Calculations Based on Half-Life

So far, our discussion has been mainly qualitative. We now consider the topic of half-lives from a more quantitative point of view. This approach enables us to determine the half-life of a radioisotope or the age of an object. 

As noted earlier, radioactive decay is a first-order kinetic process. Its rate, therefore, is proportional to the number of radioactive nuclei Nin a sample  

The first-order rate constant, k, is called the decay constant. 

The rate at which a sample decays is called its activity, and it is often expressed as number of disintegrations per unit time. The becquerel (Bq) is the SI unit for expressing activity. A becquerel is defined as one nuclear disintegration per second. An older. 

As a radioactive sample decays, the amount of radiation emanating from the sample decays as well. For example, the half-life of cobalt-60 is 5.26 yr. The 4.0-mCi sample of cobalt-60 would, after 5.26 yr, have a radiation activity of 2.0 mCi, or 7.5 x 10 Bq. 

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