Basic principles of radiometric age dating

Radiometric age dating is a powerful chronological tool. It is based on the accumulation of the daughter nuclide produced by the decay of the parent isotope. If the decay rate is known, and if one can measure the amounts of parent element and daughter isotope, then it is 

This relationship is transformed into an equality by introduction of a proportionality constant, 1, which represents the probability that an atom will decay within a stated period of time. The numerical value of A is unique for each radionuclide and is expressed in units of reciprocal time. Thus, the equation describing the rate of decay of a radionuclide is 

Equation (8.3) is the basic equation that describes all radioactive decay processes. It gives the number of atoms (N) of a radioactive parent isotope remaining at any time t from a starting number N0 at time t = 0. 

What about the daughter isotope If the original number of atoms of the stable daughter isotope is taken to be zero at / - 0, and no daughter atoms are added to or lost from the system 

Equation (8.5) gives the number of stable radiogenic daughter atoms ( ) at any time t formed by decay of a radioactive parent whose initial abundance at / - 0 was N0. 

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