For the quantum numbers n = 3 and l = 2, how many orbitals are described by this combination?

• A. 5
• B. 7
• C. 3
• D. 1

Answer: (A)

Verified step by step guidance

1. Recall that the quantum number \( n \) is the principal quantum number, which indicates the energy level or shell, but it does not directly determine the number of orbitals for a given \( l \).
2. The quantum number \( l \) is the azimuthal (angular momentum) quantum number, which defines the subshell or type of orbital (e.g., \( l=0 \) is s, \( l=1 \) is p, \( l=2 \) is d, etc.).
3. For a given \( l \), the magnetic quantum number \( m_l \) can take integer values from \( -l \) to \( +l \), including zero. This means the number of possible \( m_l \) values (and thus orbitals) is \( 2l + 1 \).
4. Substitute \( l = 2 \) into the formula for the number of orbitals: \( 2(2) + 1 = 5 \).
5. Therefore, for \( n = 3 \) and \( l = 2 \), there are 5 orbitals described by this combination.