The half-life of radon-222 is 2.8 days. How many days would it take for the activity due to radon in a tightly closed building to decrease to 2.8 % of its original value?

Question

Quizplus · Accepted Answer

Let the original activity be 100 units. After one half-life, the activity reduces to 50 units. After two half-lives, it reduces to 25 units (50/2). After three half-lives, it reduces to 12.5 units (25/2). After four half-lives, it reduces to 6.25 units (12.5/2). After five half-lives, it reduces to 3.125 units (6.25/2).
Hence, it takes approximately five half-lives for the activity to decrease to 2.8% of its original value.
Thus, 5 half-lives = 5 x 2.8 days = 14 days.
Therefore, the answer is choice C, 14.

The Half-Life of Radon-222 Is 2