Final answer:
The half-life of an isotope is the time it takes for half of a sample to decay. Given that after 18 years, 62.5 g remains from an original 500 g sample, we can deduce that the half-life is 6 years, since three half-lives have passed to leave 1/8th of the original sample.
Step-by-step explanation:
The question asks about the half-life of an isotope which is a concept in chemistry and physics. The half-life is defined as the amount of time it takes for half of a radioactive sample to decay. To calculate the half-life, we can observe how much of the original sample remains after a given period and use the patterns of decay to find the half-life.
Given that 62.5 g of a 500 g sample remains after 18 years, we deduce that three half-lives have passed because 62.5 g is 1/8th of the original 500 g sample. Since each half-life corresponds to the mass being halved, the original sample would have gone through three stages of decay: 500 g to 250 g, then 250 g to 125 g, and finally 125 g to 62.5 g. Knowing that three half-lives equal 18 years, we then divide 18 years by 3 to find the duration of one half-life.