Lead Isotopes as a Current Scientific Clock

By Paul Bechard

Lead isotopes are commonly used in dating rocks and provide some of the best evidence for the Earth's age. In order to be used as a natural clock to calculate the age of the earth, the processes generating lead isotopes must meet the four conditions of a natural clock: an irreversible process, a uniform rate, an initial condition, and a final condition. Dalrymple (2004) cites examples of lead isotope dating that give an age for the earth of about 4.5 billion years. Lead isotopes are important because two different lead isotopes (207Pb and 206Pb) are produced from the decay series of two different uranium isotopes (235U and 238U). Since both decay series contain a unique set of intermediate radioactive isotopes, and because each has its own half-life, independent age calculations can be made from each (Dalrymple 2004:65). The presence of a stable lead isotope that is not the product of any decay series (204Pb) allows lead isotopes to be normalized, allowing for the use of isochrons and concordia-discordia diagrams as dating tools. Two other characteristics of lead isotope measurements make it superior to other methods. First, measuring the isotope ratio of a single element can be done much more precisely than measuring isotope ratios of two differing elements. Second, using two isotopes of the same element makes the sample immune to chemical fractionation during a post-crystallization disturbance (Dalrymple 2004:168).

The commonly accepted 4.5 billion year age of the earth is derived from radiometric dating of lunar rocks and meteorites in addition to dating methods based on the Gerling-Holmes-Houtermans model. This model, which describes the accumulation of lead isotopes in meteorites, the Earth, and the Solar System, was proposed independently by E.K. Gerling, Arthur Holmes, and Fritz G. Houtermans in the 1940s (Dalrymple 2004:156). This model ultimately led to the development of isochrons, in which two isotopes are plotted against each other to calculate an age for the mineral or rock. Those who developed the method utilized 206Pb and 207Pb, lead isotopes that are the product of radioactive decay, normalized to 204Pb. The amount of 204Pb will remain constant throughout the history of a rock because it is a stable isotope that is not the product of any decay series, thus allowing for the normalization (Dalrymple 2004:161-163). Two requirements of the Gerling-Holmes-Houtermans model make it difficult to use. The first is that it requires single-stage leads, which are systems that begin at some initial lead composition and remain on the same growth curve throughout their histories (Dalrymple 2004:159). The second requirement is that assumptions about the genetic relationship between the Earth and meteorites must be made.

Although single-stage leads are difficult to find on Earth due to the constant recycling of Earth's crust, Pb-Pb isochrons remain powerful tools in making age of the Earth calculations. A Pb-Pb isochron plots 207Pb, the daughter isotope of 235U, versus 206Pb, the daughter isotope of 238U, with both normalized to 204Pb. The resulting line drawn through the plotted points will pass through a point representing the initial lead composition of the system. Although this point cannot be determined, the isochron will rotate about it as the rock ages because the initial amount of lead is constant regardless of age. An example isochron from Dalrymple (2004) is shown in Figure 4.8 below. The slope of the line gives the age of the rock. Unlike other isochrons, the slope of the Pb-Pb isochron decreases with increasing age. This is because 235U has a half-life of 704 million years, while 238U has a half-life of 4.47 billion years (Dalrymple 2004:55). The rate at which daughter isotopes accumulate is dependent on the amount of parent isotope present. Since 235U has a much shorter half-life, a larger fraction of the initial 235U present in the rock will have decayed compared to 238U. Therefore, 207Pb will accumulate at a slower rate than 206Pb, causing the isochron to decrease in slope with increasing age. The use of lead isotope ratios makes this isochron self-checking. A large scattering of measurements would indicate the sample is multi-stage rather than single-stage, making the isochron unreliable.

reliable lead isochron

Another situation in which single-stage systems give unreliable information is the extraction of lead from uranium to form lead ore. It is possible that a system could undergo a geological process that extracts lead, leaving the new system without any uranium. If that system were dated at that point in time, it would fall on the isochron and give the correct age of the mineral. However, without any uranium present, accumulation of daughter isotopes ceases even though time continues to pass. Such events produce a frozen record, giving the amount of time from crystallization to extraction of lead to form lead ore. Such ages are very useful because they can measure time forward from some known event in the past, such as the formation of the earth.

