Question

question 7 (1 point)
which of the following is a valid set of four quantum numbers? (n, l, ml, ms )
4, 0, -1, +1/2
2, 1, 0, -1/2
3, 3, -1, -1/2
1, 0, -1, +1/2
1, 1, 2, +1/2

Explanation:

Step1: Check the rules for \( l \)

The angular momentum quantum number \( l \) satisfies \( 0\leq l\leq n - 1 \).

• For \( n = 4 \), \( l = 0 \) is valid (\( 0\leq0\leq4 - 1 \)).
• For \( n = 2 \), \( l = 1 \) is valid (\( 0\leq1\leq2 - 1 \)).
• For \( n = 3 \), \( l=3 \) is invalid since \( 3

leq3 - 1=2 \).

• For \( n = 1 \), \( l = 0 \) is valid (\( 0\leq0\leq1 - 1 \)), but \( l=- 1 \) is not in the range \( 0\leq l\leq n - 1 \) (also \( l\geq0 \) always). For \( n = 1 \), \( l = 1 \) is invalid since \( 1

leq1 - 1 = 0 \).

Step2: Check the rules for \( m_l \)

The magnetic quantum number \( m_l \) satisfies \( -l\leq m_l\leq l \).

• When \( n = 4,l = 0 \), \( m_l=-1 \) is invalid since \( -0\leq m_l\leq0 \) (i.e., \( m_l = 0 \)).
• When \( n = 2,l = 1 \), \( m_l = 0 \) is valid (\( -1\leq0\leq1 \)).
• When \( n = 1,l = 0 \), \( m_l=-1 \) is invalid (\( -0\leq m_l\leq0 \)).

Step3: Check the rules for \( m_s \)

The spin - quantum number \( m_s=\pm\frac{1}{2} \). All the given \( m_s \) values (\(+\frac{1}{2},-\frac{1}{2}\)) in the options are valid.

Answer:

B. \(2,1,0,-1/2\)