To determine how much of the 59-gram sample of Bismuth-212 will remain after 121 seconds, we need to use the concept of half-life.
Given:
- Initial mass \( M_0 = 59 \) grams
- Half-life \( t_{1/2} = 60.5 \) seconds
- Total time \( t = 121 \) seconds
First, we need to calculate how many half-lives fit into 121 seconds:
\[ \text{Number of half-lives} = \frac{t}{t_{1/2}} = \frac{121}{60.5} \approx 2 \]
So, approximately 2 half-lives have passed.
Next, we will use the formula for exponential decay based on the half-life:
\[ M = M_0 \left( \frac{1}{2} \right)^n \]
where \( n \) is the number of half-lives.
Substituting the values:
\[ M = 59 \left( \frac{1}{2} \right)^2 = 59 \left( \frac{1}{4} \right) = \frac{59}{4} = 14.75 \text{ grams} \]
Thus, after 121 seconds, 14.75 grams of the Bismuth-212 sample will remain.
Therefore, the correct answer is:
14.75 g