For the principal quantum number n = 5, how many possible values can the angular momentum quantum number l have?

• A. 1
• B. 6
• C. 5
• D. 4

Answer: (C)

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$.
3. For \(n = 5\), the possible values of \(l\) are \$0, 1, 2, 3,\( and \)4$.
4. Count the number of possible \(l\) values: since \(l\) ranges from \$0\( to \)4\(, there are \)5$ possible values.
5. Therefore, the number of possible values for the angular momentum quantum number \(l\) when \(n = 5\) is \$5$.