Time since recrystallization is calculated by measuring the ratio of the amount of The quickly cooled lavas that make nearly ideal samples for K–Ar dating also preserve a record of the direction and intensity of the local magnetic field as the sample cooled past the Curie temperature of iron.The geomagnetic polarity time scale was calibrated largely using K–Ar dating.
If the mineral composition of the two sample is different, so that the sample for measuring the potassium is richer or poorer in potassium than the sample used for measuring the argon, then this will be a source of error.
Potassium is a common element found in many materials, such as micas, clay minerals, tephra, and evaporites.
In these materials, the decay product Ar is able to escape the liquid (molten) rock, but starts to accumulate when the rock solidifies (recrystallizes).
In order to do this for the example of potassium-40, we know that when time is 1.25 billion years, that the amount we have left is half of our initial amount. So let's say we start with N0, whatever that might be. We know, after that long, that half of the sample will be left. Whatever we started with, we're going to have half left after 1.25 billion years. And then to solve for k, we can take the natural log of both sides.
It might be 1 gram, kilogram, 5 grams-- whatever it might be-- whatever we start with, we take e to the negative k times 1.25 billion years. So you get the natural log of 1/2-- we don't have that N0 there anymore-- is equal to the natural log of this thing.
The severity of this problem decreases as the accuracy of our instruments increases.