Potassium–calcium dating, abbreviated K–Ca dating, is a radiometric dating method used in geochronology. It is based upon measuring the ratio of a parent isotope of potassium (40K) to a daughter isotope of calcium (40Ca). This form of radioactive decay is accomplished through beta decay. Calcium is common in many minerals, with 40Ca being the most abundant naturally occurring isotope of calcium (96.94%), so use of this dating method to determine the ratio of daughter calcium produced from parent potassium is generally not practical. However, recent advancements in mass spectrometric techniques [e.g., thermal ionization mass spectrometry (TIMS) and collision-cell inductively-coupled plasma mass spectrometry (CC-ICP-MS)] are allowing radiogenic Ca isotope variations to be measured at unprecedented precisions in an increasing variety of materials, including high Ca minerals (e.g., plagioclase, garnet, clinopyroxene) and aqueous (e.g., seawater and riverine) samples. In earlier studies, this technique was especially useful in minerals with low calcium contents (under 1/50th of the potassium content) so that radiogenic ingrowth of 40-Ca could be more easily quantified. Examples of such minerals include lepidolite, potassium-feldspar, and late-formed muscovite or biotite from pegmatites (preferably older than 60 million years ago). This method is also useful for zircon-poor, felsic-to-intermediate igneous rocks, various metamorphic rocks, and evaporite minerals (i.e. sylvite).
Method Potassium has three naturally occurring isotopes: stable 39K, 41K and radioactive 40K. 40K exhibits dual decay: through β-decay (E = 1.33 MeV), 89% of 40K decays to 40Ca, and the rest decays to 40Ar via electron capture (E = 1.46 MeV). While 40K comprises only 0.001167% of total potassium mass, 40Ca makes up 96.9821% of total calcium mass; thus, 40K decay leads to significantly greater 40Ca enrichment than any other isotope. The decay constant for the decay to 40Ca is denoted as λβ and equals 4.962×10−10 yr−1; the decay constant to 40Ar is denoted as λEC and equals 5.81×10−11 yr−1. The general equation for the decay time of a radioactive nucleus that decays to a single product is:
t = − λ ln [ N N 0 ] = − ln ( 2 ) t 1 / 2 ln [ N N 0 ] {\displaystyle t=-\lambda \ln \left[{\frac {N}{N_{0}}}\right]=-{\frac {\ln(2)}{t_{1/2}}}\ln \left[{\frac {N}{N_{0}}}\right]}
Where λ is the decay constant, t1/2 is the half-life, N0 is the initial concentration of the parent isotope, and N is the final concentration of the parent isotope. Similarly, the equation for the decay time of a radioactive nucleus that decays to more than one product is:
t = − 1 λ t ln [ λ t λ a N N 0 + 1 ] {\displaystyle t=-{\frac {1}{\lambda _{t}}}\ln \left[{\frac {\lambda _{t}}{\lambda _{a}}}{\frac {N}{N_{0}}}+1\right]}
Where a is the daughter product of interest, λa is the decay constant for daughter product a, and λt is the sum of decay constants for daughter products a and b. This approach is taken in potassium-calcium dating where argon and calcium are both products of decay and can be expressed as:
t = − 1 λ t ln [ λ t λ β Ca ∗ K 0 + 1 ] {\displaystyle t=-{\frac {1}{\lambda _{t}}}\ln \left[{\frac {\lambda _{t}}{\lambda _{\beta }}}{\frac {\ce {Ca^{\ast }}}{\ce {K0}}}+1\right]}
Where Ca* is the measured amount of radiogenic 40Ca in terms of parent isotope 40K, and K0 is the initial concentration of 40K.
Age equation Age determination using potassium–calcium dating is best done using the isochron technique. The isochron constructed for Pike's Peak in Colorado and the K/Ca age for the granites in the area were found to be 1041±32 Ma. Rb-Sr dating of the same batholith gave results of 1008±13 Ma, supporting the practicality of this method of dating. For comparison, the isochron method uses non-radiogenic 42Ca to develop an isochron. The following equation is used in the construction of the isochron plot:
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