What is argon dating
The trick is to irradiate the sample with neutrons along with samples of known age.Some of the potassium-39 forms argon-39 by an n,p reaction.Argon loss and excess argon are two common problems that may cause erroneous ages to be determined.Argon loss occurs when radiogenic K by a fast neutron reaction) can be used as a proxy for potassium.And when I look at the Wikipedia article, the discussion is so technical and defensive that I can't actually picture what is going on. As noted in the comments the wikipedia articles (at the time this question was submitted) are contradictory.There are quite a few steps to the logic of how argon-argon dating works but none are too complicated, although I won't go into all of the possible interferences.Due to the relatively heavy atomic weight of potassium, insignificant fractionation of the different potassium isotopes occurs.
This also assumes that there is no other source of argon like trapped air.
By converting potassium-39 to argon-39 then measuring the argon-39:argon-40 ratio, you can calculate the sample's potassium-40:argon-40 ratio, remembering potassium-40:potassium-39 is fixed.
The standards of known age are used to account for differences in the neutron flux during irradiation.
Potassium, an alkali metal, the Earth's eighth most abundant element is common in many rocks and rock-forming minerals.
The quantity of potassium in a rock or mineral is variable proportional to the amount of silica present.