How long will it take for a 40.0 gram sample of I-131 (half-life = 8.4 days) to decay to 1/16 its original mass?

42 days

Explanation:

Half life = 8.4 days

Starting mass = 40.0 g

Time = ?

Final Mass = 1/16 * 40 = 2.5 g

First Half life;

Remaining mass = 40 / 2 = 20g

Second Half life;

Remaining mass = 20 / 2 = 10g

Third Half life;

Remaining mass = 10 / 2 = 5g

Fourth Half life;

Remaining mass = 5 / 2 = 2.5g

Time = Number of half lives * Duration of half life = 5 * 8.4 = 42 days