Questions: Complete the table below by filling in the principal quantum number n and angular momentum quantum number I for each electron subshell listed. subshell principal quantum number n angular momentum quantum number I --- --- --- 4 f 3 s 6 d 2 p

Complete the table below by filling in the principal quantum number n and angular momentum quantum number I for each electron subshell listed.

subshell principal quantum number n angular momentum quantum number I
--- --- ---
4 f
3 s
6 d
2 p

Transcript text: Complete the table below by filling in the principal quantum number $n$ and angular momentum quantum number I for each electron subshell listed. \begin{tabular}{|c|c|c|} \hline subshell & \begin{tabular}{c} principal \\ quantum number $n$ \end{tabular} & \begin{tabular}{c} angular momentum \\ quantum number $I$ \end{tabular} \\ \hline 4 f & $\square$ & $\square$ \\ \hline 3 s & $\square$ & $\square$ \\ \hline 6 d & $\square$ & $\square$ \\ \hline 2 p & $\square$ & $\square$ \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Understanding Quantum Numbers

The principal quantum number $ n $ indicates the main energy level or shell of an electron within an atom. It is a positive integer (1, 2, 3, ...).

The angular momentum quantum number $ l $ (denoted as $ I $ in the table) determines the shape of the electron's orbital and is an integer ranging from 0 to $ n-1 $. Each value of $ l $ corresponds to a specific subshell:

$ l = 0 $ corresponds to the s subshell
$ l = 1 $ corresponds to the p subshell
$ l = 2 $ corresponds to the d subshell
$ l = 3 $ corresponds to the f subshell

Step 2: Filling in the Table

For each subshell, we identify the principal quantum number $ n $ and the angular momentum quantum number $ l $ based on the subshell notation.

4f Subshell:
- The principal quantum number $ n = 4 $.
- The angular momentum quantum number $ l = 3 $ (since it is an f subshell).
3s Subshell:
- The principal quantum number $ n = 3 $.
- The angular momentum quantum number $ l = 0 $ (since it is an s subshell).
6d Subshell:
- The principal quantum number $ n = 6 $.
- The angular momentum quantum number $ l = 2 $ (since it is a d subshell).
2p Subshell:
- The principal quantum number $ n = 2 $.
- The angular momentum quantum number $ l = 1 $ (since it is a p subshell).

Final Answer

\[ \begin{array}{|c|c|c|} \hline \text{subshell} & \text{principal quantum number } n & \text{angular momentum quantum number } l \\ \hline 4f & \boxed{4} & \boxed{3} \\ \hline 3s & \boxed{3} & \boxed{0} \\ \hline 6d & \boxed{6} & \boxed{2} \\ \hline 2p & \boxed{2} & \boxed{1} \\ \hline \end{array} \]

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