The simplest form of isotopic age computation involves substituting three measurements into an equation of four variables, and solving for the fourth. The equation is the one which describes radioactive decay:. Isochron dating exercise the equation for "age," and incorporating the computation of the original quantity of parent isotope, we get:.
Some assumptions have been made in the discussion of generic dating, for the sake of keeping the computation simple. Such assumptions will not always be accurate in the real world. If one of these assumptions has been violated, the simple computation above yields an incorrect age. 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.
However, the methods must be used with care -- and one should be cautious about investing much confidence in the resulting age 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 "Isochron dating exercise" the daughter product of radioactive decay.
For brevity's sake, hereafter I will refer to the parent isotope as Pthe daughter isotope as Dand the non-radiogenic isotope of the same element as the daughter, as D i.
In addition, it requires that these measurements be taken from several different objects which all formed at "Isochron dating exercise" same time from a common pool of materials.
Rocks which include several different minerals are excellent for this. Each group of measurements is plotted as a data point on a The X-axis of the graph is the ratio of P to D i. The Y-axis of the graph is the ratio of D to D i. If the data points on the plot are colinear, and "Isochron dating exercise" line has a positive slope, it shows an extremely strong correlation between:. This is a necessary and expected consequence, if the additional D is a product of the decay of P in a closed system over time.
It is not easily explained, in the general case, in any other way. The data points would be expected to start out on a line if certain initial conditions were met. 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:. As the rock cools, minerals form. They "choose" atoms for inclusion by their chemical properties.
This results in an identical Y-value for the data points representing each mineral matching the Y-value of the source material. In contrast, P is a different element with different chemical properties. This results in a range of X-values for the data points representing individual minerals. Since the data points have the same Y-value and a range of X-values, they initially fall on a horizontal line:. As more time passes and a significant amount of radioactive decay occurs, the quantity of P decreases by a noticeable amount in each sample, while the quantity of D increases by the same amount.
This results in a movement of the data points to the left decreasing P and upwards increasing D. Since each atom of P decays to atom of Dthe data point for each sample will move along a path with a slope of As a result, the data points with the most P the right-most ones on the plot move the greatest distance per unit time. The data points remain colinear as time passes, but the slope of the line increases:. The slope of the line is the ratio of enriched D to remaining P.
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.
An additional nice feature of isochron ages 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.
The better the fit of the data to the line, the lower the uncertainty. For further information on fitting of lines to data also known as regression analysissee:.
All radiometric dating methods require, in order to produce accurate ages, certain initial conditions and lack of contamination over Isochron dating exercise. The wonderful property of isochron methods is: This topic will be discussed in much more detail below. Where the simple methods will an incorrect age, isochron methods will generally indicate the unsuitability of the object for dating.
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 D not required or assumed to be zero.
The greater the initial D -to- D i ratio, the further the initial horizontal line sits above the X-axis. But the computed age is not affected.
If one of the samples happened to contain no P it would plot where the isochron line intercepts the Y-axisthen its quantity of D wouldn't change over time -- because it would have no parent atoms to produce daughter atoms. Whether there's a data point on the Y-axis or not, the Y-intercept of the line doesn't change as the slope of the isochron line does as shown in Figure 5. Therefore, the Y-intercept of the isochron line gives the initial global ratio of D to D i. For each sample, it would be possible to measure the amount of the D iand using the ratio identified by the Y-intercept of the isochron plot calculate the amount of D that was present when the sample formed.
That quantity of D could be subtracted out of each sample, and it would then be possible to derive a simple age by the equation introduced in the first section of this document for each sample. Each such age would match the result given by the isochron. In order to make the figures easy to read and quick to drawthe examples in this paper include few data points.
While isochrons are performed with that few data points, the best Isochron dating exercise include a larger quantity of data. If the isochron line has a distinctly non-zero slope, and a fairly large number of data points, the nearly inevitable result of contamination failure of system to remain closed will be that the fit of the data to a line will Isochron dating exercise destroyed.
