Question

Which of the following set(s) of quantum numbers is(are) NOT allowed?

• A. \( n = 3, l = 2, m_l = -1 \)
• B. \( n = 4, l = 0, m_l = -1 \)
• C. \( n = 3, l = 3, m_l = -3 \)
• D. \( n = 5, l = 3, m_l = +2 \)

Hint:

When checking quantum numbers, ensure that \( l \) is always less than \( n \) and \( m_l \) lies between \( -l \) and \( +l \).

Answer 1

The Correct Option is B, C

Step 1: Understanding quantum numbers. 
The quantum numbers \( n \), \( l \), and \( m_l \) must follow certain rules. \( l \) must be between 0 and \( n-1 \), and \( m_l \) can range from \( -l \) to \( +l \). Thus, the values must adhere to these constraints. 
 

Step 2: Analyzing the options. 
(A) \( n = 3, l = 2, m_l = -1 \): Allowed — This is a valid set of quantum numbers. 
(B) \( n = 4, l = 0, m_l = -1 \): Incorrect — The \( m_l \) value cannot be \( -1 \) when \( l = 0 \). 
(C) \( n = 3, l = 3, m_l = -3 \): Not Allowed — The value of \( l \) must be less than \( n \), so this set is not allowed. 
(D) \( n = 5, l = 3, m_l = +2 \): Allowed — This set adheres to the quantum number rules. 
 

Step 3: Conclusion. 
The correct answer is 

(B) \( n = 4, l = 0, m_l = -1 \)
(C) \( n = 3, l = 3, m_l = -3 \)