Which of the following sets of quantum numbers can describe a 3p electron?

• 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 = 2, l = 1, m_l = -1, m_s = +1/2
• D. n = 3, l = 2, m_l = 1, 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 \(n\) indicates the energy level and must be a positive integer (1, 2, 3, ...). The azimuthal quantum number \(l\) defines the subshell and can take integer values from 0 to \(n-1\). The magnetic quantum number \(m_l\) ranges from \(-l\) to \(+l\) in integer steps. The spin quantum number \(m_s\) can be either \(+\frac{1}{2}\) or \(-\frac{1}{2}\).
2. Since the problem asks for quantum numbers describing a 3p electron, identify the correct values for \(n\) and \(l\) for a 3p orbital. The principal quantum number \(n\) should be 3, and the azimuthal quantum number \(l\) for a p orbital is 1.
3. Check each set of quantum numbers to see if they satisfy the conditions for a 3p electron: verify that \(n=3\), \(l=1\), \(m_l\) is between \(-1\) and \(+1\), and \(m_s\) is either \(+\frac{1}{2}\) or \(-\frac{1}{2}\).
4. For any set where \(n\) is not 3 or \(l\) is not 1, eliminate it because it cannot represent a 3p electron. Also, ensure that \(m_l\) and \(m_s\) values fall within their allowed ranges for the given \(l\) and electron spin.
5. After evaluating all options, the set that correctly matches \(n=3\), \(l=1\), \(m_l\) within \(-1\) to \(+1\), and \(m_s=+\frac{1}{2}\) or \(-\frac{1}{2}\) will be the valid quantum numbers describing a 3p electron.