There are minor differences between isotopes of the same element, and in relatively rare circumstances it is possible to obtain some amount of differentiation between them. The effect is almost always a very small departure from homogeneous distribution of the isotopes -- perhaps enough to introduce an error of 0.002 half-lives in a non-isochron age. but it is rare and the effect is not large enough to account for extremely old ages on supposedly young formations.) as minerals form.This results in a range of X-values for the data points representing individual minerals.After the second half-life has elapsed, yet another 50% of the remaining parent isotope will decay into daughter isotopes, and so on.For all practical purposes, the original isotope is considered extinct after 6 half-life intervals. A small portion of a meteorite is vaporized in the device forming ions.
(The range of uncertainty varies, and may be as much as an order of magnitude different from the approximate value above.
Isochron methods avoid the problems which can potentially result from both of the above assumptions.
Isochron dating requires a fourth measurement to be taken, which is the amount of a different isotope of the same element as the daughter product of radioactive decay.
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.
Note that the mere existence of these assumptions do not render the simpler dating methods entirely useless.