For a principal quantum number n = 3, which of the following lists correctly represents all possible values of the angular momentum quantum number l?

• A. 1, 2, 3
• B. 1, 2
• C. 0, 1, 2, 3
• D. 0, 1, 2

Answer: (D)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) determines the energy level or shell of an electron in an atom, and it must be a positive integer (\(n = 1, 2, 3, \ldots\)).
2. Understand that the angular momentum quantum number \(l\) defines the shape of the orbital and can take integer values from \$0\( up to \)n-1\( for a given principal quantum number \)n$.
3. For \(n = 3\), list all possible values of \(l\) by starting at 0 and going up to \(n-1 = 3-1 = 2\), so \(l\) can be \$0, 1,\( or \)2$.
4. Recognize that the values \(l = 3\) or any value equal to or greater than \(n\) are not allowed because \(l\) must be less than \(n\).
5. Therefore, the correct set of possible \(l\) values for \(n = 3\) is \$0, 1, 2$, which matches the last option given.