Open Question
What is wrong with the following decay curve? Explain.
17. Radioactivity and Nuclear Chemistry
Radioactive Half-Life
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The half-life of iodine-131, an isotope used in thyroid therapy, is 8.021 days. What percentage of iodine-131 remains in a sample that is estimated to be 40.11 days old?
A
3.125%
B
0.03125%
C
96.87%
D
87.06%
E
2.236%
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 radioactive atoms in a sample to decay. For iodine-131, this is 8.021 days.
Determine the number of half-lives that have passed: Divide the total time the sample has been decaying (40.11 days) by the half-life of iodine-131 (8.021 days) to find the number of half-lives.
Use the formula for exponential decay: The remaining quantity of a radioactive isotope can be calculated using the formula \( N = N_0 \times (0.5)^n \), where \( N_0 \) is the initial quantity, \( N \) is the remaining quantity, and \( n \) is the number of half-lives.
Calculate the remaining percentage: Since the initial quantity \( N_0 \) is considered as 100%, the remaining percentage of iodine-131 is \( 100 \times (0.5)^n \).
Compare the calculated percentage with the given options to determine the correct answer.
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