Question

for the n = 3 electron shell, which of the following quantum numbers are valid? check all that apply.
□ l = 3
□ m = 3
□ l = 0
□ m = - 2
□ l = - 1
□ m = 2
done

Explanation:

Step1: Determine the range of \( l \)

For a given \( n \), the angular - momentum quantum number \( l \) ranges from \( 0 \) to \( n - 1 \). Given \( n=3 \), then \( l = 0,1,2 \). So \( l = 3 \) is invalid (because \( 3\geq n \)) and \( l=-1 \) is invalid (since \( l\geq0 \)), and \( l = 0 \) is valid.

Step2: Determine the range of \( m \)

For a given \( l \), the magnetic quantum number \( m \) ranges from \( -l \) to \( +l \).

• When \( l = 0 \), \( m = 0 \).
• When \( l = 1 \), \( m=-1,0,1 \).
• When \( l = 2 \), \( m=-2,-1,0,1,2 \).

So \( m = 3 \) is invalid (because for the maximum \( l = 2 \), \(|m|\leq2\)), \( m=-2 \) is valid (when \( l = 2 \)), and \( m = 2 \) is valid (when \( l = 2 \)).

Answer:

\( l = 0\), \(m=-2\), \(m = 2\)