To decide which element has a density most and least similar to the density of potassium, let's detail the process step-by-step.
1. Identify the Density Constants:
- The density of potassium: [tex]\(0.89 \, \text{g/cm}^3\)[/tex]
- The densities of the other elements are:
- Tin: [tex]\(7.31 \, \text{g/cm}^3\)[/tex]
- Helium: [tex]\(0.0001786 \, \text{g/cm}^3\)[/tex]
- Lithium: [tex]\(0.534 \, \text{g/cm}^3\)[/tex]
- Bismuth: [tex]\(9.78 \, \text{g/cm}^3\)[/tex]
2. Calculate the Absolute Differences:
- The absolute difference in density between potassium and each element:
- [tex]\(|7.31 - 0.89| = 6.42 \, \text{g/cm}^3\)[/tex] for Tin
- [tex]\(|0.0001786 - 0.89| = 0.8898214 \, \text{g/cm}^3\)[/tex] for Helium
- [tex]\(|0.534 - 0.89| = 0.356 \, \text{g/cm}^3\)[/tex] for Lithium
- [tex]\(|9.78 - 0.89| = 8.89 \, \text{g/cm}^3\)[/tex] for Bismuth
3. Determine the Most Similar:
- The most similar density is the smallest difference. Among [tex]\(6.42\)[/tex], [tex]\(0.8898214\)[/tex], [tex]\(0.356\)[/tex], and [tex]\(8.89\)[/tex], the smallest difference is [tex]\(0.356 \, \text{g/cm}^3\)[/tex],
- Therefore, Lithium ([tex]\(0.534 \, \text{g/cm}^3\)[/tex]) has the most similar density to potassium.
4. Determine the Least Similar:
- The least similar density is the largest difference. Among [tex]\(6.42\)[/tex], [tex]\(0.8898214\)[/tex], [tex]\(0.356\)[/tex], and [tex]\(8.89\)[/tex], the largest difference is [tex]\(8.89 \, \text{g/cm}^3\)[/tex],
- Therefore, Bismuth ([tex]\(9.78 \, \text{g/cm}^3\)[/tex]) has the least similar density to potassium.
5. Fill in the Table:
[tex]\[
\begin{tabular}{|l|c|c|c|c|}
\cline { 2 - 5 } \multicolumn{1}{c|}{} & \text{tin} & \text{helium} & \text{lithium} & \text{bismuth} \\
\hline \text{most similar to potassium} & & & X & \\
\hline \text{least similar to potassium} & & & & X \\
\hline
\end{tabular}
\][/tex]
Thus, the element with the density most similar to potassium is lithium, and the element with the density least similar to potassium is bismuth.
