To fill in the table, we need to determine the principal quantum number ([tex]$n$[/tex]) and the angular momentum quantum number ([tex]$l$[/tex]) for each subshell. Here is the detailed, step-by-step process:
1. 4 f Subshell:
- Principal quantum number ([tex]$n$[/tex]) is given as 4.
- The angular momentum quantum number ([tex]$l$[/tex]) for the 'f' subshell is 3.
- So, the values are:
- [tex]\( n = 4 \)[/tex]
- [tex]\( l = 3 \)[/tex]
2. 1 s Subshell:
- Principal quantum number ([tex]$n$[/tex]) is given as 1.
- The angular momentum quantum number ([tex]$l$[/tex]) for the 's' subshell is 0.
- So, the values are:
- [tex]\( n = 1 \)[/tex]
- [tex]\( l = 0 \)[/tex]
3. 6 d Subshell:
- Principal quantum number ([tex]$n$[/tex]) is given as 6.
- The angular momentum quantum number ([tex]$l$[/tex]) for the 'd' subshell is 2.
- So, the values are:
- [tex]\( n = 6 \)[/tex]
- [tex]\( l = 2 \)[/tex]
4. 5 sp Subshell:
- Principal quantum number ([tex]$n$[/tex]) is given as 5.
- The angular momentum quantum number ([tex]$l$[/tex]) is not specified individually as it might combine multiple subshells (s and p), but since it's not detailed here, we leave the angular momentum quantum number undefined or not provided.
- So, the value is:
- [tex]\( n = 5 \)[/tex]
We can now fill in the table accordingly:
[tex]\[
\begin{array}{|c|c|c|}
\hline
\text{subshell} & \begin{tabular}{c}
\text{principal quantum number} \, n \end{tabular} & \begin{tabular}{c}
\text{angular momentum quantum number} \, l \end{tabular} \\
\hline
4 \, f & 4 & 3 \\
\hline
1 \, s & 1 & 0 \\
\hline
6 \, d & 6 & 2 \\
\hline
5 \, sp & 5 & \, \ \\
\hline
\end{array}
\][/tex]
