### K-40 dating

Figure 02 Carbon Dating [view large image]. By this constant ratio r, any sample with a known value of N 12 would provide an initial value for N 14 , e. This constant ratio of carbon atoms in the plants or animals will no longer maintained once they expire.

## Clocks in the Rocks

The ratio r will change according to Eq. The value of N can be measured by counting the number of beta particles Figure 02 or by measuring. Figure 03 Mass Spectrometer [view large image]. The above description is over simplified and required many corrections and modifications. The ratio r is not exactly a constant, it varies with time and place and also subjected to contamination.

Therefore, the formula is more complicated and preparation of the sample is actually very immaculate.

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Consequently, the radiocarbon dates have to be converted to the calendar dates according to Figure Figure 04 Date Calibration [view large image]. Figure 05 Sample Mass [view large image]. Sample mass requirement depends on material and the method of measurement as shown in Figure 5. Carbon dating can be used for objects up to about years old.

Since the daughter product argon is not incorporated into minerals, all such atoms in a rock must have come from the decay of K that was there originally. However, this assumption may not be valid as shown in Figure The measurements obtain three different ages depending on the hydrothermal condition in the magma from the Figure 06 K Dating [view large image]. Figure 07 K Decay [view large image]. For cases where the initial quantity of the radioactive isotope is not available, the method of isochron equal time can also bypass the problem with the ratios of parent and daughter to the non-radiogenic isotope of the daughter element as illustrated in Figure The feldspars are the most abundant minerals on the Earth, and potassium is a constituent of orthoclase , one common form of feldspar.

Potassium occurs naturally as three isotopes. The radioactive potassium decays by two modes, by beta decay to 40 Ca and by electron capture to 40 Ar.

There is also a tiny fraction of the decay to 40 Ar that occurs by positron emission. The calcium pathway is not often used for dating since there is such an abundance of calcium in minerals, but there are some special cases where it is useful. The decay constant for the decay to 40 Ar is 5. Even though the decay of 40 K is somewhat complex with the decay to 40 Ca and three pathways to 40 Ar, Dalrymple and Lanphere point out that potassium-argon dating was being used to address significant geological problems by the mid 's.

The energy-level diagram below is based on data accumulated by McDougall and Harrison. For a radioactive decay which produces a single final product, the decay time can be calculated from the amounts of the parent and daughter product by. But the decay of potassium has multiple pathways , and detailed information about each of these pathways is necessary if potassiun-argon decay is to be used as a clock.

This information is typically expressed in terms of the decay constants. The assumptions made are When the radiometric clock was started, there was a negligible amount of 40 Ar in the sample. The rock or mineral has been a closed system since the starting time. The closure of the system was rapid compared to the age being determined. Dating with 39 Ar and 40 Ar depends upon the fact that the 39 K can be bombarded with neutrons in a nuclear reactor to produce an amount of 39 Ar which is proportional to the potassium content of the sample.

The conventional potassium-argon dating process is technically difficult and usually is carried out by analyzing for potassium in one part of the sample and measuring 40 Ar in another.

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## K–Ar dating

The Ar-Ar process can be done on the same small piece of a sample, analyzing for both gases in a mass spectrometer. The bombarding of a geological sample with neutrons produces a population of 39 Ar which is proportional to the 39 K content of the sample. The proportionality is related to the probability or " cross-section " for the nuclear interaction.

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One of the complications that must be monitored is that of the production of 39 Ar by neutron scattering from the calcium content of the mineral sample. There are also complications with the atomospheric argon content and various argon contamination scenarios. The details are best pursued in a dedicated text like McDougall and Harrison.

This allows the 39 Ar population to be used as a proxy for the 40 K content of the sample to make possible the calculation of the age for the sample. This simplified conceptual treatment does not give a fair picture of the detailed design and execution of age determinations for a wide variety of types of geological samples.

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But it hopefully makes the point that Ar-Ar dating can take data from small samples based on mass spectrometry. It has contributed to the vast collection of age data for earth minerals, moon samples and meteorites. The Cretaceous-Tertiary boundary in the geological age scale was associated with an iridium-rich layer which suggested that the layer was caused by an impact with an extraterrestrial object. Because that time period, commonly referred to as the K-T boundary, was associated with the extinction of vast numbers of animals in the fossil record, much effort was devoted to dating it with potassium-argon and other methods of geochronology.