Iodine-131 has a half-life of 8.1 days and is used as a tracer for the thyroid gland.If a patient drinks a sodium iodide (NaI) solution containing iodine-131, how many days will it take for the concentration of iodine-131 to drop to 5.0% of its initial concentration?

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Quizplus · Accepted Answer

To find the time it takes for the concentration of iodine-131 to drop to 5.0% of its initial concentration, we can use the half-life formula. The formula to calculate the number of half-lives (n) that have passed is given by: $n = \frac{\log(\text{final concentration/initial concentration})}{\log(0.5)}$. Here, the final concentration is 5% (or 0.05) of the initial concentration (100% or 1). Plugging the values into the formula gives: $n = \frac{\log(0.05)}{\log(0.5)} \approx 4.32$ half-lives. Since each half-life is 8.1 days, the total time is $4.32 \times 8.1 \approx 35$ days.

Iodine-131 Has a Half-Life of 8