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.
The reasoning is as follows: the atmosphere does not only contain Ar as being atmospheric argon.
However, this only works if all the excess argon did indeed come from the atmosphere.
But consider what happens if the argon came from deep within the Earth, where it was formed by Ar ratio as is found in the atmosphere, and the formula that corrects for atmospheric carbon will not correct for this.
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.
Argon, on the other hand, is an inert gas; it cannot combine chemically with anything.
As a result under most circumstances we don't expect to find much argon in igneous rocks just after they've formed.
(However, see the section below on the limitations of the method.) This suggests an obvious method of dating igneous rocks.
If we are right in thinking that there was no argon in the rock originally, then all the argon in it now must have been produced by the decay of Ar in them will be so small that it is below the ability of our instruments to measure, and a rock formed yesterday will look no different from a rock formed fifty thousand years ago.