LITMIR.BIZ

      137Ba decay data, counting numbers of decays observed in 30-second intervals. The best-fit exponential curve is shown. The points do not fall exactly because of statistical counting fluctuations

      The probability that a particular nucleus will undergo radioactive decay during a fixed length of time does not depend on the age of the nucleus or how it was created. Although the exact lifetime of one particular nucleus cannot be predicted, the mean (or average) lifetime of a sample containing many nuclei of the same isotope can be predicted and measured. A convenient way of determining the lifetime of an isotope is to measure how long it takes for one-half of the nuclei in a sample to decay – this quantity is called the half-life, t(1/2). Of the original nuclei that did not decay, half will decay if we wait another half-life, leaving one-quarter of the original sample after a total time of two half-lives. After three half-lives, one-eighth of the original sample will remain and so on. Measured half-lives vary from tiny fractions of seconds to billions of years, depending on the isotope. The number of nuclei in a sample that will decay in a given interval of time is proportional to the number of nuclei in the sample. This condition leads to radioactive decay showing itself as an exponential process, as shown above. The number N of the original nuclei remaining after a time t from an original sample of N0 nuclei is N = N0e-(t/T)

      where T is the mean lifetime of the parent nuclei. From this relation, it can be shown that t(1/2) = 0.693T.

      Ex. 1 Make the following sentences negative.

      1. Nuclear radiation occurs in other forms, including the emission of protons or neutrons. 2. The number of nuclei in a sample that will decay in a given interval of time is proportional to the number of nuclei in the sample. 3. This condition leads to radioactive decay showing itself as an exponential process, as shown above. 4. The best-fit exponential curve is shown.