For example, consider an event which removes P. The data points will tend to move varying distances, for the different minerals will have varying resistance to loss of Pas well as varying levels of D i:. In the special case where the isochron line has a zero slope "Isochron dating exercise" zero agethen gain or loss of P may move the data points, but they will all still fall on the same horizontal line.
In other words, random gain or loss of P does not affect a zero-age isochron. This is an important point. If the Earth were as young as young-Earth creationists insist, then the "contamination" which they suggest to invalidate dating methods would have no noticeable effect on the results.
As with gain or loss of Pin the general case it is highly unlikely that the result will be an isochron with colinear data points:. There are two exceptions, where it is possible for migration of D to result in an isochron with Isochron dating exercise colinear data points:. These exceptions should be of little comfort to young-Earthers, for 1 they are uncommon extremely uncommon in the case of partial resetting ; and 2 the result in both cases is an isochron age which is too young to represent the time "Isochron dating exercise" formation.
Young-Earthers necessarily insist that all ancient isochron ages are really much too old. In the real world, nothing is perfect. There are some isochron results which Isochron dating exercise obviously incorrect. The significance of isochron plots is a bit counter-intuitive in some cases.
And there are known processes which can yield an incorrect isochron age. Does this leave room to discard isochron dating as entirely unreliable? One of the requirements for isochron dating is that the samples be cogeneticmeaning that they all formed at about the same time from a common pool of material in which the relevant elements and isotopes were distributed reasonably homogeneously. As described in Figure 4this is how the data are caused
Isochron dating exercise be colinear.
Usually it is easy to determine whether or not this requirement is met. The check is not just the isochron plot itself which can in most cases indicate such a problem by failure of the data Isochron dating exercise fall on a Isochron dating exercisebut in addition the physical location and geological relationships of the samples selected for dating. If this requirement is violated, it is sometimes still possible to obtain an isochron plot with reasonably colinear data points.
The significance of the computed age, however, likely not be the last time of crystallization of each sample. It might instead be the original time at which the samples became separated from a common pool of matter, or the age of that source material itself. The resulting age is meaningfulbut it does not have the meaning which one might expect for the dating result i.
Consider an old body of rock as evidenced by its good fit to an isochron with distinctly non-zero slope with minerals which melt at different temperatures. In this example, the minerals with the lowest melting-point having the lowest P -to- D i and D -to- D i ratios:.
The rock is heated slowly, and at various times the molten portions are moved to the surface in a series of lava flows. The earliest flows will have an isotopic composition close to that of the minerals with the lowest melting points; the Isochron dating exercise flows will have an isotopic composition close to that of the minerals with the highest melting points.
The individual lava flows are not cogenetic. They did not separate at about the same time from an isotopically homogeneous pool of matter. For the sake of simplicity, we will assume three lava flows each with a composition matching the data points of the previous figure:. It is likely that at least a small amount chemical differentiation will have occurred in each melt, and that as a result the minerals of each individual lava flow will exhibit a much younger isochron the actual age of each flow:.
The data points for the overall
Isochron dating exercise of each flow fall on an isochron line representing the original crystallization time of the source material, which is much greater than the age of any of the flows. This sort of inherited Isochron dating exercise is well-understood, discussed thoroughly in the literature, and usually easily avoided by proper selection of samples. Note also that chemical differentiation at the time of the latest melting resulting in the round data points in Figure 17 induces significant scatter into the isochron plot if any measure other than whole-rock is made:.
It is also possible to obtain an Isochron dating exercise with colinear data, whose age has no significance whatsoever. The only reasonably common way is by mixing of materials. Consider two entirely independent sources of material, A and Beach with a different isotopic composition:. If these sources were mixed together into a single rock, in such a way that the different samples of the rock ended up with different proportions of A and Bwithout chemical differentiation, the end result would be something like this:.
When plotted on an isochron diagram, the mixed data points are all colinear with A and B:.
Mixing would appear to be a pernicious problem. Since A and B can be completely unrelated to each other, their individual compositions could plot to a fairly wide range of locations on the graph.