Which one of the following sets of quantum numbers can correctly represent a 3p orbital?

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

Answer: (B)

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 (\(n = 1, 2, 3, \ldots\)).
2. The azimuthal (angular momentum) quantum number \(l\) defines the subshell and can take integer values from \$0\( to \)n-1\(. For a 3p orbital, since \)p\( corresponds to \)l = 1\(, \)l\( must be 1 when \)n = 3$.
3. The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), including zero. For \(l = 1\), \(m_l\) can be \(-1\), \$0\(, or \)+1$.
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 set of quantum numbers against these rules: the correct set for a 3p orbital must have \(n = 3\), \(l = 1\), \(m_l\) within \(-1\) to \(+1\), and \(m_s = \pm \frac{1}{2}\). The set \(n = 3\), \(l = 1\), \(m_l = 0\), \(m_s = +\frac{1}{2}\) fits all these criteria.