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Consider some molten rock in which isotopes and elements are distributed in a reasonably homogeneous manner.
Its composition would be represented as a single point on the isochron plot: Note that the above is somewhat simplified.
Now that the mechanics of plotting an isochron have been described, we will discuss the potential problems of the "simple" dating method with respect to isochron methods.
The amount of initial wouldn't change over time -- because it would have no parent atoms to produce daughter atoms.
The equation is the one which describes radioactive decay: If one of these assumptions has been violated, the simple computation above yields an incorrect age.
An additional nice feature of isochron ages is that an "uncertainty" in the age is automatically computed from the fit of the data to a line.
A routine statistical operation on the set of data yields both a slope of the best-fit line (an age) and a variance in the slope (an uncertainty in the age).
Age "uncertainty" When a "simple" dating method is performed, the result is a single number.
There is no good way to tell how close the computed result is likely to be to the actual age.