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)

1.1625 g

18.6 g

9.3 g

2.325 g

Answer 1

To find the original mass of the Bismuth-212 sample, we can use the formula for exponential decay based on the half-life:

\[
N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}
\]

Where:
- \( N \) is the remaining quantity of the substance (4.65 g),
- \( N_0 \) is the original quantity (which we need to find),
- \( t \) is the time elapsed (121 seconds),
- \( T_{1/2} \) is the half-life of the substance (60.5 seconds).

Now we can rearrange the equation to solve for \( N_0 \):

\[
N_0 = N \left(\frac{1}{2}\right)^{-\frac{t}{T_{1/2}}}
\]

Substituting in the known values:

1. First, calculate the exponent:

\[
-\frac{t}{T_{1/2}} = -\frac{121 \text{ s}}{60.5 \text{ s}} \approx -2
\]

2. Next, calculate \( \left(\frac{1}{2}\right)^{-2} \):

\[
\left(\frac{1}{2}\right)^{-2} = 4
\]

3. Finally, substitute back into the rearranged equation to find \( N_0 \):

\[
N_0 = 4.65 \text{ g} \times 4 = 18.6 \text{ g}
\]

Thus, the original mass of the Bismuth-212 sample was **18.6 g**.