Radionuclides secular equilibrium

If the half-life of the mother nuclide is much longer than those of the succeeding radionuclides (secular equilibrium), eq. (4.48) becomes much simpler, provided that radioactive equilibrium is established. As in this case At A2, A3... Aa, all terms are small compared with the first one, giving... 

An understanding of the concept of secular equilibrium is also important for such age determinations using U-Th series radionuclides. Owing to the longevity of Th, and the number of parent atoms remains essentially... 

Since Ra and " Ra are both produced by recoil from the host mineral, it might be assumed that the production rates are equal. However, the relative recoil rates can be adjusted by considering that the parent nuclides near the mineral surface may not be in secular equilibrium due to ejection losses i.e., the activity of Th may be lower than that of Th due to recoil into groundwater of the intermediate nuclide Ra. Krisnaswami et al. (1982) calculated that the recoil rate of " Ra is 70% that of Ra if radionuclides are depleted along the decay chain in this way. 

Secular Equilibrium A condition that occurs when a chain of radionuclides has reached a steady state condition, in which the rate of decay of daughter nuclides is balanced by their rate of formation by decay of each parent. In this condition, the radioactivity (measured in disintigrations per minute) of each radionuclide in a chain is the same. 

Figure 11,8 Composite decay curves for (A) mixtures of independently decaying species, (B) transient equilibrium, (C) secular equilibrium, and (D) nonequilibrium, a composite decay curve b decay curve of longer-lived component (A) and parent radio nuclide (B, C, D) c decay curve of short-lived radionuclide (A) and daughter radionuclide (B, C, D) d daughter radioativity in a pure parent fraction (B, C, D) e total daughter radioactivity in a parent-plus-daughter fraction (B). In all cases, the detection coefficients of the various species are assumed to be identical. From Nuclear and Radiochemistry, G. Friedlander and J. W. Kennedy, Copyright 1956 by John Wiley and Sons. Reprinted by permission of John Wiley and Sons Ltd.

Radionuclide disequilibrium any deviation from secular equilibrium. 

Secular equilibrium when the rate of decay of the parent radionuclide is equal to that... 

An interesting concept that must always be taken into account in cyclotron-produced radionuclides is the saturation activity characteristic of each target and each nuclear reaction. The saturation activity is the activity of the radionuclide in which the secular equilibrium is obtained between the activity produced in the target and the disintegration of the radioisotope. The activity produced at a target can be calculated by the equation... 

These equations are the same as those derived for radioactive equilibrium between mother and daughter nuclide (eqs. (4.23) and (4.24)) i.e. in secular equilibrium the relations in section 4.4 are not only valid for the directly succeeding daughter nuclide, but also for all following radionuclides of the decay series. This has already been applied in the examples given in section 4.4. 

If secular equilibrium is not established, the activities of succeeding radionuclides can also be calculated by use of the equations given in this section. An example is the decay of the naturally occurring Po ( Po " Pb °Pb...). The... 

In a decay chain shown in Table 1 at secular equilibrium the activities of the coupled radionuclides are equal. In a closed system, this occurs after roughly hve half-lives of the shorter-lived daughter have elapsed ( parent and daughter refer to the first and subsequent nuclides in the decay series being considered). For example, Rn (half-life = 3.8 d) is in secular equilibrium with its parent, Ra (half-life = 1,620 yr), in 20d. 

A conceptual analogy of secular equilibrium is two linked water tanks of equal bottom area, each being drained by siphons of different internal diameter (Fig. 5.14). In this analogy, the higher tank contains a height of water, Hp, representing total number of parent radionuclides, Np. The inner diameter of the siphon draining the upper tank represents the decay constant of the parent, Xp. The... 

Chemical yields are determined from tracer activities added to the analytical aliquots however, the yields can also be determined from short-lived activities that are present in the sample due to secular radioactive equilibrium. For example, the chemical yield of uranium can be determined from the recovery of an added tracer activity, but in plutonium samples it can also be determined from There is a 0.00245% branch for the decay of Pu by Qt-particle emission. If it is known that the plutonium sample was last purified more than a month ago, one can assume that 6.75-day in the analytical samples is in equilibrium with ""Pu, with a concentration defined by the branching ratio of activityf U)/activity( Pu) = 2.45 X 10 Similarly, radium is traced with 3.66-day " Ra, in secular equilibrium with the decay of 1.9-year Th. Use of intrinsic short-lived radionuclides as tracers requires that the time at which they were isolated from their parent activities is known precisely. 

Important note ( ) Specific activity of the parent radionuclide alone without considerin decaying radionuclides in secular equilibrium with it. ( ) The three stable lead isoto daughters of the three natural decay series, and hence are called radiogenic lead isoto] the naturally occurring lead isotope Pb. the activity of each )es are the ultimate jes by contrast with... 

Assuming secular equilibrium for the two decay chains, the activity of U is equal to that of its parent radionuclide, i.e., and is simply given by ... 

Therefore, the total specific activity of natural uranium metal in secular equilibrium and considering all the activities of its daughter radionuclides is 179.414 MBq.kg". ... 

Therefore, for natural thorium, the specific activity of the radionuclide Th is 4.046 MBq.kg. However, because the radionuclide is also in secular equilibrium with all its decaying daughters, the total specific activity of natural thorium in secular equilibrium is given by the previous specific activity times the number of decaying radionuclides in the 4n decay chain as follows ... 

SECULAR EQUILIBRIUM The condition that the activity of a daughter radionuclide is equal to that of its parent. A necessary precondition is that the daughto half-life is much smaller than that of the parent. 

The values have been determined on the basis of consideration of the worldwide distribution of activity concentrations for these radionuclides. Consequently, they are valid for the natural decay chains in secular equilibrium that is, those decay chains headed by U, U or Th, with the value given to be applied to the parent of the decay chain. The values can also... 

In an undisturbed (closed) system, that is to say one at secular or radioactive equilibrium, °Po has the same activity as other radionuclides in this series. Preceded by its immediate parent (half-life 5.013 days), fractionation occurs, and it equilibrates with its grandparent, namely Pb. 

Generally, the decay of a radioactive nuclide results in a longer-lived or even stable daughter nuclide. In this respect, radionuclide generator systems where the daughter nuclide presents a shorter half-life are a welcome exception from the general properties of P decay. In particular, for a clinical application, a state of a radioactive equilibrium is mandatory. Thus, mainly the transient and secular equilibria of radionuclide generations are relevant for... 

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