Rates of Decay Half-Lives

The word radioactive sounds scciry, but science and medicine are stuffed with useful, friendly applications for radioisotopes. Many of these applications are centered on the predictable decay rates of various radioisotopes. These predictable rates are characterized by half-lives. The half-life of a radioisotope is simply the amount of time it tcikes for exactly half of a sample of that isotope to decay into daughter nuclei. For excimple, if a scientist knows that a sample originally contained 42 mg of a certain radioisotope and measures 21 mg of that isotope in the sample four days later, then the half-life of that radioisotope is four days. The half-lives of radioisotopes range from seconds to billions of yecirs. 

Radioactive dating is the process scientists use to date Scimples based on the amount of radioisotope remaining. The most famous form of radioactive dating is Ccirbon-14 dating, which has been used to date human remains and other organic artifacts. However, radioisotopes have also been used to date the Earth, the solar system, and even the universe. 

To calculate the remaining amount of a radioisotope, use the following formula  

If a sample originally contained 1 g of thorium-234, how much of that isotope will the sample contain one year later  

76 X10 g. Table 20-1 tells you that thorium-234 has a half-life of 24.1 days, so that s T. The time elapsed (t) is 365 days, and the original sample was 1 g (Aq). Plugging these values into the half-life equation gives you 

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