A certain radioactive element has a half-life of 20 d.The time it will take for 7/8 of the atoms originally present to disintegrate is
A)20 d
B)40 d
C)60 d
D)80 d
E)100 d

Question

Quizplus · Accepted Answer

Half-life of the radioactive element is 20 days. This means that in every 20 days, half of the original atoms will disintegrate. Therefore, after 20 days the remaining fraction of atoms will be 1/2, after 40 days it will be 1/4, after 60 days it will be 1/8, and after 80 days it will be 1/16.

We need to find the time it will take for 7/8 of the atoms originally present to disintegrate. This means that we need one remaining eighth of the original amount, which corresponds to 3 half-lives (since 1/2 x 1/2 x 1/2 = 1/8). Therefore, the time it will take will be 3 x 20 = 60 days.

A Certain Radioactive Element Has a Half-Life of 20 D