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).
Isochron methods avoid the problems which can potentially result from both of the above assumptions.
(For brevity's sake, hereafter I will refer to the parent isotope as ).
In addition, it requires that these measurements be taken from several different objects which all formed at the same time from a common pool of materials.
Note that the mere existence of these assumptions do not render the simpler dating methods entirely useless.
In many cases, there are independent cues (such as geologic setting or the chemistry of the specimen) which can suggest that such assumptions are entirely reasonable.
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.
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.
However, the methods must be used with care -- and one should be cautious about investing much confidence in the resulting age...
especially in absence of cross-checks by different methods, or if presented without sufficient information to judge the context in which it was obtained.
Since the data points have the same Y-value and a range of X-values, they initially fall on a horizontal line: half-lives will include zero within its range of uncertainty.