Ar dating is a major method that researchers have used to understand the structural evolution of the Maria Fold and Thrust Belt.
Argon-argon dating works because potassium-40 decays to argon-40 with a known decay constant. This led to the formerly-popular potassium-argon dating method.
So now we know J, and we have measured the R-value of the sample we're actually interested in dating, so we can use these data to solve the equation for t, giving us the age we're looking for.
You will note that this means that we have to be able to date some rocks accurately using some method other than Ar-Ar, so that we can find a standard to use for the determination of J; fortunately we can do this, and geologists have put a lot of effort into identifying rocks which can be accurately dated and used as standards.
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Measuring the Ar emitted from the standard, and knowing the time t that it was formed, we can put these figures into the equation above and solve it for J.
The other important advantage of Ar-Ar dating is the extra data gained from step heating: instead of heating the irradiated sample to the highest possible temperature all at once, and so releasing all the argon all at once, we can increase the temperature in steps starting at a low temperature. Well, different minerals within the rock will give up their argon at different temperatures, so each step will give us a ratio of K from which these are derived must have appeared in the same ratio in each mineral, because both isotopes of potassium have the same chemical properties.
This means that if the rock cooled rapidly enough that all the minerals in it have the same date, and if there has been no argon loss, and if there is no excess argon added to the system, then the dates we calculate at each step of the heating will be the same date.
For these reasons Ar-Ar dating has largely superseded K-Ar dating, although the simpler method is still employed in some cases where it is known to be unproblematic or where Ar-Ar is unsuitable for some technical reason.
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However, scientists discovered that it was possible to turn a known proportion of the potassium into argon by irradiating the sample, thereby allowing scientists to measure both the parent and the daughter in the gas phase.