In discussions of radioactivity, the half-life of an isotope refers to the time it takes for one-half of the sample to decay. If we start with 100 g of a radioactive substance whose half-life is 15 days, after 15 days 50 g of the substance will remain. After 30 days, 25 g will remain, and after 45 days, 12.5 g remains, and so on.
Example
A radioactive substance has a half-life of 20 minutes. If we begin with a 500 g sample, how much of the original sample remains after two hours?
Explanation
The easiest way to attack these questions is to start with the original amount of the sample, then draw arrows representing each half-life. Two hours is 120 minutes, so that’s six half-lives. At the end of the stated time period, 7.8 g remains.