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%

Answer: (A)

Verified step by step guidance

1. 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.
2. 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.
3. Substitute the given values into the formula: \( t = 40.11 \) days and \( t_{1/2} = 8.021 \) days.
4. Calculate the exponent: \( t/t_{1/2} = 40.11 / 8.021 \). This will give you the number of half-lives that have passed.
5. 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.