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

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

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