What is the maximum number of f orbitals that can exist in a given shell?

• A. 5
• B. 3
• C. 7
• D. 1

Answer: (C)

Verified step by step guidance

1. Recall that the number of orbitals in a subshell is determined by the magnetic quantum number \( m_l \), which ranges from \( -l \) to \( +l \), where \( l \) is the azimuthal quantum number associated with the subshell type.
2. Identify the value of \( l \) for the f subshell. For f orbitals, \( l = 3 \).
3. Calculate the number of possible \( m_l \) values for \( l = 3 \). Since \( m_l \) ranges from \( -3 \) to \( +3 \), the total number of values is \( 2l + 1 = 2 \times 3 + 1 \).
4. Evaluate the expression \( 2l + 1 \) to find the number of f orbitals in a given shell, which corresponds to the maximum number of f orbitals possible.
5. Understand that each orbital can hold two electrons with opposite spins, but the question only asks for the number of orbitals, so the answer is the number of \( m_l \) values calculated.