Dating method 4 Extinct nuclides for relative ages

4 Dating method 4 Extinct nuclides for relative ages 

The half-lives of many nuclides are much shorter than the age of the Earth. For 

Start from the equation for the growth of the daughter D = Dq + Po(1 - If the parent is an extinct nuclide, it would have completely decayed to the daughter. That is, for extinct nuclide, 

Below we use the Al- Mg system as an example for clarity in derivation. Al undergoes (3+-decay to Mg. With a half-life of 0.71 million years, if there was any initial Al, it would have completely decayed away to Mg. In terms of isotopic ratios, it is assumed that the Al/ Al ratio in the early solar system was uniform spatially and decreased exponentially with time to zero. The amount of Mg at the present day may be written as 

Converting the above equation into a linear equation similar to the isochron equation requires a couple of steps. First, we normalize the above equation to a stable and nonradiogenic Mg isotope ( Mg), yielding 

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