Let's look at each description in turn and determine if an element with atomic number [tex]\( Z \leq 92 \)[/tex] matches:
1. An element in Period 2 and Group 8A:
- Helium (He) is in Period 2 and Group 8A.
- Hence, we check Yes and give the symbol He.
2. A metal in Group 7A:
- There are no metals in Group 7A. Group 7A consists of nonmetals.
- Hence, we check No and leave the symbol blank.
3. A halogen with a lower atomic number than barium (Z=56):
- Fluorine (F) is a halogen with an atomic number lower than barium.
- Hence, we check Yes and give the symbol F.
4. A main-group element in Period 2:
- Lithium (Li) is a main-group element in Period 2.
- Hence, we check Yes and give the symbol Li.
Let's put these answers in the table:
\begin{tabular}{|c|c|c|c|}
\hline description & \multicolumn{2}{|c|}{\begin{tabular}{l}
Does any element \\
with [tex]$Z \leq 92$[/tex] match \\
the description?
\end{tabular}} & \begin{tabular}{l}
If you checked yes, give \\
the symbol of an \\
element with [tex]$Z \leq 92$[/tex] \\
that matches.
\end{tabular} \\
\hline An element in Period 2 and Group 8A. & Yes & No & He \\
\hline A metal in Group 7A. & Yes & No & \\
\hline \begin{tabular}{l}
A halogen with a lower atomic number \\
than barium.
\end{tabular} & Yes & No & F \\
\hline A main-group element in Period 2. & Yes & No & Li \\
\hline
\end{tabular}
This completes the solution.
