Determine the number of electrons that can have the following set of quantum numbers.
n = 4, l = 3,  m_l = – 1

• A. 2 e^-
• B. 4 e^-
• C. 6 e^-
• D. 3 e^-

Answer: (A)

Verified step by step guidance

1. Understand the quantum numbers: n is the principal quantum number, l is the azimuthal quantum number, and ml is the magnetic quantum number. These numbers describe the energy level, shape, and orientation of an electron's orbital, respectively.
2. Identify the type of orbital: For n = 4 and l = 3, the orbital is a 4f orbital. The azimuthal quantum number l = 3 corresponds to an f orbital.
3. Determine the possible values of ml: The magnetic quantum number ml can range from -l to +l, including zero. For l = 3, ml can be -3, -2, -1, 0, 1, 2, 3.
4. Focus on the given ml value: The problem specifies ml = -1. This means we are considering only the orbitals with this specific orientation.
5. Determine the number of electrons: Each orbital can hold a maximum of 2 electrons with opposite spins. Therefore, for ml = -1, there can be 2 electrons.