COMPOSITION OF TERRESTRIAL PLANETS AND CHONDRITIC METEORITES

The close similarity in the abundances of elements heavier than oxygen in chondritic meteorites and the solar atmosphere (Figure 1.5) suggests a chondritic composition as a reasonable assumption for the composition of the inner rocky planets—Mercury, Venus, Earth, and Mars. However, even simple considerations show that there may be important differences in chemical composition between meteorites and the inner planets. For example, Table 10.1 gives the densities of the four terrestrial planets and chondritic meteorites (Brown and Mussett, 1993). The table shows that the terrestrial planets have densities, which when corrected for their different internal pressure, vary significantly from that of chondritic meteorites. In fact, Mars with an uncompressed density of ∼ 3,700 kg m–3 is the only planet which lies in the chondritic range of 3,400–3,900 kg m–3. Earth, Venus, and Mercury are denser than chondrites, and the Earth's moon is less. The only sufficiently abundant element to influence such strong density difference is iron, because its atomic mass 56 is much higher than that of the next three most abundant elements, O(16), Mg(24), and Si(28).

More subtle is the evidence that volatile elements have been systematically depleted in terrestrial planets. Figure 10.1 shows a plot of the ratio of volatile elements, K and Rb to refractory (less volatile) elements U and Sr, respectively, in meteorites, inner planets, and the moon (Halliday and Porcelli, 2001). This shows the volatile depleted nature of the moon relative to the Earth, and the Earth and Mars relative to meteorites. The most depleted ratio in angrites is understandable as they are differentiated meteorites (Chapter 9).

The systematic decrease in iron metal/silicate ratios and systematic variations in ratios of volatile elements to refractory trace elements were probably caused by decreasing condensation pressures and temperatures, respectively, in the solar nebula away from the sun (Brown and Mussett, 1993).

The time-dependent accumulation of helium and lead from the radioactive decay of uranium in minerals and rocks was suggested by Rutherford in 1905 as a means of determining their absolute ages. This seminal idea has been assiduously pursued in the last century by unorthodox physicists and chemists to detect and quantitatively measure numerous radioactive isotopes of widely varying lifetimes and abundances in natural systems. Absolute age determination based on these isotopes, called radiometric dating, now plays a central role in a broad range of Earth and planetary sciences: paleoseismology; paleomagnetism; paleooceanography; igneous, metamorphic and sedimentary petrology; geomorphology; geochemistry; tectonics; nucleosynthesis; cosmochemistry; planetary science; geobiology; paleoclimatology; paleoanthropology; and archeology. Assuming that the reader has only college level knowledge of physics, chemistry, and mathematics, this concise book (about 200 pages) focuses on the essential principles of radiometric dating in order to enable the students and teachers in various fi elds to quickly fi gure out the criteria to be met by parent-daughter systems and samples relevant to their specialization. This book draws heavily on three classic review articles which, in my view, capture the intellectual appeal and beauty of the subject for a very wide audience (Wetherill et al., 1981; Wasserburg, 1987; Allegre, 1987). I believe that this book will succeed in improving students’ understanding and appreciation of radiometric dating results generated and published by professionals. I hope it would also stimulate interest in students to take up isotope geology as a serious study and reach out for the excellent and comprehensive books on the subject.

The material presented in each of the 11 chapters is self-contained. However, the reader is urged to read all the chapters, as they are strung together into a concise, continuous, and easily comprehensible narrative to illuminate the subject as a whole. Vital points behind radiogenic isotope chronometry are stressed upon more than once. The reference list is mainly for students interested in further reading.

Chapter 1 covers the basic facts of nuclear and atomic physics, nuclear binding energy as a measure of nuclear stability, and the variety and relative abundance of different elements in the sun and the primitive meteorites. Chapter 2, then, moves on to the transformation of composition of nuclides, either spontaneously (radioactivity) or by external agents (induced nuclear reactions), and highlights the role of feeble natural radioactivity, both in driving and dating planetary processes.

