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20 December, 18:20

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?

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Answers (1)
  1. 20 December, 21:48
    0
    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
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