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Isotopes

John Wiley & Sons

Chapter One

Isotope geology is concerned with the measurement and interpretation of the variations of the isotope composition of certain elements in natural materials. These variations are the result of two quite different processes:

1. the spontaneous decay of the nuclei of certain atoms to form stable nuclei of other elements and the accumulation of these radiogenic daughter atoms in the minerals in which they formed and

2. the enrichment (or depletion) of certain stable atoms of elements of low atomic number in the products of chemical reactions as a result of changes in state such as evaporation and condensation of water and during physical processes such as diffusion.

The interpretation of the changes in the isotope compositions of the affected elements has become a powerful source of information in all branches of the earth sciences. The use of this investigative tool requires a thorough understanding of geological, hydrological, biospheric, and atmospheric processes occurring on the Earth and elsewhere in the solar system. In addition, the interpretation of isotopic data requires knowledge of the relevant principles of atomic physics, physical chemistry, and biochemistry. The decay of unstable atoms is accompanied by the emission of nuclear particles and radiant energy, which togetherconstitute the phenomenon of radioactivity. The discovery of this process near the end of the nineteenth century was a milestone in the history physics and greatly increased our understanding of the Earth.

1.1 DISCOVERY OF RADIOACTIVITY

The rise of geology as a science is commonly associated with the work of James Hutton in Scotland. He emphasized the importance of very slow but continuously acting processes that shape the surface of the Earth. This idea conflicted with Catastrophism and foreshadowed the concept of Uniformitarianism, developed by Hutton in his book Theory of the Earth, published in 1785. His principal point was that the same geological processes occurring at the present time have shaped the history of the Earth in the past and will continue to do so in the future. He stated that he could find "no vestige of a beginning-no prospect of an end" for the Earth. Hutton's conclusion regarding the history of the Earth was not well received by his contemporaries. However, as time passed, geologists accepted the principle of Uniformitarianism, including the conviction that very long periods of time are required for the deposition of sedimentary rocks whose accumulated thickness amounts to many miles. In 1830, Charles Lyell published the first volumes of his Principles of Geology. By the middle of the nineteenth century, geologists seemed to be secure in their conviction that the Earth was indeed very old and that long periods of time are required for the deposition of the great thickness of sedimentary rocks that had been mapped in the field.

The apparent antiquity of the Earth and the principle of Uniformitarianism were unexpectedly attacked by William Thomson, better known as Lord Kelvin (Burchfield, 1975). Thomson was Britain's most prominent physicist during the second half of the nineteenth century. His invasion into geology profoundly influenced geological opinion regarding the age of the Earth for about 50 years. Between 1862 and 1899 Thomson published a number of papers in which he set a series of limits on the possible age of the Earth. His calculations were based on considerations of the luminosity of the Sun (Thomson, 1862), the cooling history of the Earth, and the effect of lunar tides on the rate of rotation of the Earth. He initially concluded that the Earth could not be much more than 100 million years old. In subsequent papers, he further reduced the age of the Earth. In 1897, Lord Kelvin (he was raised to peerage in 1892) delivered his famous lecture, "The Age of the Earth as an Abode Fitted for Life" (Thomson, 1899), in which he narrowed the possible age of the Earth to between 20 and 40 million years.

These and earlier estimates of the age of the Earth by Lord Kelvin and others were a serious embarrassment to geologists. Kelvin's arguments seemed to be irrefutable, and yet they were inconsistent with the evidence as interpreted by geologists on the basis of Uniformitarianism. Ironically, one year before Lord Kelvin presented his famous lecture, the French physicist Henri Becquerel (1896) had announced the discovery of radioactivity. Only a few years later it was recognized that the disintegration of radioactive elements is an exothermic process. Therefore, the natural radioactivity of rocks produces heat, and the Earth is not merely a cooling body, as Lord Kelvin had assumed in his calculation.

