It is based on the fact that some of the radioactive isotope of Potassium, Potassium-40 (K-40) ,decays to the gas Argon as Argon-40 (Ar-40).
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.
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.
When rocks are heated to the melting point, any Ar-40 contained in them is released into the atmosphere.
When the rock recrystallizes it becomes impermeable to gasses again.
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.
Finally, we must consider the possibility of argon loss.
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