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K decays with a half-life of 1.248×10 9 years. 89% of those decays are to stable 40 Ca by beta decay , whilst 11% are to 40 Ar by either electron capture or positron emission .
K decay leads to significantly greater 40 Ca enrichment than any other isotope. [8] The decay constant for the decay to 40 Ca is denoted as λ β and equals 4.962 × 10 −10 yr −1; the decay constant to 40 Ar is denoted as λ EC and equals 5.81 × 10 −11 yr −1. The general equation for the decay time of a radioactive nucleus that decays ...
K (0.0117%), 41 K (6.7302%). 39 K and 41 K are stable. The 40 K isotope is radioactive; it decays with a half-life of 1.248 × 10 9 years to 40 Ca and 40 Ar. Conversion to stable 40 Ca occurs via electron emission in 89.3% of decay events. Conversion to stable 40 Ar occurs via electron capture in the remaining 10.7% of decay events. [3]
Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ is a positive rate called the exponential decay constant, disintegration constant, [1] rate constant, [2] or transformation constant: [3]
In all of the above examples, the initial nuclide decays into just one product. [37] Consider the case of one initial nuclide that can decay into either of two products, that is A → B and A → C in parallel. For example, in a sample of potassium-40, 89.3% of the nuclei decay to calcium-40 and 10.7% to argon-40. We have for all time t:
However, if the mineral contains any potassium, then decay of the 40 K isotope present will create fresh argon-40 that will remain locked up in the mineral. Since the rate at which this conversion occurs is known, it is possible to determine the elapsed time since the mineral formed by measuring the ratio of 40 K and 40 Ar atoms contained in it.
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The decay energy is the mass difference Δm between the parent and the daughter atom and particles. It is equal to the energy of radiation E . If A is the radioactive activity , i.e. the number of transforming atoms per time, M the molar mass, then the radiation power P is: