For an electron in the principal energy level n = 4, what are the possible values of the angular momentum quantum number l?

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

Answer: (D)

Verified step by step guidance

1. Recall that the angular momentum quantum number \(l\) depends on the principal quantum number \(n\) and can take integer values from 0 up to \(n-1\).
2. Given that the principal quantum number \(n = 4\), determine the range of possible \(l\) values by listing all integers starting from 0 up to \(n-1\).
3. Write down the possible values of \(l\) as \(l = 0, 1, 2, 3\) because these are all the integers less than 4.
4. Understand that \(l\) cannot be equal to \(n\) (which is 4 in this case), so \(l = 4\) is not a valid value for the angular momentum quantum number when \(n=4\).
5. Conclude that the correct set of possible \(l\) values for \(n=4\) is \$0, 1, 2,\( and \)3$.