INTRODUCTION

The calculation of a radiometric age (strictly speaking, radioactive decay interval) of a natural object is ultimately based on the decrease in the concentration of a parent isotope in that object during the interval. The measurement of the initial and final concentrations (directly or otherwise) in terms of an internationally accepted unit (moles per unit weight of the sample) is always subject to analytical errors or uncertainties. These analytical errors will be reflected (propagated) in the final age result. In this chapter we will consider generally accepted methods of estimating analytical error in a measured quantity, and how it will affect the final result based on this measurement (Cunningham, 1981).

The absolute error in a measurement is the discrepancy between the measured value and its ‘true’ value. Except in the case of counting discrete objects, a measurement of a physical quantity in terms of an internationally-accepted unit will always be subject to an uncertainty. The true value that we are seeking is unknowable, unless it is already known in some other way. So, it is necessary to state from the results within what range of values the true value is likely to occur and the confidence that can be placed on the validity of this statement. The statement of a result without any indication, with a certain confidence, of the range of values bracketing the true value has virtually no significance to end users. The idea of errors is, therefore, not something of only secondary or peripheral interest in an experiment. On the contrary, it is related to the purpose of the experiment, the method of doing it and the relevance of the results to a significant scientific question. The quotation in the beginning of this chapter reflects the importance of error limits to an experimentally measured date or age.

SYSTEMATIC AND RANDOM ERRORS

Before proceeding further on error estimates, we must distinguish between two types of experimental errors—determinate or systematic, and indeterminate or random. Determinate errors generally shift the measured result in one direction with respect to the true value. They are often reproducible, and, in many cases, may be measured, and or corrected for by careful and meticulous experimentation.

INTRODUCTION

The variety and relative abundances of the 90 elements in the Solar System must have been produced somewhere else before its formation about 4.6 by ago. The earliest time some or all of them could have been produced somewhere is 13.7 billion of years ago when the universe is believed to have originated in a spectacular explosion—Big Bang—of what is known as a singularity in cosmological parlance. At least three sets of observations support the Big Bang theory.

1. Expanding universe Hubble discovered that galaxies are receding from each other at a speed proportional to the distance between them, based on red shifts of light coming from distant galaxies. This implies that at some time in the past all the matter in the universe must have been concentrated at one point.

2. Big Bang nucleosynthesis According to the Standard Cosmological model, the matter in the universe 30 minutes after the explosion must have consisted mostly of hydrogen (H) and helium (He) with only traces of deuterium (2H) and helium (3He), as confirmed by recent observations.

3. Cosmic microwave background Theory also predicts that the universe must now be filled with an isotropic background radiation in the microwave region of the electromagnetic spectrum as a relic of the initial radiation from the Big Bang. Penzias and Wilson (Penzias and Wilson, 1965) have indeed detected such a cosmic microwave background radiation corresponding to black body emission at 2.7 K.

The predicted sequence of events within the first 3 minutes of the Big Bang, according to the Standard Cosmological model, is given in Table 3.1.

STELLAR NUCLEOSYNTHESIS

For geologists used to events on a time scale of at least a few thousand years, incredibly short time intervals like 10–50, 10–43, and 10–35s make no sense. Even a comparatively much longer time interval like 10–10 s is so short that light with a velocity of as high as 3,00,000 kilometres per second will cover just about 3 centimetres in this interval. The important point for geologists to note is that Big Bang, or cosmological nucleosynthesis, was restricted to only H and He and to within the first 3 minutes.

INTRODUCTION

Simply stated, the present Earth is very different from the early Earth. The main objective of geology is to reconstruct the time sequence and nature of the key or major processes that shaped the Earth over 4.5 Gy. Schumm (1991) cautions that this task will be quite formidable by quoting a metaphorical statement of Pretorius in a different context, as follows:

To extend this metaphor further, some of the missing pages of the book of genesis of the Earth may have to be found in the libraries of experiments carried out on other planets.

In this chapter we will consider how radiogenic isotope geochemistry has provided firm constraints on the timing of some major or large scale events in Earth's history.