Arock sample contains 4.5g of potassium-40 and 31.5g of its daughter isotope (argon-40). how old is the rock sample if potassium-40 has a half-life of 1.3 billion years?

There is a starting mass of 36g of Potassium-40. After 1.3 billion years, there would be 18g of Argon-40. After 2.6 billion years, half of the remaining Potassium-40 would have decayed, leaving 9g of Potassium-40 and giving us 27g of Argon-40. Following this pattern, we see that three half-lives, or 3.9 billion years, have passed. The age of the rock sample is 3.9 billion years.

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