How many electrons in an atom can have the quantum numbers n = 3, l = 2, m_l = 0?

• A. 2
• B. 1
• C. 6
• D. 4

Answer: (A)

Verified step by step guidance

1. Understand the meaning of each quantum number: \(n\) is the principal quantum number indicating the energy level, \(l\) is the azimuthal (angular momentum) quantum number indicating the subshell or orbital shape, and \(m_l\) is the magnetic quantum number indicating the orientation of the orbital within the subshell.
2. Given \(n = 3\), \(l = 2\), and \(m_l = 0\), identify the type of orbital: \(l = 2\) corresponds to a d orbital, and \(m_l = 0\) specifies one particular orientation of that d orbital.
3. Recall that each orbital (defined by \(n\), \(l\), and \(m_l\)) can hold a maximum of 2 electrons, which differ by their spin quantum number \(m_s\) (either \(+\frac{1}{2}\) or \(-\frac{1}{2}\)).
4. Since \(m_l = 0\) specifies a single orbital within the d subshell, the number of electrons that can have these quantum numbers is the number of possible spins for that orbital, which is 2.
5. Therefore, the maximum number of electrons with \(n = 3\), \(l = 2\), and \(m_l = 0\) is 2.