Which of the following combinations of principal quantum number n and angular momentum quantum number l are not allowed?

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

Answer: (B)

Verified step by step guidance

1. Recall the quantum number rules: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)), and the angular momentum quantum number \(l\) must satisfy \$0 \leq l \leq n - 1$.
2. For each given pair \((n, l)\), check if \(l\) is less than \(n\) and greater than or equal to zero. If \(l\) is outside this range, the combination is not allowed.
3. Evaluate \(n = 1, l = 0\): since \(l = 0\) and \$0 \leq 0 \leq 1 - 1 = 0$, this combination is allowed.
4. Evaluate \(n = 2, l = 2\): since \(l = 2\) but \(l\) must be less than or equal to \(n - 1 = 1\), this combination is not allowed.
5. Evaluate \(n = 4, l = 0\) and \(n = 3, l = 1\): both satisfy \$0 \leq l \leq n - 1$, so these combinations are allowed.