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Matter consists of atoms making up more than 110 elements. Each element has different varieties called isotopes and some of these isotopes are radioactive. Isotopes differ in the number of neutrons in nucleus and the radioactive isotopes decay by emitting particles.
Radiometric dating is based on the decay of radioactive isotopes in to stable isotopes. The above illustration is the U238 - Pb206 series. U238 is the parent isotope and the others are daughter isotopes. The Pb206 is the final daughter isotope and the one used in radiometric dating.
The theory is that as a parent isotope decays, the percentage of the parent isotope decreases, while the percentage of the daughter isotopes increases. This only works perfectly in a closed system, that is one in which there is no gain or loss of parent or daughter isotope. Such a closed system does not exist.
When dating a rock; a scientist does not hook it up to his ACME dating machine to get a date. They actually measure only the ratio of parent or daughter isotopes in the rock. These ratios can be the result of radioactive decay, parent and daughter isotope entering or leaving the system, or the original isotopic make up of the system.
How this relates to the age of the rock is all theory. It involves theories about the formation of the rock and its history since it was formed.
In dating any object with out a documented date, a scientists:
Radio-isotope dating relies on the following assumptions: