Which of the following is a valid set of quantum numbers (n, l, m_l) for an electron in an atom?

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

Answer: (A)

Verified step by step guidance

1. Recall the rules for quantum numbers: 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\(. So, \)l\( must satisfy \)0 \leq l \leq n-1$.
3. The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), inclusive. So, \(m_l\) must satisfy \(-l \leq m_l \leq l\).
4. Check each set of quantum numbers against these rules: for example, for \(n=1\), \(l\) can only be 0; for \(n=2\), \(l\) can be 0 or 1; for \(n=4\), \(l\) can be 0, 1, 2, or 3.
5. Verify that \(m_l\) values fall within the allowed range for each \(l\). For instance, if \(l=3\), then \(m_l\) must be between \(-3\) and \(+3\). Any \(m_l\) outside this range is invalid.