Determine the number of electrons that can have the following set of quantum numbers:n = 3, m_l = 0.

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

Answer: (C)

Verified step by step guidance

1. Understand the quantum numbers: The principal quantum number (n) indicates the energy level, and the magnetic quantum number (ml) specifies the orientation of the orbital within a subshell.
2. Identify the possible values for the azimuthal quantum number (l) when n = 3. The possible values for l are 0, 1, and 2, corresponding to the s, p, and d subshells, respectively.
3. Determine which subshells can have ml = 0. For l = 0 (s subshell), ml = 0 is possible. For l = 1 (p subshell), ml = 0 is also possible. For l = 2 (d subshell), ml = 0 is possible as well.
4. Calculate the number of electrons for each subshell with ml = 0. Each orbital can hold a maximum of 2 electrons. Therefore, for each subshell (s, p, and d) with ml = 0, there can be 2 electrons.
5. Sum the electrons from each subshell: 2 electrons from the s subshell, 2 electrons from the p subshell, and 2 electrons from the d subshell, resulting in a total of 6 electrons that can have the given set of quantum numbers.