Radioactive decay chains

The atomic weight of the nuclides in these decay chains changes by four atomic mass units after the emission of each alpha particle so they are commonly labeled as the 4n, 4n -t 1,4n -i- 2, and 4n -i- 3 decay chains according to atomic weight of the 

FIGURE 1.3 The natural radioactive decay chain of the 4n + 2 series, beginning with 

Uranium 92 Protactinium 91 Thorium 90 Actinium 89 Radium 88 Francium 87 Radon 86 Astatine 85 Polonium 84 Bismuth 83 Lead 82 Thallium 81 

FIGURE 1.4 The natural radioactive deeay ehain of the 4n -r 3 series, beginning with nraninm-235 and ending with lead-207. 

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The analysis of steady-state and transient reactor behavior requires the calculation of reaction rates of neutrons with various materials. If the number density of neutrons at a point is n and their characteristic speed is v, a flux effective area of a nucleus as a cross section O, and a target atom number density N, a macroscopic cross section E = Na can be defined, and the reaction rate per unit volume is R = 0S. This relation may be appHed to the processes of neutron scattering, absorption, and fission in balance equations lea ding to predictions of or to the determination of flux distribution. The consumption of nuclear fuels is governed by time-dependent differential equations analogous to those of Bateman for radioactive decay chains. The rate of change in number of atoms N owing to absorption is as follows ... 

Table 4—Radioactive decay chains for the longer-lived radioisotopes of cerium including those which have been identified in environmental studies...

This results in the transmutation of parent element X into daughter Y, which has an atomic number two less than X. The particular isotope of element Y which is formed is that with an atomic mass of four less than the original isotope of X. Note that, as in chemical reactions, these nuclear reactions must be numerically balanced on either side of the arrow. Many of the heavy elements in the three naturally occurring radioactive decay chains (see below) decay by a-emission. 

Many of the heavy elements in the three natural radioactive decay chains also decay by -emission. 

The American scientist B. B. Boltwood appreciated as early as 1907 that radioactive decay can tell us about the age of the Earth. The best estimate until that time was around 98 million years, which Lord Kelvin deduced in the 1860s by considering how long it would take for the hot core to cool down. Boltwood calculated that the planet could be as much as two billion years old. The current estimate of more than twice this value is supported by a host of other radiometric methods which look at the relative abundances of parent and daughter isotopes in radioactive decay chains. 

Figures 8.1 and 8.2 show the short-lived radioactive decay chains for 226Ra and 228Ra, respectively, to illustrate the relationship of the progeny to the two radium isotopes. Long-lived radionuclides continue both the chains.

To understand the behavior of U-series nuclides, we start by discussing closed systems. These models form the basis for more complicated open-system models discussed later. Here we discuss the behavior of generic radioactive decay chains that apply to all the naturally occurring actinide chains. 

The equations and solutions for closed-system radioactive decay chains have been known since Bateman (1910). To understand the behavior of these systems, however, it is useful to express them as a linear system of ordinary differential equations and use some basic results from linear algebra to discuss the general solutions. This treatment helps to elucidate the ideas of secular equilibrium and relaxation to equihbrium. 

Common radioisotope sources of alpha particles are listed in Table 5.6. All but the first one listed are members of radioactive decay chains. Decay chains are classified into four groups according to their mass numbers. They are Th-series whose mass number is 4N (N is integer), U-series of 4N+2, Ac-series of 4N+3 and Np-series of 4N-fl. An Np-series does not exist naturally because the half-life of its longest-lived member is... 

Because of its ability to accept U and Th, monazite is one of the most radioactive minerals after uraninite, thorianite or thorite. It is the most common radioactive mineral (Overstreet 1967), and in many rocks the main host of U and Th. The possibility for monazite to accept Pb in the same site as U and Th is obviously important for geochronology. Pb produced by U and Th has a place in the structure (Quarton et al. 1984). Therefore there is a not a natural tendency for Pb to be released from monazite, as might be anticipated by considering the structure of zircon. Another consequence of the ability of monazite to incorporate various ions is that, in the three U and Th decay chains, most elements can be incorporated in the A site. If all actinides and a small amount of Ra (because Ba is favourably partitioned) can be accepted in monazite, all elements with half-lives greater than about one year are incorporated in the mineral structure. This suggests that at any moment in the radioactive decay chains of U and Th, there is little tendency for any intermediate decay products to escape from the mineral structure. 

This recoil led to ejection of into the wall of the instrument. The use of the recoil of the daughter to effect its sqiaration was enq>loyed by O. Hahn beginning in 1909 and played a c tral role in elucidating the difiierrait natural radioactive decay chains. 

In many radioactive decay chains the half-life of the parent is longer than that of the daughter but it is short enough that a change in the disintegration rate of the parait is observable during the period of observation of the experiment. In such cases the system... 

Rivers also transport U/Th series nuclides in particulate phase to the sea. These nuclides exist in two forms in the particulate phase, one as a part of their lattice structure and the other as surface coating resulting from their adsorption from solution. Analysis of suspended particulate matter from rivers shows the existence of radioactive disequilibria among the members of the same radioactive decay chain. In general, particulate phases are characterized by Ra/ °Th activity ratios... 

The radioactive decay of thorium-232 occurs in multiple steps, called a radioactive decay chain. The second product produced in this chain is actinium-228. Which of the following processes could lead to this product starting with thorium-232 ... 

Some nuclei cannot gain stability by a single emission. Consequently, a series of successive emissions occurs as shown for uranium-238 in figure 21.3. Decay continues until a stable nucleus—lead-206 in this case—is formed. A series of nuclear reactions that begins with an unstable nucleus and terminates with a stable one is known as a radioactive decay chain or a nuclear disintegration series. Three such series occur in nature iu-anium-238 to lead-206, uranium-235 to lead-207, and thorium-232 to lead-208. All of the decay processes in these series are either alpha emissions or beta emissions. 

The steps below show three of the steps in the radioactive decay chain for 9oTh. The half-life of each isotope is shown below the symbol of the isotope, (a) Identify the type of radioactive decay for each of the steps (i), (ii), and (iii). (b) Which of the isotopes shown has the highest activity (c) Which of the isotopes shown has the lowest activity (d) The next step in the decay chain is an alpha emission. What is the next isotope in the chain [Sections 21.2 and 21.4]... 

Lead can exist as four stable isotopes ° Pb, Pb, Pb, and Pb. Which of these isotopes of lead has the greatest cosmic abundance Rationalize your answer. Lead-205 is unstable and undergoes electron capture. Write the nuclear reaction for this process. Lead-206 is produced from Rn by a radioactive decay chain. Show the nuclear reactions for each step of the chain. 

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