Radioactive decay, elucidation

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. 

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. 

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. 

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. 

Today, physical chemistry has accomplished its great task of elucidating the microcosmos. The existence, properties and combinatory rules for atoms have been firmly established. The problem now is to work out where they came from. Their source clearly lies outside the Earth, for spontaneous (cold) fusion does not occur on our planet, whereas radioactive transmutation (breakup or decay), e.g. the decay of uranium to lead, is well known to nuclear geologists. The task of nuclear astrophysics is to determine where and how each species of atomic nucleus (or isotope) is produced beyond the confines of the Earth. 

On the other hand, Hansen et al. [28] measured A -x-ray intensity ratios for various elements following A -capture decay of radioactive nuclides and pointed out that the KP/Ka ratios by electron capture (EC) decay are considerably different from those by photon and electron impact ionization. Paic and Pecar [29] found that the Kp/Ka ratios for Ti, V, Cr, and Fe by EC are smaller by almost 10% than those by photoionization (PI), but no appreciable difference was observed for Cu and Zn. A similar excitation mode dependence was measured for Mn by Arndt et al. [30]. They stated that the reason for the difference is due to the excess 3d electron in EC and the large shakeoff probability in PI. Rao et al. [31] also observed smaller KP/Ka intensity ratios by EC for Mn and Fe. Since no appreciable difference was found for high-Z elements, they concluded that the difference observed for 3d elements can be ascribed to the chemical effect. It is usual that the chemical forms of the samples for EC measurements are different from those for PI. In order to elucidate the excitation mode dependence on the Kp/Ka ratios in 3d elements, it is necessary to perform theoretical calculations which takes into account the chemical effect as well as the difference in the electron configurations. 

Once it became clear that radioactive elements were decaying to new elements, which were themselves radioactive, a great deal of effort was expended in working out the decay sequences. In most cases the new elements were at first obtained in quantities too small to be weighed and were distinguished from each other only by the type of decay they exhibited and the rate at which the decay occurred. Three decay series were elucidated the uranium series proceeded through radium and terminated with the stable radium G the thorium series ended in the stable thorium D and the actinium series ended in actinium D. Between them, these series contained around 25 new radioelements. 

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