Question

Which of the following is not a permissible arrangement of electrons in an atom?

• A. \( n = 5, l = 3, m = 0, s = +\frac{1}{2} \)
• B. \( n = 3, l = 2, m = -3, s = -\frac{1}{2} \)
• C. \( n = 3, l = 2, m = -2, s = -\frac{1}{2} \)
• D. \( n = 4, l = 0, m = 0, s = -\frac{1}{2} \)

Hint:

Ensure that the magnetic quantum number \( m \) is within the range from \( -l \) to \( +l \). Any value outside this range is not allowed.

Answer 1

The Correct Option is B

Step 1: Quantum numbers must satisfy specific conditions: - \( l \) can range from 0 to \( n-1 \), - \( m \) can range from \( -l \) to \( +l \), - \( s \) can only take values \( +\frac{1}{2} \) or \( -\frac{1}{2} \).
Step 2: In option (B), \( n = 3 \), \( l = 2 \), and \( m = -3 \). However, the magnetic quantum number \( m \) must lie between \( -l \) and \( +l \). Since \( l = 2 \), the possible values of \( m \) are -2, -1, 0, 1, and 2. Therefore, \( m = -3 \) is not a permissible value.
Step 3: Hence, option (B) is not a permissible arrangement of electrons.