How many f orbitals exist in a single energy level where the principal quantum number n = 4?

• A. 5
• B. 1
• C. 7
• D. 3

Answer: (C)

Verified step by step guidance

1. Recall that the number of orbitals for a given type (s, p, d, f) depends on the azimuthal quantum number \( l \). For f orbitals, \( l = 3 \).
2. The number of orbitals for a given \( l \) is given by the formula \( 2l + 1 \). This counts the possible magnetic quantum numbers \( m_l \) ranging from \( -l \) to \( +l \).
3. Substitute \( l = 3 \) into the formula: \( 2(3) + 1 = 7 \). This means there are 7 f orbitals in any energy level where f orbitals exist.
4. Since the principal quantum number \( n = 4 \) allows \( l \) values from 0 up to \( n-1 = 3 \), f orbitals are present at this energy level.
5. Therefore, the number of f orbitals at \( n = 4 \) is 7, corresponding to the 7 possible orientations of the f orbitals.