Which of the following is a possible set of quantum numbers for an electron in an atom?

• A. n = 3, l = 3, m_l = 2, m_s = -1/2
• B. n = 2, l = 1, m_l = 0, m_s = +1/2
• C. n = 0, l = 0, m_l = 0, m_s = +1/2
• D. n = 1, l = 1, 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 (\(n = 1, 2, 3, \ldots\)).
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. That is, \(m_l = -l, -(l-1), \ldots, 0, \ldots, (l-1), l\).
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 to determine if they are possible. For example, if \(n=3\), then \(l\) must be between \$0\( and \)2\(. If \)l=3$ is given, this violates the rule, so that set is not possible.