Question

which of the following is not a valid set of four quantum numbers? (n, l, ml, ms )
4, 0, 0, +1/2
2, 1, 0, -1/2
3, 2, -1, -1/2
1, 0, 0, +1/2
1, 1, 0, +1/2

Explanation:

Valid quantum number rules: \( n \geq 1 \); \( l = 0,1,...,n-1 \); \( m_l = -l,...,0,...,+l \); \( m_s = \pm \frac{1}{2} \).

• \( 4,0,0,+1/2 \): \( l=0 \leq 4-1=3 \), valid.
• \( 2,1,0,-1/2 \): \( l=1 \leq 2-1=1 \), valid.
• \( 3,2,-1,-1/2 \): \( l=2 \leq 3-1=2 \), valid.
• \( 1,0,0,+1/2 \): \( l=0 \leq 1-1=0 \), valid.
• \( 1,1,0,+1/2 \): \( l=1 \), but \( n-1=0 \), so \( l=1 > 0 \), invalid.

Answer:

1, 1, 0, +1/2