A second problem is that for technical reasons, the measurement of argon and the measurement of potassium have to be made on two different samples, because each measurement requires the destruction of the sample.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.Argon can mobilized into or out of a rock or mineral through alteration Ar and potassium, there is not a reliable way to determine if the assumptions are valid.Argon loss and excess argon are two common problems that may cause erroneous ages to be determined.But we know that the amount as a function of time-- so if we say N is the amount of a radioactive sample we have at some time-- we know that's equal to the initial amount we have.We'll call that N sub 0, times e to the negative kt-- where this constant is particular to that thing's half-life.The severity of this problem decreases as the accuracy of our instruments increases.Still, as a general rule, the proportional error in K-Ar dating will be greatest in the youngest rocks.
Potassium, an alkali metal, the Earth's eighth most abundant element is common in many rocks and rock-forming minerals.However, the Argon, a noble gas, constitutes approximately 0.1-5% of the Earth's present day atmosphere.Because it is present within the atmosphere, every rock and mineral will have some quantity of Argon.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 quantity of potassium in a rock or mineral is variable proportional to the amount of silica present.Therefore, mafic rocks and minerals often contain less potassium than an equal amount of silicic rock or mineral.K has a half-life of 1.248 billion years, which makes it eminently suitable for dating rocks.Potassium is chemically incorporated into common minerals, notably hornblende, biotite and potassium feldspar, which are component minerals of igneous rocks.