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.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.This will be discussed in more detail in the section on Gill's paper below.The "generic" method described by Gonick is easier to understand, but it does not handle such necessities as: (1) varying levels of uncertainty in the X- versus Y-measurements of the data; (2) computing an uncertainty in slope and Y-intercept from the data; and (3) testing whether the "fit" of the data to the line is good enough to imply that the isochron yields a valid age.Isochron methods avoid the problems which can potentially result from both of the above assumptions.
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.
The wonderful property of isochron methods is: if one of these requirements is violated, it is nearly certain that the data will indicate the problem by failure to plot on a line.
(This topic will be discussed in much more detail below.) Where the simple methods will produce an incorrect age, isochron methods will generally indicate the unsuitability of the object for dating.
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.