# Relationship between radioactive isotope and radioactive dating

If you multiply the average lifetime by the natural logarithm of 2 (the number 0.6931), you get the half-life.You can read more about half-life, mean lifetime, and exponential decay in any algebra II book or the Wikipedia article on half-life.Half of the extraordinary heat of the Earth that erupts on its surface volcanically and drives the titanic motions of the continents is due to radioactivity, scientists find.This new discovery shows that the planet still retains an extraordinary amount of heat it had from its primordial days.The sum of all the lifetimes of the atoms, divided by the original number of atoms, is the mean lifetime.In other words, the mean lifetime is simply the arithmetic average of the lifetimes of the individual atoms.The lifetime units are time units such as seconds or years.The half-life of a radioactive element is the amount of time it takes for half of a sample of the element to decay away.

It is equal to the inverse of the mean lifetime: For example, radium-226 has a half-life of 1,602 years, an mean lifetime of (1,602)/ln2 = 2,311 years, and a decay rate of 1/(2,311) = 0.000433 per year.The scientists at the Kam LAND Collaboration detailed their findings online July 17 in the journal Nature Geoscience.To get the mean (or average) lifetime of a radioactive element, you take a sample of the radioactive atoms and wait for all of them to decay away, and keep track of how long each atom lasts.In other words, 0.0433 percent of the radium decays away each year, or 433 parts per million per year.The decay rate units are the inverse of time units, for example, years = 0.99 curie.

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