Let's analyze and fill in the missing values for the elements in the periodic table provided.
1. Bromine:
Given value: [tex]\( A = 97 \)[/tex]
[tex]\[
\text{Bromine atomic radius} = \frac{97 \, \text{pm}}{100} = 0.97 \, \text{Å}
\][/tex]
2. Chlorine:
Given value: [tex]\( 0.97 \, \text{Å} \)[/tex]
3. Phosphorus:
Given value: [tex]\( 1.28 \, \text{Å} \)[/tex]
Next, we need to fill in:
1. Magnesium:
The atomic radius of Magnesium can be estimated using the average of Chlorine and Phosphorus radii.
[tex]\[
\text{Magnesium atomic radius} = \frac{\text{Chlorine atomic radius} + \text{Phosphorus atomic radius}}{2}
\][/tex]
[tex]\[
\text{Magnesium atomic radius} = \frac{0.97 \, \text{Å} + 1.28 \, \text{Å}}{2} = \frac{2.25 \, \text{Å}}{2} = 1.125 \, \text{Å}
\][/tex]
2. Sodium:
The atomic radius of Sodium can be estimated using the average of Phosphorus and Bromine radii.
[tex]\[
\text{Sodium atomic radius} = \frac{\text{Phosphorus atomic radius} + \text{Bromine atomic radius}}{2}
\][/tex]
[tex]\[
\text{Sodium atomic radius} = \frac{1.28 \, \text{Å} + 0.97 \, \text{Å}}{2} = \frac{2.25 \, \text{Å}}{2} = 1.125 \, \text{Å}
\][/tex]
Thus, the filled-in table with atomic radii is:
[tex]\[
\begin{tabular}{|l|r|}
\hline Element & \begin{tabular}{r}
Atomic Radius \\
$(\AA)$
\end{tabular} \\
\hline Bromine & 0.97 \\
\hline Chlorine & 0.97 \\
\hline Magnesium & 1.125 \\
\hline Sodium & 1.125 \\
\hline Phosphorus & 1.28 \\
\hline
\end{tabular}
\][/tex]
By comparing the atomic radii:
- Chlorine and Bromine have the same atomic radius of [tex]\(0.97 \, \text{Å}\)[/tex].
- Magnesium and Sodium also share the same atomic radius of [tex]\(1.125 \, \text{Å}\)[/tex].
- Phosphorus has a slightly larger atomic radius of [tex]\(1.28 \, \text{Å}\)[/tex].
This comparison highlights the relative sizes of the atomic radii for these elements within their respective periods and groups.
