Challenge The table shows the amounts of radioisotopes in three different samples. To the nearest gram, how much will be in Sample B and Sample C when Sample A has 16.2 g remaining? Sample Radioisotope Half-life Amount (g) A cobalt-60 5.27 y 64.8 B tritium 12.32 y 58.4 C strontium-90 28.79 y 37.6
Radioactive decay follows first-order kinetics and radioactive decay rates are measured inhalf-lives. Each radioactive nuclide has a characteristic half-life (t ). 1/2-live is the timerequired for half of a radioisotope’s nuclei or the atoms in a sample to decay into itsproducts. An isotope’s half-life help us to determine the amount remaining in the sample.In the given table, radioisotopes with their half-lives and the amount is given. In a givencobalt-60 source, half of the nuclei decay every 5.27 years, both the amount of materialand the intensity of the radiation is reduced to half every 5.27 years. For a givensubstance, the intensity of radiation that it produces is directly proportional to the rate ofdecay of the substance and the amount of the substance.The amount of radioactive element remaining in the sample is given by:Where ‘N’ is the remaining amount, ‘N ’ is th0initial amount, ‘n’ is the number ofhalf-lives that have passed.In the case of Cobalt-60,The remaining amount, N = 16.2gInitial amount, N 064.8gTherefore ‘n’ is:In the case of tritium (sample B),The remaining amount, N = x gInitial amount, N 058.4g‘n’ is 2 (from the previous step)Hence ‘N’ is calculated as :The amount remaining in sample B is 14.6 g .In the case of strontium-90 (sample C),The remaining amount, N = x gInitial amount, N 037.6g‘n’ is 2 (from the first step)Hence ‘N’ is calculated as :The amount remaining in sample C is 9.4 g .