Which of the following combinations of principal quantum number n and angular momentum quantum number l is impossible?

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

Answer: (C)

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 \(l\) can take integer values from \$0\( up to \)n-1\( for each \)n$.
2. For each given pair \((n, l)\), check if \(l\) satisfies the condition \$0 \leq l \leq n-1$.
3. Evaluate \(n = 1, l = 0\): since \(l = 0\) and \(n-1 = 0\), this is allowed.
4. Evaluate \(n = 4, l = 0\): since \(l = 0\) and \(n-1 = 3\), this is allowed.
5. Evaluate \(n = 2, l = 2\): since \(l = 2\) but \(n-1 = 1\), \(l\) cannot be equal to or greater than \(n\), so this combination is impossible.