the sample must be due to radioactive decay. With all of this in mind, if we find that a rock sample has 31 Ar40 atoms for every 1 K40 atom, and the half-life of K40 is 1.3 billion years, how much time has passed in years since that rock was geologically active (aka it was last liquified
Potassium-Argon dating is a common method of determining the age of rocks based on the time they were last liquified, and thus we can determine the age of a surface by examining the ratio of the parent K40 to the decay product Ar40. This works because argon is a gas, which is free to bubble out of liquified rock whenever the rock is hot enough to no longer be in it's solid state (think of magma covering a surface). This means that just after the rock solidifies, there should be effectively no Ar40 remaining and that any Ar40 that we do find in the rock at the time of the collection of the sample must be due to radioactive decay.
With all of this in mind, if we find that a rock sample has 31 Ar40 atoms for every 1 K40 atom, and the half-life of K40 is 1.3 billion years, how much time has passed in years since that rock was geologically active (aka it was last liquified)?
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