Question

Which of the following set of quantum numbers is not correct?

• A. \(n=2,l=1,m_l=-1,m_s=\pm\frac{1}{2}\)
• B. \(n=2,l=0,m_l=\pm1,m_s=\pm\frac{1}{2}\)
• C. \(n=2,l=1,m_l=-1,m_s=-\frac{1}{2}\)
• D. \(n=2,l=0,m_l=0,m_s=-\frac{1}{2}\)

Answer 1

The Correct Option is B

Each quantum number must follow these rules:  
- Principal quantum number \( n \): any positive integer (here \( n = 2 \), valid)  
- Azimuthal quantum number \( l \): \( 0 \leq l < n \)  
- Magnetic quantum number \( m_l \): ranges from \( -l \) to \( +l \) in integers  
- Spin quantum number \( m_s \): \( +\frac{1}{2} \) or \( -\frac{1}{2} \)

For Option (2):  
Given \( l = 0 \), then \( m_l \) must be only 0, not \( \pm 1 \).  
So having \( m_l = \pm 1 \) with \( l = 0 \) is not valid.  
Hence, this set of quantum numbers is incorrect.
 

The correct option is (B): \(n=2,l=0,m_l=\pm1,m_s=\pm\frac{1}{2}\)