Disintegration constant

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

The disintegration constant of 55Fe is 0.2665 years 1. Calculate the half-life of the radioisotope. 

The disintegration constant of a radioisotope is 0.07452 hours 1. What is the half-life of that radioisotope ... 

The half-life of 45Ca is 165 days. Calculate the disintegration constant of the radioisotope. 

Half-life period of a given radioactive substance is independent of the amount of substance present initially. It depends only on disintegration constant of the element. 

Thus the amounts present at equilibrium are inversely proportional to their disintegration constant or directly proportional to their half-lives. 

When the disintegration constant of the nuclide produced is s , the rate of production of the nuclides is expressed as eq. (4.4) ... 

We next evaluate the specific rate (disintegration) constant, k. 0.693, 0.693 0.693... 

The law thus obtained differs from the empirical formula of G-eiger and NuttaU in this respect, that it is not linear in v, but in 1 jv however, since the variation of v is confined to comparatively narrow limits, from -y = 1-4 X 10 cm./sec. to w = 2-0 X 10 cm./sec., the difference is slight. In consequence of the large factor in the second term— in which V appears— the range of values of the disintegration constant is extremely wide. 

We next evaluate the specific rate (disintegration) constant, k. 

The proportionality constant k is known as the decay or disintegration constant. Integration of this equation proceeds as follows ... 

The decay constant is sometimes also called the disintegration constant. The half-life and the decay constant give the same information, so either may be used to characterize decay. Another useful concept in radioactive decay is the average lifetime. Average lifetime is the reciprocal of decay constant. 

The disintegration of an unstable nucleus is an event so completely unpredictable and random that the only thing which can be said is that an imstable nucleus will decay within a given period of time. For a particular isotope, the proportion of nuclei that decay in a given time is a constant known as its disintegration constant. If the decline in activity of a radioactive isotope is plotted against time (Figure 13.2) a typical exponential form is obtained. 

Another constant for any given radioisotope is the time that is required for the original activity to fall by a half. This is referred to as the half-Ufe and is used more commonly than the disintegration constant because it is of much more practical utility. The half-life, t,/, of a given isotope and its decay constant, k, may be tied in a relationship as follows... 

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