Box 2.7 RADIOACTIVE DECAY AND HALF-LIVES The \'half-life\' of a radioactive elem

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Box 2.7 RADIOACTIVE DECAY AND HALF-LIVES The 'half-life' of a radioactive element is defined as the time taken tor the original radioactive atoms of that element to decay spontaneous life will another element or isotope. If the rate of decay is rapid, then be relatively short, as is the case for l4C (half-life 5700 years) which is often used for radiocarbon dating of archaeological artefacts and materials. It only a few half-lives for the concentrations of an original radiogenic element to fall to negligible quantities. This is why 4C dating is no use for dating anc geological materials-after only 8 half-lives (45 600 years), less any original 14C would remain. If radiogenic elements are not replenish taken for half of v to form the half-life takes than 0.4% of ed by the decay of other radiogenic isotopes, then they will eventually be lost altogether This is thought to have been the case with the decay of26Al, which has a half- life of 0.73 Ma. Studies of CI carbonaceous chondrites suggest proportion of the aluminiu nebula was the unstable isotope 26Al. This was originally created during a supernova explosion pre-dating the birth of our Solar System, and cannot be replenished by the spontaneous decay of any other radiogenic elements. The decay of 26Al may have contributed significantly to the heating of planetary embryos but, because of its relatively short half-life compared to the age of the Solar System, any remaining 26Al has long since vanished within the terrestrial planets. Whilst such short-lived isotopes will have been important heat sources during the early stages of terrestrial planet evolution, study of Earth materials indicates that it is the isotopes of the elements uranium (U), thorium (Th) and potassium (K) which are responsible for most of the radiogenic heating that has occurred throughout the history of our planet. These isotopes all have particularly long half-lives (see Table 2.6), and were present in sufficient quantities after condensation and accretion to ensure that they have remained that a significant m present at the time of condensation of the solar abundant within present-day Earth. Table 2.6 Half-lives of common isotopes in the Earth's crust and mantle. The Earth today. ntinuing decay of these isotopes is an important internal heat source within th Isotope Half-life (10yT) Present rate of heat generation in the Earh (1o-12 generatic 004 0% 1.04 2.8 235 238 232Th 40K 0.71 4.50 13.9 1.30 Values are in kg of average Earth materials, not of the isotope concerm

Explanation / Answer

Half life is the term used to describe the amount of time in which a radioactive substance decays to half its original.

If the original is 100%, after the first half life 50% of the original amount remains. After the second half life, 25% of the original amount remains. And this continues.

Here, for the radiactive substance X, after two half lives, one quarter of the original substance remains since the formation of the earth.

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