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

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

Answer: (B)

Verified step by step guidance

1. Understand that quantum numbers describe the properties of electrons in an atom. The principal quantum number (n) indicates the energy level, and the spin quantum number (ms) indicates the electron's spin direction.
2. For n = 2, the possible values for the azimuthal quantum number (l) are 0 and 1, corresponding to the s and p subshells, respectively.
3. For l = 0 (2s subshell), the magnetic quantum number (ml) can only be 0, and there are two possible electrons with ms = +1/2 and ms = -1/2.
4. For l = 1 (2p subshell), the magnetic quantum number (ml) can be -1, 0, or +1. Each ml value can have two electrons with ms = +1/2 and ms = -1/2.
5. Count the electrons with ms = -1/2: In the 2s subshell, there is 1 electron, and in the 2p subshell, there are 3 electrons (one for each ml value), totaling 4 electrons with ms = -1/2.