How many d orbitals exist in a single energy level where the principal quantum number n = 3 of an atom?

• A. 3
• B. 10
• C. 5
• D. 7

Answer: (C)

Verified step by step guidance

1. Recall that the number of orbitals in a subshell depends on the azimuthal quantum number \( l \). For d orbitals, \( l = 2 \).
2. The number of orbitals for a given \( l \) is given by the formula \( 2l + 1 \).
3. Substitute \( l = 2 \) into the formula: \( 2(2) + 1 = 5 \).
4. Therefore, there are 5 d orbitals in any energy level that contains a d subshell.
5. Since \( n = 3 \) includes the d subshell (because \( l \) can be 0, 1, or 2 for \( n = 3 \)), the number of d orbitals at \( n = 3 \) is 5.