Suppose `3.0 xx 10^7` radon atoms are trapped in a basement at a given time. The basement is sealed against further enetry of the gas. The half - life of radon is 3.83 days. How many radon atoms remain after` 31` days?

Explanation

During each half-life, the number of radon atoms is reduced by a factor of two. Thus , we determine the number of half-lives in a period of `31 J` days and reduced the number of radon atoms by a factor of two for each one. In a period of `31 days`, there are `31 days//3.83` days` =8.1` half-lives. In `8` half -lives, the number of radon atoms is reduced by a factor of `.2^8 =256` , Ignoring the difference between `8` and `8.1` half- lives, we find that the number of atoms ramaining is `3.0 xx 10^(7)//256 =1.2 xx10^(5)`