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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.

\[
\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Time \\
Elapsed
\end{tabular} & \begin{tabular}{c}
Amount \\
Remaining (\mu g)
\end{tabular} \\
\hline
3.0 days & $\frac{216}{2} = 108 \, \mu g$ \\
\hline
6.0 days & $\frac{108}{2} = 54 \, \mu g$ \\
\hline
9.0 days & $\frac{54}{2} = \square \, \mu g$ \\
\hline
\end{tabular}
\]

Answer :

Fermium-253 is a radioactive isotope with a half-life of 3.0 days. This means that every 3 days, the amount of fermium-253 in a sample will be reduced to half of its initial quantity due to radioactive decay.

To fill in the missing value in the table provided, follow these steps:

  1. Initial Amount (0 days):

    • The initial amount of fermium-253 is 216 micrograms.

  2. After 3.0 days:

    • Amount remaining: [tex]\frac{216}{2} = 108 \text{ micrograms}[/tex]

  3. After 6.0 days:

    • Amount remaining: [tex]\frac{108}{2} = 54 \text{ micrograms}[/tex]

  4. After 9.0 days:

    • Amount remaining: [tex]\frac{54}{2} = 27 \text{ micrograms}[/tex]

Therefore, after 9.0 days, 27 micrograms of fermium-253 should remain in the sample.

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