# Concept half life used radiometric dating

The half-life of \(\ce\)-238 is \(4.5 \times 10^9\) years.The end product of the decay of \(\ce\)-238 is \(\ce\)-206.\(\ce\)-14 dating procedures have been used to determine the age of organic artifacts. Half-life is defined as the amount of time for half of the volume of a radioactive element to decay to the daughter isotope.After 4 hours, only \(3.75 \: \text\) of our original \(60 \: \text\) sample would remain the radioactive isotope \(\ce\)-240.Example \(\Page Index\) A sample of \(\ce\)-225 originally contained 80 grams and after 50 days only 2.55 grams of the original \(\ce\)-225 remain. Solution We are going to tackle this problem similar to the last problem.

The half-lives of many radioactive isotopes have been determined and they have been found to range from extremely long half-lives of 10 billion years to extremely short half-lives of fractions of a second.The quantity of radioactive nuclei at any given time will decrease to half as much in one half-life.For example, if there were \(100 \: \text\) of \(\ce\)-251 in a sample at some time, after 800 years, there would be \(50 \: \text\) of \(\ce\)-251 remaining and after another 800 years (1600 years total), there would only be \(25 \: \text\) remaining.A useful concept is half-life, which is the time required for half of the starting material to change or decay.Half-lives can be calculated from measurements on the change in mass of a nuclide and the time it takes to occur.

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