A radioactive isotope of the element potassium decays to produce argon. If the ratio of argon to potassium in a mineral is found to be 7:1, how many half-lives have occurred since the mineral cooled below its closure temperature?

After three half-lives, it is 7:1

Explanation:

The rate at which the decay of the radioactive isotope is said to be half-life and is represented as the half-life of the atoms and the matter to disintegrate itself. The two radioactive isotopes are K 40 and Ar 40. After the K-Ar dating, they contain minerals such as the clay mica and the temphra minerals and Half-life of the K 40 is 1.3 more than 100,000 years i. e 10x9 years for Ar 40. Thus the K 40 has to divide as three half-lives have passed if the ratio of argon to potassium atoms is 7:1. At the end of one half-life, the ratio of the number of argon to potassium atoms is 1:1. and two half lives its 3:1 thus after the third half-life it becomes as 7:1.