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

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

Answer: (A)

Verified step by step guidance

1. Recall the allowed ranges for each quantum number: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)).
2. The azimuthal quantum number \(l\) can take integer values from \$0\( up to \)n-1\( for a given \)n\(, i.e., \)l = 0, 1, 2, \ldots, n-1$.
3. The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), including zero, i.e., \(m_l = -l, -(l-1), \ldots, 0, \ldots, (l-1), l\).
4. The spin quantum number \(m_s\) can only be \(+\frac{1}{2}\) or \(-\frac{1}{2}\).
5. Check each set of quantum numbers against these rules. For example, verify if \(m_s = +1\) is allowed (it is not, since \(m_s\) must be \(\pm \frac{1}{2}\)), and confirm that \(l\) is less than \(n\) in each case.