The proportion of argon to radioactive potassium in the sample today is observable, and the decay constant of potassium is readily calculable by measuring the amount of argon produced from the decay of K after a specified time.But the age of the rock and the proportion of argon to radio-potassium in the sample originally are not observable.As any first-year student of algebra soon learns, a single equation with two unknown variables cannot be solved.
For example, in the The decay constant has dimensions of reciprocal seconds.
In the special case in which parent and daughter atoms are present in equal quantities, the age of the specimen is the half-life of the parent isotope: The first assumption, that the amount of the daughter isotope in the original rock is known, is the weakest assumption.
Radiometric dating is based on the decay rate of these isotopes into stable nonradioactive isotopes.
To date an object, scientists measure the quantity of parent and daughter isotope in a sample, and use the atomic decay rate to determine its possible age.
His book, The Mythology of Modern Dating Methods, documents approximately 200 quotes by secular geologists indicating problems with the various dating methods.