For a given principal quantum number n, what are the possible values of the angular momentum quantum number l?

• A. l can be any integer from 1 up to n - 1
• B. l can be any integer from 0 up to n - 1
• C. l can be any integer from 0 up to n
• D. l can be any integer from 1 up to n

Answer: (B)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) defines the main energy level or shell of an electron in an atom and can take positive integer values: \(n = 1, 2, 3, \ldots\).
2. Understand that the angular momentum quantum number \(l\) defines the shape of the orbital and is dependent on \(n\).
3. The allowed values of \(l\) range from \$0\( up to \)n - 1\(, inclusive. This means for each \)n\(, \)l\( can be \)0, 1, 2, \ldots, n-1$.
4. Note that \(l = 0\) corresponds to an s orbital, \(l = 1\) to a p orbital, \(l = 2\) to a d orbital, and so on, which helps visualize the types of orbitals possible for each energy level.
5. Therefore, the correct statement is that for a given principal quantum number \(n\), the angular momentum quantum number \(l\) can be any integer from \$0\( up to \)n - 1$.