To determine how much of the Bismuth-212 sample remains after 121 seconds, we need to understand how many half-lives fit into that time period.
The half-life of Bismuth-212 is 60.5 seconds. To find out how many half-lives have passed in 121 seconds, we do the following calculation:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{121 \text{ seconds}}{60.5 \text{ seconds}} \approx 2 \]
Since approximately 2 half-lives have passed, we can calculate the remaining mass of the sample using the formula for exponential decay based on half-lives:
\[ \text{Remaining mass} = \text{Initial mass} \times \left(\frac{1}{2}\right)^{n} \]
where \( n \) is the number of half-lives.
In this case, the initial mass is 59 grams, and after 2 half-lives:
\[ \text{Remaining mass} = 59 \text{ g} \times \left(\frac{1}{2}\right)^{2} \] \[ \text{Remaining mass} = 59 \text{ g} \times \frac{1}{4} = 14.75 \text{ g} \]
Therefore, after 121 seconds, approximately 14.75 grams of the Bismuth-212 sample will remain. Thus, the correct response is:
14.75 g
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