Question

The table illustrates the decay in mass of a 59-gram sample of Bismuth-212 as time progresses.





After 121 seconds, how many grams of the sample will remain if Bismuth-212 has a half-life of 60.5 seconds?

(1 point)
Responses

3.69 g
3.69 g

7.38 g
7.38 g

29.5 g
29.5 g

14.75 g

Answer 1

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**