Question

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

Explanation:

To determine valid quantum numbers for \( n = 3 \):

• Azimuthal quantum number (\( l \)): \( l \) ranges from \( 0 \) to \( n - 1 \). For \( n = 3 \), \( l \) can be \( 0, 1, 2 \). So \( l = 0 \) is valid; \( l = 3 \) (since \( 3 \geq 3 \), invalid) and \( l = -1 \) (negative, invalid) are not.
• Magnetic quantum number (\( m \)): \( m \) ranges from \( -l \) to \( +l \). For \( l = 0 \), \( m = 0 \); for \( l = 1 \), \( m = -1, 0, +1 \); for \( l = 2 \), \( m = -2, -1, 0, +1, +2 \). So \( m = -2 \) (valid when \( l = 2 \)), \( m = 2 \) (valid when \( l = 2 \)) are valid; \( m = 3 \) (exceeds \( l \) range, invalid) is not.

Answer:

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