To determine how much fermium-253 remains in the sample after 3.0, 6.0, and 9.0 days, we use the concept of half-life, which is the time it takes for half of the radioactive substance to decay.
Given:
- Initial mass of fermium-253: 216 micrograms
- Half-life of fermium-253: 3.0 days
1. After 3.0 days, one half-life has passed.
- The amount remaining = Initial mass × (1/2)
- Amount remaining after 3.0 days = 216 micrograms × (1/2) = 108 micrograms
2. After 6.0 days, two half-lives have passed.
- The amount remaining = Initial mass × (1/2)²
- Amount remaining after 6.0 days = 216 micrograms × (1/2)² = 216 micrograms × 1/4 = 54 micrograms
3. After 9.0 days, three half-lives have passed.
- The amount remaining = Initial mass × (1/2)³
- Amount remaining after 9.0 days = 216 micrograms × (1/2)³ = 216 micrograms × 1/8 = 27 micrograms
So, the completed table with the amounts remaining at the specified times is:
\begin{tabular}{|c|c|}
\hline \begin{tabular}{c}
Time \\
Elapsed
\end{tabular} & \begin{tabular}{c}
Amount \\
Remaining
\end{tabular} \\
\hline 3.0 days & 108 \\
\hline 6.0 days & 54 \\
\hline 9.0 days & 27 \\
\hline
\end{tabular}
