Radioactive nuclide decay

A sample of 100 mg of a radioactive nuclide decay to 81.85 mg of the same in exactly 7 days. The decay constant for this disintegration and the half life of the nuclide. Calculated ... 

FIGURE 19.6 The radioactive nuclide decays via a series of alpha and beta emissions to the stable nuclide ° Pb. 

In the type of process described here, a radioactive nuclide decays to produce a daughter, which is also radioactive. In a general way, this is similar to the reaction scheme in which a transient state (intermediate) is produced as A —> B —> C, but there are also some significant differences depending on the relative half-fives of the parent and daughter. One significant difference between radioactive decay and chemical reactions is that the latter are reversible to some extent, so they tend toward equilibrium. Radioactive decay proceeds to completion. If subscripts 1,2, and 3 are used to represent the parent, daughter, and final product, respectively, the number of nuclei can be expressed as Ni,Nz, and N3. The rate constants... 

One of the most important properties of a radioactive nuclide is its lifetime. At present it is not possible to predict theoretically when any particular nucleus in a sample will decay. However, the number of nuclides in a sizeable sample that will decompose in a given time can be measured, and it is found that this rate of decay is characteristic of a given isotope. In fact, the rate of decay of an isotope is constant and unvarying. That is, if a fraction of a radioactive nuclide decays in a certain time interval f, then the same fraction of the remainder will decay in another increment of time f, irrespective of external conditions. Nuclear reactions are not affected by outside influences such as temperature and pressure and it is not possible to significantly alter the constant rate of radioactive decay. For example, radioactive strontium-90, an important... 

In how many half-lives will 10.0 g of a radioactive nuclide decay to less than 10% of its original value ... 

Different radioactive nuclides decay into their daughter nuclides at different rates. Some nuclides decay quickly while others decay slowly. The time it takes for half of the parent nuclides in a radioactive sample to decay to the daughter nuclides is called the half-life. Nuclides that decay quickly have short half-lives and are very active (many decay events per unit time), while those that decay slowly have long half-lives and are less active (fewer decay events per unit time). For example, Th-232 is an alpha emitter that decays according to the nuclear reaction ... 

When a radioactive nuclide decays, electrons are stripped from the parent atom by its recoil and decay products are formed as positive ions. These ions can attract liquid and even solid material, thus forming clusters of atoms or particles in the submicron region ranging from 0.001 to 0.01 pm. Air is permanently ionised by radiation from the natural radioactivity of air and by cosmic radiation which consists mostly of positively charged particles, 85% protons, 10% alpha particles with a smaller percentage of positively charged stripped nuclei of heavier elements, such as Fe, Co and Ni, etc. Production of an ion pair requires 35.6 eV if ionisation is by alpha particles and 32.5 eV if by fast electrons. In the free atmosphere, the rate of production of small ions is in balance with the rate of neutralisation by recombination and the rate of attachment to condensation nuclei. Condensation nuclei are mostly the Aitken nuclei, which are submicrometre particles in the range 0.005 to 0.01 pm. 

The rate at which a sample of a radioactive nuclide decays is expressed in terms of half-life. This quantity is the time required for half of the atoms of a sample of a given nuclide to decay. For example, it takes 37.2 min for half of the nuclei of chlorine-38 to decay to argon-38. After 37.2 min, 0.50 g of a 1.0 g sample of chlorine-38 will remain, and there will be 0.50 g of argon-38. After two half-lives (74.4 min), the fraction of chlorine-38 that remains will be 1 of 1, or... 

Two radioactive nuclides decay by successive first-order processes ... 

Each radioactive nuclide decays at its own characteristic rate. That rate is completely independent of the temperature, pressure, or volume of the sample, or whether the sample is a pure element, part of a compound, or part of a mixture. The most convenient way to distinguish the decay rate of different nuclides is to state their half-lives. The half-life (ti ) of a radioactive substance is the time it takes for one half of the atoms that were present... 

We can use Fig. 17.13 to predict the type of disintegration that a radioactive nuclide is likely to undergo. Nuclei that lie above the band of stability are neutron rich they have a high proportion of neutrons. These nuclei tend to decay in such a way that the final n/p ratio is closer to that found in the band of stability. For example, a l4C nucleus can reach a more stable state by ejecting a (3 particle, which reduces the n/p ratio as a result of the conversion of a neutron into a proton (Fig. 17.15) ... 

As shown in Example, Equation is used to find a nuclear half-life from measurements of nuclear decays. Equation is used to find how much of a radioactive substance will remain after a certain time, or how long it will take for the amount of substance to fall by a given amount. Example provides an illustration of this t q)e of calculation. In Section 22-1. we show that Equation also provides a way to determine the age of a material that contains radioactive nuclides. 

