A radioactive isotope of the element potassium decays to produce argon. If the ratio of the number of argon to potassium atoms is found to be 7:1, how many half-lives have occurred since the sample of radioactive potassium started to decay

Three (3) half-lives have occurred since the sample of radioactive potassium started to decay

Explanation:

Argon to potassium ratio after 1 half life = 1:1

After 2 half lives = 75/25

= 3:1

After 3 half lives = 87.5/12.5

= 7:1

Since the ratio of the number of argon to potassium atoms is found to be 7:1, then Three (3) half-lives have occurred