are too short-lived to be useful, but the longer-lived ones have uses in geology, geochronology, and oceanography. Consider a daughter (e.g., 234 U) that is both radiogenic and radioactive. The rate of change of its abundance is its rate of production less its rate of decay: The steady-state condition is: and So that: This is the condition that a system to which a system will eventually return if perturbed; i.e., the (radioactive) equilibrium condition. The rate at which a system returns to equilibrium occurs at a predictable rate. Therefore, the extent of disequilibrium is a function of time and can be used for geochronology.
Activities Traditionally, decay series nuclides were measured by measuring their decay (using alpha or gamma detectors). As a consequence, the abundances were traditionally reported as their (radio)activity: the number of decays per unit time (usually dpm, although the SI unit is the bacquerel, dps). Activity is related to atomic abundance through the basic equation: o the quantity on the left is the activity. The activity is written as the isotope in parentheses, e.g., ( 234 U). Well now mainly use activity and this notation. The longer-lived nuclides are now measured by mass spectrometry, but use of activity has stuck, partly because it is useful. Radioactive equilibrium is the condition where activities of parent and daughter are equal.
234 U- 238 U Dating 234 U is the great-granddaughter of 238 U, and the first long-lived daughter in the chain. Well ignoring the two short-lived intermediates (assuming they quickly come to equilibrium). The half-live of 234 U is 246,000 yrs, that of 238 U is 4.47 billion years. On times scales of interest in this system, the abundance (and activity) of 238 U does not change. The activity of 234 U then can be expressed as: After long times, the activity ratio will be 1. Before that, it will be a function of time. If we know the initial ratio, we can use it as a geologic clock. Coral carbonates incorporate U from seawater, which has ( 234 U/ 238 U) 1.15 (why?). After many half-lives, the ratio will decline to 1. Hence we can use this to date corals. Unfortunately, ( 234 U/ 238 U) hasnt been exactly constant through time.
230 Th- 234 U Dating 234 U α-decays to 230 Th (half-life: 75,000 yrs). Disequilibrium between U and Th is greater than among U isotopes, and in this sense this is a better geochronological tool. We can consider two possibilities: o 234 U and 238 U were also in disequilibrium (e.g., corals), in which case we much take account of the ( 234 U/ 238 U) ratio. o 234 U and 238 U were also in equilibrium (volcanic rocks), in which case we can ignore 234 U and treat 230 Th as if it were the direct daughter of 238 U. For the former case: This technique has been extensively used for dating corals (which exclude Th, so the ratio on the left starts at close to 0). Because corals also incorporate C, it has been used to calibrate 14 C dates beyond the point where they can be calibrated by dendrochronology. Because reef-building corals live at sealevel, dating of fossil corals has provided a record of sealevel change as the last glacial period ended. This tells us how ice volume changed. It is also used to date carbonates in caves, and by dating spelothem coatings on cave painting, constrain the age of the cave paintings.
230 Th- 238 U Dating In volcanic rocks, we can assume 234 U and 238 U are in equilibrium. Here we divide by the activity of the long-lived Th isotope, 232 Th (half-life 14 billion years). It does not decay appreciably on the time scales of interest. The relevant equation is: If we plot a series of cogenetic samples on a ( 230 Th/ 232 Th) vs ( 238 U/ 232 Th) plot, the slope will be a function of time. Unlike the conventional isochron equation, the intercept is also a function of time. The line pivots around the equipoint and after many half-lives will have a slope of 1: the equiline.
Decay Series Summary Shorter-lived radionuclides have also been used for dating, including 226 Ra (t 1/2 = 1600 yr), 231 Pa (t 1/2 33,000 yrs), and 210 Pb (t 1/2 = 22 yrs). Short-lived radionuclides are also used to place constraints on rates and extent of melting in the mantle, on mantle Th/U ratios, and on sedimentation rates and processes within the ocean related to adsorption phenomena (of Th in particular). (Youll have to take EAS6560 to learn about these!)
