In the third principal energy level (n = 3), how many different values of the angular momentum quantum number l are possible?

• A. 3
• B. 4
• C. 1
• D. 2

Answer: (A)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) determines the energy level and can take positive integer values: \(n = 1, 2, 3, \ldots\)
2. The angular momentum quantum number \(l\) depends on \(n\) and can take integer values from \$0\( up to \)n-1\(, inclusive. So, for a given \)n\(, \)l = 0, 1, 2, \ldots, (n-1)$.
3. For \(n = 3\), list all possible values of \(l\): \(l = 0, 1, 2\).
4. Count the number of different \(l\) values: there are 3 values (\$0\(, \)1\(, and \)2$).
5. Therefore, the number of different angular momentum quantum numbers \(l\) possible for \(n = 3\) is 3.