Secular equilibrium, radioactive isotopes

Although there are three Rji isotopes in the U- and Th-decay series, only is sufficiently long lived tm= 3.8 days) to be a useful estuarine tracer. Radioactive decay of Ra continuously produces Rn, which because of its short half-life is generally in secular equilibrium in seawater. Being chemically non-reactive except for very weak Van der Waals bonding makes this isotope a unique marine tracer in that it is not directly involved in biogeochemical cycles. 

The half-lives of 238U, 235U, and 232Th are all very much longer than those of the radioactive daughter isotopes in their decay chains. Therefore, a condition known as secular equilibrium is quickly established in which the decay rates of the daughter isotopes in the decay chain equal that of the parent isotope. In a closed system, once secular equilibrium is... 

The experimentally measured rates of decay of radioactive atoms show that the decay is first order, where the number of atoms decomposing in a unit of time is proportional to the number present—this can be expressed in the following equation dN/dt = —X N. Another term used for characterizing rate of decay is half-life (t 1/2), the time required for half of the initial number of atoms to decay. Isotopes are considered to be in secular equilibrium, when the rate of decay of the parent is equal to that of its daughter. 

The error caused by the assumption that the activities of parent and daughter radioactive isotopes are in secular equilibrium in a closed system (Eq. (5.26)) as a function of the ratio of the parent daughter (P D) half lives. Very small errors exist as t /2,p/t /2.D becomes greater than 50. 

Radiogenic radioactive isotopes exist a limited time from formation to decay. Their content depends on the rates of these two processes. That is why the concentration of each radiogenic radioactive isotope is subject to the so-called radioactive secular equilibrium. At this equilibrium rates of its formation and decay are equal. Radioactive stationary equilibrium takes longer by about one order of the magnitude to settle than half-life of the longest-living intermediate member of the series (except for the parent element of the series). The isotope amounts of two intermediate members of the series are subject to equality ... 

At the beginning of the 20th century, radium was used to estabhsh the standard prototype of the curie. Actually, one curie is exactly equal to the radioactivity of a source that has the same radioactivity as 1 g of the radionuchde radium-226 in secular equilibrium with its derivative, radon-222 (or emanation). In spite of the new mandatory SI unit of radioactivity, the bec-querel, symbol Bq, the curie, Ci, is sometimes still in use (1 Ci = 37 GBq). Twenty-five isotopes are now known radium-226, the most common isotope, has a half-life of 1620 years. This isotope is purged from radium and sealed in minute tubes, which are used in the treatment of cancer and other diseases. Radium is used in the production of self-luminous paints, neutron sources, and in medicine for the treatment of disease. Some of the more recently discovered radioisotopes, such as Co or Cs, are now being used in place of radium. Some of these sources are much more powerful, and others are safer to use. Inhalation, injection, or body exposure to radium can cause cancer and other bodily disorders. The maximum permissible burden in the total body for Ra is 7.4 kBq. 

Uranium as the main starting material for nuclear energy production is a naturally radioactive element, composed of the three long-lived isotopes U, and In undisturbed natural deposits, these isotopes appear in a secular decay equilibrium with their daughter products of the 4n+2 and 4n+3 series, which are presented in a simplified version in Figs. 3.1. and 3.2. 

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