Multiple Choice
How long will it take for 20% of the C-14 atoms in a sample of C-14 to decay, given that the half-life of C-14 is approximately 5730 years?
21. Nuclear Chemistry
Radioactive Half-Life
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The half-life of Strontium-85 is 65 days. How much of an 80 mg sample is left after 260 days?
A
40 mg
B
5 mg
C
20 mg
D
10 mg
Verified step by step guidance1
Understand the concept of half-life: The half-life of a substance is the time it takes for half of the sample to decay. For Strontium-85, this is 65 days.
Determine the number of half-lives that have passed in 260 days. Divide the total time by the half-life: \( \frac{260}{65} \).
Calculate the remaining amount of Strontium-85 after each half-life. Start with the initial amount of 80 mg and apply the half-life decay formula: \( \text{Remaining amount} = \text{Initial amount} \times \left( \frac{1}{2} \right)^n \), where \( n \) is the number of half-lives.
Substitute the values into the formula: \( \text{Remaining amount} = 80 \text{ mg} \times \left( \frac{1}{2} \right)^n \).
Evaluate the expression to find out how much of the sample is left after 260 days.
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