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What does it mean when we say that strontium-90, a waste product of nuclear power plants, has a half-life of 28.8 years?
11. Nuclear Chemistry
Radioactive Half-Life
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The half-life of arsenic-74 is about 18 days. If a sample initially contains 100.00 mg arsenic-74, what mass (in mg) would be left after 72 days?
A
0.0625 mg
B
6.25 mg
C
25 mg
D
12.5 mg
E
50 mg
Verified step by step guidance1
Understand the concept of half-life: The half-life of a radioactive isotope is the time required for half of the isotope to decay. For arsenic-74, this is 18 days.
Calculate the number of half-lives that have passed in 72 days: Divide the total time (72 days) by the half-life (18 days) to find the number of half-lives.
Determine the fraction of arsenic-74 remaining: Use the formula \( \left( \frac{1}{2} \right)^n \), where \( n \) is the number of half-lives calculated in the previous step.
Calculate the remaining mass: Multiply the initial mass (100.00 mg) by the fraction remaining to find the mass of arsenic-74 left after 72 days.
Review the options provided: Compare your calculated mass with the given choices to identify the correct answer.
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