Becquerel's discoveries attracted the attention of several young scientists, among them Marie (Manya) Sklodowska who came to Paris in 1891 from her native Poland to study at the Sorbonne. On July 25, 1895, she married Pierre Curie, a physics professor at the Sorbonne. After Becquerel reported his discoveries regarding salts of uranium, Marie Curie decided to devote her doctoral dissertation to a systematic search to determine whether other elements and their compounds emit similar radiation (Curie, 1898). Her work was rewarded when she discovered that thorium is also an active emitter of penetrating radiation. Turning to natural uranium and thorium minerals, she noticed that these materials are far more active than the pure salts of these elements. This important observation suggested to her that natural uranium ore, such as pitchblende, should contain more powerful emitters of radiation than uranium. For this reason, Marie and Pierre Curie requested a quantity of uranium ore from the mines of Joachimsthal in Czechoslovakia and, in 1898, began a systematic effort to find the powerful emitter whose presence she had postulated. The search eventually led to the discovery of two new active elements, which they named polonium and radium. Marie Curie coined the word "radioactivity" on the basis of the emissions of radium. In 1903, the Curies shared the Nobel Prize for physics with Henri Becquerel for the discovery of radioactivity.

1.2 INTERNAL STRUCTURE OF ATOMS

Every atom contains a small, positively charged nucleus in which most of its mass is concentrated. The nucleus is surrounded by a cloud of electrons that are in motion around it. In a neutral atom, the negative charges of the electrons exactly balance the total positive charge of the nucleus. The diameters of atoms are of the order of [10.sup.-8] centimeters (cm) and are conveniently expressed in angstrom units (1 Å = [10.sup.-8] cm). The nuclei of atoms are about 10,000 times smaller than that and have diameters of [10.sup.-12] cm, or [10.sup.-4] Å. The density of nuclear matter is about 100 million tons per cubic centimeter. The nucleus contains a large number of different elementary particles that interact with each other and are organized into complex patterns within the nucleus. It will suffice for the time being to introduce only two of these, the proton (p) and the neutron (n), which are collectively referred to as nucleons. Protons and neutrons can be regarded as the main building blocks of the nucleus because they account for its mass and electrical charge. Briefly stated, a proton is a particle having a positive charge that is equal in magnitude but opposite in polarity to the charge of an electron. Neutrons have a slightly larger mass than protons and carry no electrical charge. Extranuclear neutrons are unstable and decay spontaneously to form protons and electrons with a "halflife" of 10.6 min. The other principal components of atoms are the electrons, which swarm around the nucleus. Electrons at rest have a small mass (1/1836.1 that of hydrogen atoms) and a negative electrical charge. The number of extranuclear electrons in a neutral atom is equal to the number of protons. The protons in the nucleus of an atom therefore determine how many electrons that atom can have when it is electrically neutral. The number of electrons and their distribution about the nucleus in turn determine the chemical properties of that atom.

1.2a Nuclear Systematics

The composition of atoms is described by specifying the number of protons and neutrons that are present in the nucleus. The number of protons (Z) is called the atomic number and the number of neutrons (N) is the neutron number. The atomic number Z also indicates the number of extra-nuclear electrons in a neutral atom. The sum of protons and neutrons in the nucleus of an atom is the mass number (A). The composition of the nucleus of an atom is represented by the simple relationship

(1.1) A = Z + N

Another word for atom that is widely used is nuclide. The composition of any nuclide can be represented by means of a shorthand notation consisting of the chemical symbol of the element, the mass number written as a superscript, and the atomic number written as a subscript. For example, [sup.14.sub.6]C identifies the nuclide as an atom of carbon having 6 protons (therefore 6 electrons in a neutral atom) and a total of 14 nucleons. Equation 1.1 indicates that the nucleus of this nuclide contains 14 - 6 = 8 neutrons. Similarly, [sup.23.sub.11]Na is a sodium atom having 11 protons and 23 - 11 = 12 neutrons. Actually, it is redundant to specify Z when the chemical symbol is used. For this reason, the subscript (Z) is sometimes omitted in informal usage.

