A radioactive element has a half life of 4 days. The fraction that has decayed in 16 days is?

Answer Details

The half-life of a radioactive element is the time it takes for half of its atoms to decay. So if the half-life of an element is 4 days, it means that after 4 days, half of the atoms will decay, and after another 4 days, half of the remaining atoms will decay, and so on.
To find the fraction that has decayed in 16 days, we need to determine how many half-lives have occurred. Since the half-life of the element is 4 days, there are 4 half-lives in 16 days.
Each half-life reduces the amount of radioactive material by half. So after 1 half-life, half of the material is left. After 2 half-lives, only a quarter of the material remains. After 3 half-lives, there is only an eighth left. After 4 half-lives, only a sixteenth is left.
Therefore, the fraction that has decayed in 16 days is 1 - 1/16 = 15/16.
So the answer is (15)/16.