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The half-life of iodine-124 is 4 days. A technician measures a [tex]$40\text{ mCi}$[/tex] sample of iodine-124.

a. How many half-lives of iodine-124 occur in 16 days?

Answer :

To solve the problem of determining how many half-lives of iodine-124 occur in 16 days, follow these steps:

1. Understand the concept of half-life: The half-life of a substance is the amount of time it takes for half of the substance to decay. For iodine-124, the half-life is 4 days.

2. Determine the total time period given: In this problem, the technician is observing the sample for a total of 16 days.

3. Calculate the number of half-lives in the given time period: To find out how many half-lives occur within a certain period, you divide the total time period by the half-life of the substance.

[tex]\[
\text{Number of half-lives} = \frac{\text{Total time period}}{\text{Half-life period}}
\][/tex]

Substituting the given values:

[tex]\[
\text{Number of half-lives} = \frac{16\ \text{days}}{4\ \text{days/half-life}}
\][/tex]

4. Perform the division:

[tex]\[
\text{Number of half-lives} = 4
\][/tex]

So, four half-lives of iodine-124 occur in 16 days.

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