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The slope is proportional to the geologic age of the system.In practice, the isochron approach has many inherent advantages.If a number of samples are analyzed and the results are shown to define a straight line within error, then a precise age is defined because this is only possible if each is a closed system and each has the same initial ratio and age.The uncertainty in determining the slope is reduced because it is defined by many points.The uranium and thorium decay systems offer a multitude of radiometric dating options.Uranium 238 decays through a series of steps to Lead 206.

They also measure the sand grains in the bottom bowl (the daughter isotope, such as lead-206 or argon-40, respectively).

In this case, it is a big advantage to present the data in a form in which the abundance of both the parent and daughter isotopes are given with respect to the abundance of the initial background daughter.

The incremental additions of the daughter type can then be viewed in proportion to the abundance of parent atoms. It has already been shown—7—that the number of daughter atoms present from radioactive decay , is called the initial ratio.

The radiometric dater then uses the half-life of all four isotopes to find an age range the rock should be in.

The half-lives of the cascade from uranium-235 to lead-207 has been been extrapolated to about 704 million years and the cascade form uranium-238 to lead-206 has been calculated to about 4.47 billion years.

Uranium 235 decays to lead 207, and Thorium 232 decays to lead 208.

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