Question

If a sample of Bismuth-212 weighs 4.65 grams (g) after 121 seconds (s), what was the original mass of the sample given that Bismuth-212 has a half-life of 60.5 seconds (s)?

(1 point)
Responses

18.6 g
18.6 g

1.1625 g
1.1625 g

2.325 g
2.325 g

9.3 g

Answer 1

To find the original mass of the Bismuth-212 sample, we can use the half-life formula. The half-life of Bismuth-212 is 60.5 seconds, which means after each half-life, half of the remaining sample will have decayed.

First, determine the number of half-lives that have passed in 121 seconds:

\[
\text{Number of half-lives} = \frac{\text{Time elapsed}}{\text{Half-life}} = \frac{121 \, \text{s}}{60.5 \, \text{s}} \approx 2
\]

Since approximately 2 half-lives have passed, we can express the remaining mass of the sample using the formula:

\[
m = m_0 \left( \frac{1}{2} \right)^n
\]

where:
- \( m \) is the remaining mass (4.65 g),
- \( m_0 \) is the original mass,
- \( n \) is the number of half-lives (which we calculated to be about 2).

Let’s calculate:

\[
4.65 = m_0 \left( \frac{1}{2} \right)^2
\]

\[
4.65 = m_0 \cdot \frac{1}{4}
\]

To find \( m_0 \):

\[
m_0 = 4.65 \cdot 4 = 18.6 \, \text{g}
\]

Therefore, the original mass of the sample was **18.6 g**.