Question

Which of the following sets of quantum numbers is correct for an electron in a 4f orbital?

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

Hint:

For an \( f \)-orbital, the azimuthal quantum number \( l \) must be 3, and magnetic quantum numbers must lie between \( -3 \) and \( +3 \).

Answer 1

The Correct Option is A

Step 1: Understanding quantum numbers.
- The principal quantum number \( n \) represents the energy level. For a 4f orbital, \( n = 4 \).
- The azimuthal quantum number \( l \) defines the subshell. For an f-orbital, \( l = 3 \).
- The magnetic quantum number \( m \) can take values from \( -l \) to \( +l \), i.e., \( -3, -2, -1, 0, 1, 2, 3 \).
- The spin quantum number \( s \) can be \( +\frac{1}{2} \) or \( -\frac{1}{2} \).
Step 2: Evaluating the options.
- Option (A) correctly follows these rules.
- Option (B) is incorrect since \( l = 4 \) is not valid for a 4f orbital.
- Option (C) is incorrect since \( m = +4 \) is not a valid value for \( l = 3 \).
- Option (D) is incorrect as it corresponds to a 3d orbital.