One of the problems with radioactive nuclides such as Pu is that their decay cannot be stopped, so... 

Radioactive dating is most valuable in estimating the age of materials that predate human records, such as the Earth itself Calculating the age of a sample from the amounts of its radioactive nuclides and their decay products... 

Analyses of this type are correct only if all of the product nuclide comes from radioactive decay. This is not known with certainty, but when age estimates using different pairs of nuclides give the same age and samples from different locations also agree, the age estimate is likely to be accurate. Note also that 3.8 X 10 years agrees with the qualitative limits derived from naturally occurring radioactive nuclides. 

Radioactivity serves as a useful clock only for times that are the same order of magnitude as the decay half-life. At times much longer than t j2, the amount of radioactive nuclide is too small to measure accurately. At times much... 

The concept most commonly used when dealing with radioactive nuclides is activity. By definition, the activity of a number of atoms of a nuclide is the number of decay events per unit of time. The law of radioactivity tells us that this activity is equal to the decay constant times the number of atoms. 

Suppose the initial number of nuclei of a radioactive nuclide is N0, and that the half-life is T. Then the amount of parent nuclei remaining at a time t can be written as Nx = NQ( /2)(tlT>. This relationship is called the radioactive decay equation. What is the number of daughter nuclei present at time t, expressed in terms of N0 and Nx ... 

Decay Constant (A,)—The fraction of the number of atoms of a radioactive nuclide which decay in unit time (see Disintegration Constant). 

The rate at which radioactive atoms decay is unaffected by the chemical or physical form of the nucleide and depends only on the number N of atoms present and the decay constant Vs-1 for that particular nuclide. In a single... 

Mass-spectroscopic technique has also been used with non-fissile targets after pile or cyclotron bombardment to determine the mass-numbers of radioactive nuclides. In one case, the branching ratios of certain isotopes for and electron capture decay (where different elements are produced by the two routes) were determined from the amount of the stable end-products of radioactive decay, using the mass-spectrometer to identify the isotopes concerned and to correct for any stable impurities of the elements concerned (98). For some purposes, mass-spectroscopic separations could be very valuable technically such as the... 

The concentration of the radioactive nuclide (reactant, such as Sm) decreases exponentially, which is referred to as radioactive decay. The concentration of the daughter nuclides (products, including Nd and He) grows, which is referred to as radiogenic growth. Note the difference between Equations l-47b and l-47c. In the former equation, the concentration of Nd at time t is expressed as a function of the initial Sm concentration. Hence, from the initial state, one can calculate how the Nd concentration would evolve. In the latter equation, the concentration of Nd at time t is expressed as a function of the Sm concentration also at time t. Let s now define time t as the present time. Then [ Nd] is related to the present amount of Sm, the age (time since Sm and Nd were fractionated), and the initial amount of Nd. Therefore, Equation l-47b represents forward calculation, and Equation l-47c represents an inverse problem to obtain either the age, or the initial concentration, or both. Equation l-47d assumes that there are no other ot-decay nuclides. However, U and Th are usually present in a rock or mineral, and their contribution to " He usually dominates and must be added to Equation l-47d. 

Many homogeneous reactions, known as reversible reactions, go both ways toward equilibrium. The common exception is the decay of radioactive nuclides. Consider the following reversible reaction... 

The above condition of equal activity of all radioactive nuclides in a decay chain (except for branch decays) is known as secular equilibrium. More detailed solutions for the concentration evolution of intermediate species can be found in Box 2-6. 

The second effect is on the diffusive loss of daughters of radioactive nuclides. For example, decays into many daughters and finally becomes AH the... 

For use in geochronology, the decay constant of a radioactive nuclide must be constant and must be accurately known. For a-decay and most (3-decays, the decay constant does not depend on the chemical environment, temperature, or pressure. However, for one mode of 3-decay, the electron capture (capture of K-shell electrons), the decay "constant" may vary slightly from compound to compound, or with temperature and pressure. This is because the K-shell (the innermost shell) electrons may be affected by the local chemical environment, leading to variation in the rate of electron capture into the nucleus. The effect is typically small. For example, for Be, which has a small number of electrons and hence the K-shell is easily affected by chemical environments, Huh (1999) showed that the decay constant may vary by about 1.5% relative (Figure l-4b). Among decay systems with geochronological applications, the branch decay constant of °K to °Ar may vary very slightly (<1% relative). 

This method is used mainly for short-lived radioactive nuclides produced by cosmic ray spallation, such as °Be, A1, Si, C1, and Ar (Table 5-1). Because these nuclides have relatively short half-lives, if there was any initial amount of the nuclides at the beginning of Earth history, the initial amount would have completely decayed away. The small amount that can be found in... 

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