Which of the following sets of quantum numbers is not allowed for an electron in an atom?

• A. n = 4, l = 2, m_l = -2, m_s = -1/2
• B. n = 3, l = 3, m_l = 0, m_s = +1/2
• C. n = 2, l = 1, m_l = 0, m_s = +1/2
• D. n = 1, l = 0, m_l = 0, m_s = -1/2

Answer: (B)

Verified step by step guidance

1. Recall the allowed ranges for each quantum number: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)), the azimuthal quantum number \(l\) can take integer values from \$0\( to \)n-1\(, the magnetic quantum number \)m_l\( ranges from \)-l\( to \)+l\(, and the spin quantum number \)m_s\( can be either \)+\frac{1}{2}\( or \)-\frac{1}{2}$.
2. Examine each set of quantum numbers to check if \(l\) is within the allowed range for the given \(n\). For example, verify if \(l \leq n-1\) for each set.
3. Check if the magnetic quantum number \(m_l\) lies within the range \(-l \leq m_l \leq +l\) for each set.
4. Confirm that the spin quantum number \(m_s\) is either \(+\frac{1}{2}\) or \(-\frac{1}{2}\) in each case.
5. Identify the set where any of these conditions fail. Specifically, look for a case where \(l\) is not less than \(n\), which would make the set of quantum numbers not allowed.