Question

Which of the following sets of quantum numbers is not possible for the electron?

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

Hint:

Remember: For any given \( n \), \( l \) must always be less than \( n \).

Answer 1

The Correct Option is C

Quantum numbers follow these rules:
- Principal quantum number: \( n = 1, 2, 3, \ldots \)
- Azimuthal quantum number: \( l = 0, 1, 2, \ldots, (n-1) \)
- Magnetic quantum number: \( m = -l, -(l-1), \ldots, 0, \ldots, +(l-1), +l \)
- Spin quantum number: \( s = \pm\frac{1}{2} \)
In option (3), \( n = 3 \Rightarrow l \) can be 0, 1, or 2. But \( l = 3 \) is invalid for \( n = 3 \), so this option is not possible.