Determine the number of electrons that can have the following set of quantum numbers.
n = 4, m_L = – 1, m_s = –1/2

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

Answer: (D)

Verified step by step guidance

1. Understand the quantum numbers: n is the principal quantum number, mL is the magnetic quantum number, and ms is the spin quantum number.
2. The principal quantum number n = 4 indicates the fourth energy level, which can have s, p, d, and f subshells.
3. The magnetic quantum number mL = -1 specifies the orientation of the orbital within a subshell. For p orbitals (l = 1), mL can be -1, 0, or +1. For d orbitals (l = 2), mL can be -2, -1, 0, +1, or +2.
4. The spin quantum number ms = -1/2 indicates the spin of the electron. Each orbital can hold two electrons with opposite spins: +1/2 and -1/2.
5. Determine the number of electrons: For mL = -1 and ms = -1/2, each orbital with mL = -1 can hold one electron with ms = -1/2. Count the orbitals with mL = -1 in the n = 4 level (4p and 4d subshells) to find the total number of electrons.