The Nature of Radioactive Decay

There are several modes by which radioactive decay can occur. The characteristics of the three most common modes were elucidated in 1903 by Rutherford and Frederick Soddy (1877-1956) and named alpha (a), beta (p), and gamma (y) decay after the first three letters of the Greek alphabet. 

Rutherford has been called the father of nuclear physics. His lifetime of accomplishments earned him the Nobel Prize in chemistry (not physics) in 1908, knighthood in 1914, the Order of Merit in 1921, and a place in the periodic table—element 104, rutherfordium (Rf). Soddy, an English chemist, received his own Noble Prize in 1921 for developing the concept of isotopes. 

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Finally, the last member of the noble gases, radon, was discovered by the German chemist Frederick Dom in 1900. A radioactive element and the heaviest elemental gas known, radon s discovery not only completed the Group 8A elements, but also advanced our understanding about the nature of radioactive decay and transmutation of elements. 

Radioactive materials are all around us and can be very beneficial to us in our daily lives. Unfortunately, many people react in fear when they hear the word radioactive. An understanding of the nature of radioactive decay, however, and the uses of radioactive isotopes is something to be appreciated. 

For a proper approach to any radiometric problem, both familiarity with techniques and understanding of the nature of radioactive decay with related statistical aspects are required. 

Radon gas is formed in the process of radioactive decay of uranium. The distribution of naturally occurring radon follows the distribution of uranium in geological formations. Elevated levels have been observed in certain granite-type minerals. Residences built in these areas have the potential for elevated indoor concentrations of radon from radon gas entering through cracks and crevices and from outgassing from well water. 

The sequences of radioactive decays that lead to lead are well-known and the rates of decay have been carefully measured. We shall consider the sequence based upon the relatively slow decomposition of the most abundant uranium isotope, mass 238 (natural abundance, 99%) ... 

Earth s natural energy that heats the water in the hot spring is the energy of radioactive decay. Just as a piece of radioactive material is warmer than its surroundings due to thermal agitation from radioac-... 

The isotopes ofHe do notalways occur in all natural samples in their usual proportion. Because helium has only two stable isotopes, variations in their abundance ratio are usually attributed to 3He. But in cases where radioactive alpha decays have enriched 4He, that reason for 4He richness is usually fairly obvious. One example is He in rocks containing uranium. The 4He/3He ratio is about 100 times greater than solar in the Earth s atmosphere because the history of radioactive decay of uranium in the Earth (Rutherford ) and its outgassing has enriched our atmosphere in daughter 4He. 

The laws of radioactive decay are the basis of chronology by nuclear methods. From the variation of the number of atoms with time due to radioactive decay, time differences can be calculated rather exactly. This possibility was realized quite soon after the elucidation of the natural decay series of uranium and thorium. Rutherford was the first to stress the possibility of determining the age of uranium minerals from the amount of helium formed by radioactive decay. Dating by nuclear methods is applied with great success in many fields of science, but mainly in archaeology, geology and mineralogy, and various kinds of chronometers are available. 

Let us briefly discuss again the limitations of radioactive decay measurement. The observation of the radioactive decay of a single atom is possible, consequently, with efficient apparatus for the detection of the decay particles and a radioactive species with a half-life of seconds and minutes, it is possible to detect all or nearly all of a small number of radioactive atoms in the presence of a large number of nonradioactive atoms with radiation detection techniques. However, as the half-life increases, the time taken to carry out an experiment with a small number of radioactive atoms naturally increase, for half-lives, of say, 10 years efficient detection of the radioactive decay products becomes impossible unless the measurement can be continued for 10 years. Therefore, studies of long-lived radioactive isotopes invariably use very large numbers of atoms and the apparatus detects the decay of only a small fraction of the total during the experiment. In this situation the mass spectrometric detection sensitivity surpasses by far the sensitivity of radioactive counting methods. 

A comprehensive description of the nature of radioactivity and its interaction with matter is beyond the scope of this chapter, and such information can easily be found elsewhere (Shleien et al., 1998 CPEP, 2003 Tykva, 2004). Here we give only a brief sketch of the basic principles. Radioactivity is a natural phenomenon, discovered in 1896 by Henri Becquerel. The nuclei of some atoms are unstable and decay spontaneously, emitting ionizing radiation to attain a more energetically favorable state. Radioisotopes are characterized by the nature of the... 

Not all nuclei are unstable. Only unstable nuclei im-dergo change and produce radioactivity in the process of radioactive decay. Three types of natural radiation emitted by unstable nuclei are alpha particles, beta particles, and gamma rays. This radiation is collectively termed ionizing radiation. 

In Figure 4.8 the ratio of the number of nuclei at any time t to the original number at time / = 0 (i.e. N/Nq) has been plotted on both a linear (left) and logarithmic (right) scale as a function of t. The linearity of the decay curve in the semi-logarithmic graph illustrates the exponential nature of radioactive decay. Since A oc N, the equation can be rewritten as... 

There are many instances where a parent decays to a daughter which itself decays to a third species (i.e. a "grand-daughter ). The chains of radioactive decay in the naturally occurring heavy elements include as many as 10 — 12 successive steps (Fig. 1.2). 

Even if the experimental design and execution are perfect so that the determinant error is eliminated in experiments involving radioactivity there is always a random error due to the statistical nature of radioactive decay. Each radioactive atom has a certain probability of decay within any one time interval. Consequently, since this probability allows unlikely processes to occur occasionally and likely processes not to occur in any particular time interval, the number of decays may be more or less than the number in another similar... 

The statistical nature of radioactive decay also leads to an uneven distribution of decays in time which is important when handling dead-time corrections and discussing required system time resolution. Let us first assume that a decay has occurred at time t = 0. What is then the differential probability that the next decay will take place within a short time interval, dr, after a time interval t has passed Two independ t processes must then occur in series. No decay may take place within the time interval from 0 to r, probability P 0),... 

In Molecular Imaging (MI) with radiotracers, molecules labeled with radioactive atoms, which undergo the process of radioactive decay are localized and quantified to produce what are cedled molecular images. According to the tracer principle, these molecules are often identical to a natural substance within the body, such as glucose. 

The foundations of modern geochronology were laid at the turn of the century in the work of Rutherford and Soddy (1903) on natural radioactivity. They showed that the process of radioactive decay is exponential and independent of chemical or physical conditions. Thus rates of radioactive decay may be used for measuring geological time. Isotopic systems used in age calculations are listed in Table 6.1 and Box 6.1. In this section we discuss two of the most common techniques used in geochronological calculations — isochron diagrams and model age calculations. This is followed by a discussion of the significance of the calculated ages. 

The other more short-lived actinides must be made synthetically by using high-energy collisions in a particle accelerator. These machines collide a particle such as a gamma ray with an atom of the naturally formed actinide elements. They split after collision the other elements are formed in the process of radioactive decay. The first of these new elements were named after the planets in a similar fashion to uranium (planet Uranus) — neptunium (Neptune) and plutonium (Pluto). The rest have been named for historical themes or places in which they were first created. 

The naturally occurring radioactive decay series that begins with IfU stops with formation of the stable Pb nucleus. The decays proceed through a series of alpha-particle and beta-particle emissions. How many of each type of emission are involved in this series ... 

Natural distributions of elements in subsurface geologic formations can give rise to ground water or soil zone contamination. Two examples of note are the generation of radioactive decay products (e.g., radon gas, radium) from natural thorium and uranium, and the release of naturally occurring arsenic or selenium from earth materials. 

On account of the statistical nature of radioactive decay it is advisable to perform each measurement three times. 

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