A great deal of information about nuclides can be shown on a diagram in which each nuclide is represented by a square in coordinates Z and N. Figure 1.1 is a part of such a chart of the nuclides. Each element on this chart is represented by several nuclides having different neutron numbers arranged in a horizontal row. Atoms which have the same Z but different values of N are called isotopes. The isotopes of an element have identical chemical properties and differ only in their masses. Nuclides that occupy vertical columns on the chart of the nuclides have the same value of N but different values of Z and are called isotones. Isotones are therefore atoms of different elements. The chart also contains nuclides that occupy diagonal rows. These have the same value of A and are called isobars. Isobars have different values of Z and N and are therefore atoms of different elements. However, because they contain the same number of nucleons, they have similar but not identical masses.

1.2b Atomic Weights of Elements

The masses of atoms are too small to be conveniently expressed in grams. For this reason, the atomic mass unit (amu) is defined as one-twelfth of the mass of [sup.12.sub.6]C. In other words, the mass of [sup.12.sub.6]C is arbitrarily fixed at 12.00 ... amu, and the masses of all other nuclides and subatomic particles are expressed by comparison to that of [sup.12.sub.6]C. The masses of the isotopes of the elements have been measured by mass spectrometry and are known with great precision and accuracy.

The total number of different nuclides is close to 2500, but only 270 of these are stable, including long-lived radioactive isotopes that still occur naturally because of their slow rate of decay. The stable nuclides, along with a small number of naturally occurring long-lived unstable nuclides, make up the elements in the periodic table. Many elements have two or more naturally occurring isotopes, some have only one, and two elements (technetium and promethium) have none. These two elements therefore do not occur naturally on the Earth. However, they have been identified in the optical spectra of certain stars where they are synthesized by nuclear reactions.

The relative proportions of the naturally occurring isotopes of an element are expressed in terms of percent by number. For example, the statement that the isotopic abundance of [sup.85.sub.37]Rb is 72.15 percent means that in a sample of 10,000 Rb atoms 7215 are the isotope [sup.85.sub.37]Rb. When the masses of the naturally occurring isotopes of an element and their abundances are known, the atomic weight of that element can be calculated. The atomic weight of an element is the sum of the masses of its naturally occurring isotopes weighted in accordance with the abundance of each isotope expressed as a decimal fraction. For example, the atomic weight of chlorine (Cl) is calculated from the masses and abundances of its two naturally occurring isotopes:

Isotope Mass × Abundance

[sup.35.sub.17]Cl 34.96885 × 0.7577 = 26.4958

[sup.35.sub.17]Cl 36.96590 × 0.2423 = 8.9568

Atomic weight = 35.4526 amu

The abundances of the naturally occurring isotopes of the elements and their measured masses are listed in tables such as those of the Handbook of Chemistry and Physics (Lide and Frederikse, 1995).

Although the atomic weights of the elements are expressed in atomic mass units, it is convenient to define the gram atomic weight, or mole, which is the atomic weight of an element in grams. One mole of an atom or a compound contains a fixed number of atoms or molecules, respectively. The number of atoms or molecules in one mole is given by Avogadro's number, which is equal to 6.022045 × [10.sup.23] atoms or molecules per mole.

1.2c Binding Energy of Nucleus

The definition of the atomic mass unit provides an opportunity to calculate the mass of a particular nuclide by adding the masses of protons + electrons ([M.sub.H] = 1.00782503 amu) and of the neutrons ([M.sub.n] = 1.00866491 amu) of which it is composed. These calculated masses are consistently greater than the measured masses. It appears, therefore, that the mass of an atom is less than the sum of its parts. This phenomenon is an important clue to an understanding of the nature of the atomic nucleus. The explanation of the observed mass defect is that some of the mass of the nuclear particles is converted into binding energy that holds the nucleus together. The binding energy ([E.sub.B]) is calculated by means of Einstein's equation:

(1.2) [E.sub.B] = [DELTA]m [c.sup.2]

where [DELTA]m is the mass defect and c is the speed of light in a vacuum (2.99792458 × [10.sup.10] cm/s).

The calculation of the binding energy requires a review of the relationship between units of mass and energy. The basic unit of energy in the cgs system (centimeter, gram, second) is the erg. However, the amount of energy released by a nuclear reaction involving a single atom is only a small fraction of one erg.

Continues...

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Excerpted from Isotopes by Gunter Faure Teresa M. Mensing Excerpted by permission.
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