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Fermium-253 is a radioactive isotope of fermium that has a half-life of 3.0 days. A scientist obtained a sample that contained 216 micrograms of fermium-253.

Complete the table to show how much fermium-253 should remain in the sample at the indicated times after the scientist obtained the sample.
[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Time Elapsed} & \text{Amount Remaining} \\
\hline
3.0 days & $\square$ \\
\hline
6.0 days & $\square$ \\
\hline
9.0 days & $\square$ \\
\hline
\end{tabular}
\][/tex]


Sagot :

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}