Which of the following is a correct set of quantum numbers for an electron in a 3d orbital?

• A. n = 3, l = 0, m_l = 0, m_s = +1/2
• B. n = 3, l = 1, m_l = 0, m_s = -1/2
• C. n = 3, l = 2, m_l = 1, m_s = +1/2
• D. n = 2, l = 2, m_l = -2, m_s = +1/2

Answer: (C)

Verified step by step guidance

1. Recall the meaning and allowed values of each quantum number: the principal quantum number \(n\) determines the energy level and must be a positive integer (1, 2, 3, ...).
2. The azimuthal quantum number \(l\) defines the subshell and can take integer values from 0 to \(n-1\). For a 3d orbital, since \(n=3\), \(l\) must be 2 (because \(l=0\) is s, \(l=1\) is p, and \(l=2\) is d).
3. The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), including zero. For \(l=2\), \(m_l\) can be -2, -1, 0, 1, or 2.
4. The spin quantum number \(m_s\) can only be \(+\frac{1}{2}\) or \(-\frac{1}{2}\), representing the two possible spin states of an electron.
5. Check each given set of quantum numbers against these rules to determine which set correctly corresponds to an electron in a 3d orbital.