Question

complete the table below by filling in the principal quantum number n and angular momentum quant
subshell\tprincipal
quantum number n\tangular momentum
quantum number l
4s\t\t
5d\t\t
2p\t\t
6f\t\t

Explanation:

To solve for the principal quantum number \( n \) and angular momentum quantum number \( l \) for each subshell, we use the following rules:

• The principal quantum number \( n \) is the number in the subshell notation (e.g., for \( 4s \), \( n = 4 \)).
• The angular momentum quantum number \( l \) is determined by the subshell type:
• \( s \)-subshell: \( l = 0 \)
• \( p \)-subshell: \( l = 1 \)
• \( d \)-subshell: \( l = 2 \)
• \( f \)-subshell: \( l = 3 \)

For \( 4s \):

Step1: Find \( n \)

The subshell is \( 4s \), so \( n = 4 \).

Step2: Find \( l \)

\( s \)-subshell corresponds to \( l = 0 \).

For \( 5d \):

Step1: Find \( n \)

The subshell is \( 5d \), so \( n = 5 \).

Step2: Find \( l \)

\( d \)-subshell corresponds to \( l = 2 \).

For \( 2p \):

Step1: Find \( n \)

The subshell is \( 2p \), so \( n = 2 \).

Step2: Find \( l \)

\( p \)-subshell corresponds to \( l = 1 \).

For \( 6f \):

Step1: Find \( n \)

The subshell is \( 6f \), so \( n = 6 \).

Step2: Find \( l \)

\( f \)-subshell corresponds to \( l = 3 \).

Filled Table:

subshell	principal quantum number \( n \)	angular momentum quantum number \( l \)
\( 5d \)	\( 5 \)	\( 2 \)
\( 2p \)	\( 2 \)	\( 1 \)
\( 6f \)	\( 6 \)	\( 3 \)

Answer:

• \( 4s \): \( n = 4 \), \( l = 0 \)
• \( 5d \): \( n = 5 \), \( l = 2 \)
• \( 2p \): \( n = 2 \), \( l = 1 \)
• \( 6f \): \( n = 6 \), \( l = 3 \)