Os-182 has a half-life of 21.5 hours. How many grams of a 10.0 gram sample would

have decayed after exactly three half-lives?

8.75 g

Explanation: The half-life of Os-182 is 21.5 hours, which means it takes 21.5 hours for a sample of Os-182 to decay to a half of its initial amount.

We are given;

Mass of Os-182 sample = 10.0 g

Number of half lives = 3

Half life = 21.5 hours

We need to determine the mass that decayed after 3 half lives

Using the formula;

Remaining mass = Initial mass * (1/2) ^n, where n is the number of half lives

Therefore;

Mass remaining = 10.0 g * (1/2) ^3

=1.25 g

Thus, to get the mass that decayed;

Mass that decayed = Initial mass - remaining mass

= 10.0 g - 1.25 g

= 8.75 g

Hence, the mass of Os-182 that decayed is 8.75 g