Open Question
Use the following decay curve for iodine-131 to answer problems a to c: (5.4) b. Complete the number of days on the horizontal axis.
11. 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 that the problem involves radioactive decay, which follows first-order kinetics. The half-life is the time it takes for half of the radioactive isotope to decay.
Use the formula for first-order decay: \( N_t = N_0 \times (0.5)^{t/t_{1/2}} \), where \( N_t \) is the remaining quantity, \( N_0 \) is the initial quantity, \( t \) is the time elapsed, and \( t_{1/2} \) is the half-life.
Substitute the given values into the formula: \( t = 40.11 \) days and \( t_{1/2} = 8.021 \) days.
Calculate the exponent: \( t/t_{1/2} = 40.11 / 8.021 \). This will give you the number of half-lives that have passed.
Determine the remaining percentage of iodine-131 by calculating \( (0.5)^{t/t_{1/2}} \) and then multiply by 100 to convert it to a percentage.
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