The difficulties with single-stage systems can be circumnavigated with multi-stage systems. Though multi-stage lead samples cannot be used for generating isochrons, they can be used to produce valuable information through concordia-discordia plots. These plots are also self-checking and are useful for dating old rocks with complex histories. The plots can still produce valuable and accurate data using rocks that have been subjected to heating and metamorphic events (Dalrymple 2004:78). This utility is due to the fact that the concordia-discordia method uses the simultaneous decay of 238U to 206Pb and 235U to 207Pb to tabulate age. A sample concordia diagram from Dalrymple (2004) is shown in Figure 4.7 below. The change in ratios of parent to daughter isotopes over time is used to construct an age curve called a concordia. Since lead loss from a mineral does not fractionate the isotopes, the resulting change in parent to daughter isotope ratios will fall on a line called discordia, which connects the original age on concordia to the age on concordia of lead loss. This method requires minerals that contain either no initial lead or negligible amounts of initial lead, but some such minerals can be found in igneous and metamorphic rocks (Dalrymple 2004:76-78).

uranium-lead concordia diagram

As stated above, the Gerling-Holmes-Houtermans model requires that assumptions about the genetic relationship between the Earth and meteorites be made. Houtermans calculated the time required for lead composition of primordial lead samples to decay to the lead composition of young ores. He used young terrestrial ores to obtain data for young ores and assumed the lead composition of the meteorite Canyon Diablo was representative of primordial lead. His result was 4.5 ± 0.3 billion years, which is approximately today's accepted value (Dalrymple 2004:165).

Houtermans did not provide a justification as to why the origins of the Earth and meteorites should be related, but Claire C. Patterson did. Patterson suggested that Earth lead would fall on the meteorite isochron if it had evolved in a closed system with the same initial lead composition as the meteorite over the past 4.55 billion years. He supported this argument with lead measurements taken from deep ocean sediment. He later partnered with V.R. Murthy to strengthen the argument by showing that the meteoritic geochron and terrestrial geochron are nearly identical and probably evolved from the same uranium-lead system (Dalrymple 2004:166-167).

Some Creationist groups are attacking the reliability of radioisotope dating. The RATE team cites isochrons obtained using Earth samples to claim that one of four types of discordance result when the mineral isochron method is applied as a test of the assumptions of radioisotope dating. Since radioisotope data gathered by the RATE team demonstrates all four categories of isochron discordance, the team states that "the assumptions of radioisotope dating must be questioned" (Austin 2005:376). Paul S. Taylor, writing for the ChristianAnswers.Net website, also calls the assumptions of radioisotope dating into question. He cites the problem of initial amounts of daughter isotope and the assumption of closed systems in addition to other arguments (Taylor 1998).

Despite the questions raised by the RATE team and other groups, lead isotopes are generally considered to be a reliable method for dating the Earth, giving an approximate age of 4.5 billion years. The presence of three lead isotopes can be used to generate powerful tools for age calculations. These methods are self-checking and more reliable than those which rely on isotopes of differing elements. These methods have also provided logical evidence connecting the formation of the earth to the formation of meteorites and other bodies of the Solar System. When taken in combination with other dating tools, compelling evidence for an ancient earth is found.

Sources:
  1. Austin, Steven A. 2005. Do radioisotopic clocks need repair? Testing the assumptions of isochron dating using K-Ar, Rb-Sr, Sm-Nd, and Pb-Pb isotopes. Chapter 5 (pp 325-524) in L. Vardiman, A. A. Snelling, and E. F. Chaffin (eds.) Radioisotopes and the Age of the Earth, Volume II: Results of a Young-Earth Creationist Research Initiative, Institute for Creation Research, El Cajon, California, 818 p.
  2. Dalrymple, Brent G. 2004. Ancient Earth, Ancient Skies. Stanford University Press, 247p.
  3. Taylor, Paul S. Radioactive Age Estimation Methods - Do They Prove the Earth is Billions of Years Old? http://www.christiananswers.net/q-eden/edn-radioactive.html Copyright: 1998. Accessed: Dec 13, 2005.