Nuclear-decay constant

The left-hand side of Equation 19.1, dNjdt, is the number of disintegrations taking place per unit time. Each radionuclide has its own characteristic nuclear-decay constant. The minus sign indicates that the decay results in a decrease in N. Equation 19.1 indicates that the rate of decay of any radionuclide is directly proportional... 

Equation 19.3 states that if, at time / = 0, there are No radioactive atoms having a nuclear-decay constant A, then at any later time t there will be N radioactive atoms remaining, and (iVo — N) radioactive atoms will have undergone radioactive decay during the time t. 

Relationship between nuclear decay constant and half-life this is derived from the previous equation at... 

Half-Lives and Decay Constants. Each nuclear state, whether an unstable ground state or an excited level, has a characteristic probabiUty... 

In a description of nuclear properties, the half-life,, is quoted rather than the decay constant. This quantity is the time it takes for one-half of the original nuclei to decay. That is,... 

Notice that both the electric charge and the total number of nuclear particles (nucleons) are conserved in the nuclear decomposition. Careful study of the rate of this nuclear decay shows that in a given period of time a constant fraction of the nuclei present will undergo decomposition. This observation allows us to characterize or describe the rate of nuclear decay in a very simple manner. We simply specify the length of time it takes for a fixed fraction of the nuclei initially present to decay. Normally we pick the time for... 

One of the reasons why thermonuclear weapons have to be serviced regularly is the nuclear decay of the tritium that they contain. Suppose a tritium sample of mass 1.00 g is stored. What mass of that isotope will remain after 5.0 a (1 a = 1 year) The decay constant of tritium is 0.0564 a-1. 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

Chemical forms with at least one radioactive atomic nucleus are radioactive substances. The capability of atomic nuclei to undergo spontaneous nuclear transformation is called radioactivity. Nuclear transformations are accompanied by emission of nuclear radiation (Severa and Bar 1991). The average number of nuclei that disintegrate per unit time (= activity) is directly proportional to the total number of radioactive nuclei. The time for 50% of the original nuclei to disintegrate (= half-life or Tb 1/2) is equal to In 2/decay constant for that element (Kiefer 1990). Radiations... 

It is usually not possible or practical to control a given system input at an exact level in practice, most inputs are controlled around set levels within certain factor tolerances. Thus, controlled system inputs exhibit some variation. Variation is also observed in the levels of otherwise constant system outputs, either because of instabilities within the system itself (e.g., a system involving an inherently random process, such as nuclear decay) or because of the transformation of variations in the system inputs into variations of the system output (see Figures 2.17 and 2.18) or because of variations in an external measurement system that is used to measure the levels of the outputs. This latter source of apparent system variation also applies to measured values of system inputs. 

Quantitative estimates of the concentration levels of these 16 elements could be obtained by using silver standards containing known amounts of the elements of interest. Two standards were prepared at Brookhaven National Laboratory. Although we have established that the elements in these standards are homogeneously distributed, we have not completed their calibrations. Moreover the standards were not useful for scandium, tin, and iridium. For these elements the concentrations were calculated relative to those of elements for which good standards were available, using nuclear cross-sections and decay constants from the literature (7). 

The differential form of the spectrum can be integrated over all electron momenta to obtain the total decay constant. The expression, for a constant nuclear matrix element, to be integrated is... 

The decay constant is now reduced to an expression with the nuclear- matrix element, M(= Mjf ), and the strength parameter, g, written ... 

The decay constant of plutonium-239, a waste product from nuclear reactors, is 2.88 X 10 5 year-1. What is the half-life of 239Pu ... 

Radioactive contamination Contamination with radioactive matter Radioactive decay Change of unstable atomic nuclei into other stable or unstable nuclei, associated with emission of nuclear radiation Radioactive equilibria Definite ratios between the activities of mother and daughter nuclides, given by their decay constants... 

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