Which of the following lists all possible values of the angular momentum quantum number l for the principal quantum number n = 4?

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

Answer: (C)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) determines the energy level and size of the orbital, 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 \(n = 4\), list all possible values of \(l\) by starting at \$0\( and increasing by 1 until you reach \)n-1\(, which is \)4 - 1 = 3$.
4. Therefore, the possible values of \(l\) are \$0, 1, 2,\( and \)3$.
5. Compare these values to the options given and identify the correct list that includes all these values without any extras.