Which of the following orbitals cannot exist according to the rules for the principal quantum number n and the angular momentum quantum number l?

• A. 4f
• B. 3p
• C. 1s
• D. 2d

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\( for each \)n$.
2. Identify the possible values of \(l\) for each given \(n\). For example, if \(n=2\), then \(l\) can be \$0\( or \)1$ only.
3. Match each orbital notation to its corresponding \(n\) and \(l\) values: the letter corresponds to \(l\) as follows: \(s \rightarrow l=0\), \(p \rightarrow l=1\), \(d \rightarrow l=2\), \(f \rightarrow l=3\).
4. Check if the given \(l\) value is allowed for the specified \(n\). For example, for \$2d\(, \)n=2\( and \)l=2\(, but since \)l\( must be less than \)n\(, \)l=2\( is not allowed when \)n=2$.
5. Conclude that orbitals where \(l \geq n\) cannot exist, so the \$2d$ orbital is invalid according to the quantum number rules.