Noble Isotope Geochemistry Isotopes of all 6 noble gases are produced to some degree by nuclear processes: o 4 He by alpha decay o 40 Ar by 40 K decay o heavy Xe isotopes (and Kr) by U fission o Rn by U decay o Extinct radionuclides: 129 Xe/ 130 Xe varies in the Earth (and solar system) due to decay of the fossil radionuclide 129 I (t 1/2 = 16 Ma). Other Xe isotopes also show effects of 244 Pu fission (t 1/2 = 82 Ma), but hard to separate from 238 U fission. o Ne by nuclear reactions initiated by interactions with neutrons and α-particles (these can also produce 3 He). o All to some degree by cosmic-ray interactions (in the atmosphere or at the surface of planetary bodies). The last two processes affect other elements, but are more significant on the noble gases because they are so rare.
Helium He is the only element for which the Earth is not a closed system - it is light enough to bleed to space from the atmosphere. He continually leaks from the Earth to replace it; residence time in the atmosphere is a couple of million years. The usual (but not universal) convention in the case of 3 He is to put the radiogenic isotope in the denominator, i.e., 3 He/ 4 He. Ratios are commonly reported relative to the atmospheric value (1.4 x 10 -6 ) as R/R A. These ratios are very low in the crust because it is outgassed and 4 He is produced by α- decay (a wee-tad of 3 He is produced by interactions on Li such as 6 Li(n,α) 3 He - limiting the ratio to ~0.01 R/R A. Higher ratios are found in mantle-derived volcanic rocks - telling us that the mantle has not been completely outgassed. OIB have higher 3 He/ 4 He (in most, but not all, cases), indicating they come from a less degassed reservoir. This supports the notion that OIB are produced by mantle plumes that rise from the deepest part of the mantle.
He in seawater High 3 He/ 4 He values were first discovered in deep ocean water over mid- ocean ridges - pumped into the ocean by hydrothermal systems (this led to the discovery of black smokers). 3 He/ 4 He is still used to prospect for hydrothermal vents and as a tracer of ocean circulation.
Ne Isotopes Ne isotopes vary in the solar system due to o mass dependent fractionation o cosmogenic production (not relevant to planetary interiors) o nucleogenic production, particularly of 21 Ne through reactions such as 18 O(α,n) 21 Ne. Atmospheric Ne is depleted in light Ne isotopes in proportion to mass - indicating mass dependent fractionation, due to preferential escape of lighter Ne isotopes. o The degree to which this happened in the early Earth or in the precursor materials that formed the Earth is not entirely clear. Ne in mantle-derived rocks is less light isotope- depleted and some ratios approach those in the Sun. Mantle and crustal Ne (including Ne dissolved in old groundwater and petroleum) is also enriched in 21 Ne - a consequence of nucleogenic production. MORB tend to have higher 21 Ne/ 22 Ne than OIB. Nucleogenic production rate depends on U/Ne ratio - so these data also suggest the OIB reservoir is less degassed than the MORB ones. Most or all volcanic rocks suffer some atmospheric contamination, so the data lie on line point to atmospheric Ne.
K-Ar 40 Ca is the principal product of 40 K decay, but is so abundant the 40 Ca/ 44 Ca ratio doesnt change much. Since Ar is a rare gas, radiogenic 40 Ar is readily detected. Because volcanic rocks almost completely degas upon eruption, Ar/K ratios are near 0, and any initial Ar can, to a first approximation, be neglected (or assumed to have the atmospheric ratio). Because of the short half-life of 40 K, 40 Ar builds up rapidly, so this is an excellent system for dating relatively young materials (as young as 10s of thousands of years). Since Ar is a rare gas, it is quite mobile and the K-Ar system is readily reset (but it can be an advantage if you are dating low-T events or processes, like catagenesis (genesis of oil and gas). In a commonly used version of this technique, the sample is irradiated with neutrons in a reactor, producing 39 Ar from 39 K (the principal K isotope). The K/Ar ratio can be determined from the 39 Ar/ 36 Ar ratio simultaneously with the 40 Ar/ 36 Ar ratio - this is known as 40-39 dating. The 40 Ar/ 36 Ar ratio of the atmosphere is constant at 396. The initial ratio of the solar system was <<1: Thus virtually all the Ar in the atmosphere is radiogenic - derived from degassing of the Earths interior. This helps us understand this process. o To account for the Ar in the atmosphere requires a K concentration in the silicate Earth of ~120 ppm. Estimates of K in the Earth range from about 160 to 240 ppm. This implies that 50% to 75% of the Earths Ar is now in the atmosphere. Conversely, as much as 50% may still be in the mantle (crust has very little). 40 Ar/ 36 Ar ratios in MORB are higher (up to 40,000) than they are in OIB (up to ~10,000). Since this depends on the K/Ar ratio, it also indicates that the MORB source reservoir is more degassed than the OIB source reservoir.
