Which of the following combinations of principal quantum number n and angular momentum quantum number l represent possible atomic orbitals?

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

Answer: (D)

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\( for a given \)n$.
2. For each pair \((n, l)\), check if \(l\) satisfies the condition \$0 \leq l \leq n-1$. If this condition is true, the combination represents a possible atomic orbital.
3. Evaluate \(n = 3, l = 2\): since \(l = 2\) and \(n - 1 = 2\), this is valid because \$2 \leq 2$.
4. Evaluate \(n = 1, l = 1\): here, \(n - 1 = 0\), but \(l = 1\) which is greater than \$0$, so this is not valid.
5. Evaluate \(n = 2, l = 2\): here, \(n - 1 = 1\), but \(l = 2\) which is greater than \$1\(, so this is not valid. Similarly, \)n = 4, l = 3\( is valid because \)3 \leq 4 - 1 = 3$.