The half-life of radon-222 is 3.8 days. How much of a 300 gram sample is left after 14.8 days?
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To determine how much of a 300 gram sample of radon-222 is left after 14.8 days, we need to use the concept of half-life.
The half-life is the time it takes for half of the radioactive material to decay. In this case, the half-life of radon-222 is given as 3.8 days.
To calculate the remaining amount of radon-222 after 14.8 days, we can divide the total time by the half-life to find the number of half-lives that have elapsed.
14.8 days divided by 3.8 days per half-life equals approximately 3.89 half-lives.
Next, we need to apply the formula for exponential decay, which is:
amount remaining = initial amount × (1/2)^(number of half-lives)
Substituting the given values into the formula:
amount remaining = 300 grams × (1/2)^(3.89)
Using a calculator, we can evaluate the expression within parentheses:
amount remaining = 300 grams × 0.080785
amount remaining = 24.2355 grams
Therefore, approximately 24.2355 grams of the 300 gram sample of radon-222 will be left after 14.8 days.