Which of the following combinations of quantum numbers is 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 = 2, l = 1, m_l = 0, m_s = +1/2
• D. n = 3, l = 2, m_l = 3, m_s = +1/2

Answer: (C)

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. So, \(m_l\) must satisfy \(-l \leq m_l \leq l\).
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 allowed. For example, if \(n=1\), then \(l\) must be \$0\(; if \)l=2\(, then \)m_l\( must be between \)-2\( and \)+2$.