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

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

Answer: (A)

Verified step by step guidance

1. Recall the rules for allowed quantum numbers for electrons in atoms: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)), the azimuthal quantum number \(l\) must be an integer such that \$0 \leq l \leq n-1\(, the magnetic quantum number \)m_l\( must satisfy \)-l \leq m_l \leq +l\(, and the spin quantum number \)m_s\( can only be \)+\frac{1}{2}\( or \)-\frac{1}{2}$.
2. Check each set of quantum numbers against these rules. For the first set: \(n = 1\), \(l = 1\), \(m_l = 0\), \(m_s = +\frac{1}{2}\). Since \(l\) must be less than \(n\), verify if \(l = 1\) is allowed when \(n = 1\).
3. For the second set: \(n = 4\), \(l = 0\), \(m_l = 0\), \(m_s = -\frac{1}{2}\). Confirm that \(l = 0\) is valid for \(n = 4\), and that \(m_l\) and \(m_s\) values are within allowed ranges.
4. For the third set: \(n = 3\), \(l = 2\), \(m_l = -2\), \(m_s = -\frac{1}{2}\). Check if \(l = 2\) is valid for \(n = 3\), and if \(m_l = -2\) is within \(-l\) to \(+l\).
5. For the fourth set: \(n = 2\), \(l = 1\), \(m_l = 0\), \(m_s = +\frac{1}{2}\). Verify that all quantum numbers satisfy the allowed ranges for \(n = 2\).