Which of the following sets of quantum numbers describes a valid orbital in an atom?

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

Answer: (B)

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 \(n=1\), \(l\) must be \$0\( (since \)l\( cannot be equal to \)n\(), so \)l=1\( is invalid for \)n=1$.
5. For the set \(n=3\), \(l=2\), \(m_l=3\), since \(m_l\) must be between \(-2\) and \(+2\), \(m_l=3\) is invalid. Use these checks to identify which sets are valid.