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K-Ar dating calculation
Isochron dating is a common radiometric dating technique applied to date natural events like the crystallization of minerals as they cool, changes in rocks by metamorphism, or what are essentially naturally occurring shock events like meteor strikes. Minerals present in these events contain various radioactive elements which decay and the resulting daughter elements can then be used to deduce the age of the mineral through an isochron.
The appeal of isochron dating is that it does not presuppose the initial amount of the daughter nuclide in the decay sequence. Indeed, the initial amount is not important because it can be found through this type of dating. Isochron dating began when scientists recognized difficulties with the assumptions of radiometric dating, especially how much of the daughter products might have been present when the mineral first formed.
Isochron dating has been developed in an attempt to solve such problems.
the following assumptions must be satisfied to form an isochron. a) All specimen minerals or whole rock samples had the same initial 87Sr/86Sr ratio when the.
Isochron dating is a common technique of radiometric dating and is applied to date certain events, such as crystallization , metamorphism , shock events, and differentiation of precursor melts, in the history of rocks. Isochron dating can be further separated into mineral isochron dating and whole rock isochron dating ; both techniques are applied frequently to date terrestrial and also extraterrestrial rocks meteorites.
The advantage of isochron dating as compared to simple radiometric dating techniques is that no assumptions are needed about the initial amount of the daughter nuclide in the radioactive decay sequence. Indeed, the initial amount of the daughter product can be determined using isochron dating. This technique can be applied if the daughter element has at least one stable isotope other than the daughter isotope into which the parent nuclide decays.
All forms of isochron dating assume that the source of the rock or rocks contained unknown amounts of both radiogenic and non-radiogenic isotopes of the daughter element, along with some amount of the parent nuclide. Thus, at the moment of crystallization, the ratio of the concentration of the radiogenic isotope of the daughter element to that of the non-radiogenic isotope is some value independent of the concentration of the parent.
As time goes on, some amount of the parent decays into the radiogenic isotope of the daughter, increasing the ratio of the concentration of the radiogenic isotope to that of the daughter. The greater the initial concentration of the parent, the greater the concentration of the radiogenic daughter isotope will be at some particular time. Thus, the ratio of the daughter to non-radiogenic isotope will become larger with time, while the ratio of parent to daughter will become smaller.
An isochron diagram will only give a valid age if all samples are cogenetic , which means they have the same initial isotopic composition that is, the rocks are from the same unit, the minerals are from the same rock, etc. The mathematical expression from which the isochron is derived is  . Because the isotopes are measured by mass spectrometry , ratios are used instead of absolute concentrations since mass spectrometers usually measure the former rather than the latter.
See the section on isotope ratio mass spectrometry.
Clocks in the Rocks
The following radioactive decay processes have proven particularly useful in radioactive dating for geologic processes:. Note that uranium and uranium give rise to two of the natural radioactive series , but rubidium and potassium do not give rise to series. They each stop with a single daughter product which is stable. Some of the decays which are useful for dating, with their half-lives and decay constants are:.
Unlike other dating tools described at earth-time. The differing chemistries and half-lives of these nuclides with timescales ranging from seconds to billions of years make them exceptionally useful chronometers for variety of natural processes and materials Perhaps the most important and commonly used isotopes are U, U, Th and Ra, the first three of which are commonly used to date the formation of carbonate minerals and skeletal materials e.
The largest radioactive disequilibria are always found in the youngest materials. Over time, this signature goes away, eventually relaxing to a condition wherein the disequilibria are no longer detectable. How long this takes depends on the precision and accuracy of our measurements and the size of the original disequilibria bigger disequilibria last longer. In practice, we can usually detect U-series disequilibria for 5 to 7 half-lifes. The half-lifes of U, Th and Ra are roughly , 75 and 1.
This is a very important time period of Earth history the Pleistocene and Holocene and a time period that very few other geochronometers can address. The U-series chronometers can be used to date a wide variety of igneous, marine, terrestrial, and skeletal materials. A detailed discussion of every application is beyond the scope of this introduction, so we focus here on just the most common ones.
In the diagram below I have drawn 2 different age spectra. The bottom, green spectrum is what we would expect to see if we had an ideal sample that has no excess-Ar, and the top, blue spectrum is what we might expect if the sample contained excess-Ar in fluid inclusions. The data for each of those 7 steps is represented by one of the 7 boxes on the diagram. On an age spectrum, the ages are plotted as boxes to show how big the errors are on each step. On the green diagram I have also drawn age data points and error bars at the end of each box to help you visualise it better.
Isochron dating is useful in the determination of the age of igneous rocks, which has been attained via isochron dating of uranium in the coalified samples.
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:. Solving 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. These include:. 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.
The Iconic Isochron: Radioactive Dating, Part 2
You can find isochron outcomes that are clearly wrong. The value of isochron plots is just a bit counter-intuitive in many cases. And you can find known processes which could produce a incorrect isochron age. Does this keep space to discard isochron dating as totally unreliable? Certainly not.
Calculating Rb-Sr Isochrons
The Bible is quite clear about the origin and timeframe for the creation of Earth and the cosmos. If Scripture is inaccurate in this, then how can it be trusted in anything else? Some evolutionists throw out theistic evolution God using evolution as His creative process as a philosophical panacea, with the goal of leading people to conclude that Genesis is a myth. Like Nimrod of ancient times, they know they must provide an alternative i.
One of the indirect evidences that evolutionists universally appeal to is radioactive dating because it appears to supply the deep time their evolutionary models demand.
Lead isochrons are also an important radioactive dating process. This is a rubidium-strontium isochron for a set of samples of a Precambrian granite body.
An oversight in a radioisotope dating technique used to date everything from meteorites to geologic samples means that scientists have likely overestimated the age of many samples, according to new research from North Carolina State University. To conduct radioisotope dating, scientists evaluate the concentration of isotopes in a material. The number of protons in an atom determines which element it is, while the number of neutrons determines which isotope it is.
For example, strontium has 38 protons and 48 neutrons, whereas strontium has 38 protons and 49 neutrons. Radioactive elements, such as rubidium but not strontium or strontium , decay over time. By evaluating the concentrations of all of these isotopes in a rock sample, scientists can determine what its original make-up of strontium and rubidium were.