Cosmogenic Nuclides Cosmic rays are high energy nuclei (mainly of H and He) from space. When they collide with nuclei in the atmosphere or the surface of the Earth, they induce nuclear reactions. The resulting particles also have high energies and can induce further reactions. The one of greatest interest is 14 N(n,p) 14 C where the neutron is a secondary particle. A number of other nuclides are produced in this way that are useful in geochemistry and geochronology: 3 He, 10 Be, 21 Ne, 26 Al, and 36 Cl. Production restricted to the atmosphere or uppermost meter of the solid Earth. Some of these are used to date exposure of surfaces (lava flows, glacial moraines). 10 Be (t 1/2 15 Ma) is used to trace subduction of sediments into the mantle and also in dating sediments. 36 Cl (t 1/2 300 ka) is used to date water in hydrology. Cosmogenic nuclides are also used to date meteorites - exposure ages are much less than formation ages, telling us meteorites come from larger bodies in which they were shielded from cosmic rays.
Carbon-14 Dating 14 C in a sample of carbon withdrawn from the atmosphere (by, for example, photosynthesis) will decay according to Assuming constant production of 14 C in the atmosphere, and therefore a constant specific activity (dpm/g C), we can determine t simply by measuring the activity of 14 C in the sample (traditionally by β-counting, but increasingly by accelerator mass spectrometry). The catch is that specific activity has not been constant due to: o Variable production rates partly linked to solar activity (enhanced solar wind tends to deflect cosmic rays from the inner solar system). o Dilution by non-radiogenic carbon (anthropogenicly by fossil fuel burning, naturally as CO 2 exsolved from the ocean at the end of the last ice age. o Addition of bomb carbon from atmospheric nuclear tests. This variability requires calibration of 14 C ages by U-Th dating and dendrochronology.
Fossil Radionuclides The young Solar System was hot in many senses, including radioactive, as well see in Chapter 10. We know this from the presence of their decay products. The short-lived nuclides decay away and are now gone, but some ( 146 Sm, 129 I, 244 Pu) were still around when the Earth formed and even when some of the oldest rocks formed. Mantle Xe has higher 129 Xe/ 130 Xe than the atmosphere. This indicates much of the atmosphere has formed before 129 I had decayed away (16Ma × 5 = 80 Ma), producing high 129 Xe/ 130 Xe in a relatively Xe-poor mantle. o Degassing of the Earths interior must have been a two step process: extensive early degassing, to account for atmospheres 129 Xe deficit and much slower subsequent degassing to account for 40 Ar. There is also evidence of the presence of 244 Pu - but it complicated.
142 Nd/ 144 Nd and extinct 146 Sm Modern terrestrial rocks have higher 142 Nd/ 144 Nd than chondrites (chondrites themselves vary). This indicates the Earth, or the observable part of it - the crust and the mantle giving rise to magmas, have 146 Sm/ 144 Nd higher than chondritic. This suggests the Earth has higher than chondritic Sm/Nd. o Two common explanations: an earlier-formed low Sm/Nd crust either sunk to the bottom of the mantle or was lost through collisional erosion. o Also possible 146 Sm or 142 Nd were not uniformly distributed in solar nebula. Early Archean (~3.8 Ma) rocks from Isua, Greenland and Nuvvuagittug, Labrador (and now a few other places) have 142 Nd/ 144 Nd different than the modern terrestrial value. o 146 Sm would have been effectively extinct by then. o The precursors/sources of these rocks must have formed very early with higher and lower Sm/Nd ratios than the bulk Earth. o Among other things, it tells us that the Earth began to differentiate into incompatible element-enriched and depleted reservoirs (such as crust and residual mantle) very early.