Sure, let's determine the types of orbitals that are found in the principal energy level \( n = 3 \).
1. Principal Quantum Number (n): The principal quantum number \( n \) determines the energy level and size of the orbital. For \( n = 3 \), we need to identify which types of orbitals are allowed.
2. Azimuthal Quantum Number (l): The azimuthal quantum number \( l \) defines the shape of the orbital and can take on any integer value from 0 to \( n-1 \). For \( n = 3 \), \( l \) can be:
- \( l = 0 \) (s orbital)
- \( l = 1 \) (p orbitals)
- \( l = 2 \) (d orbitals)
So, for \( n = 3 \):
- When \( l = 0 \), it corresponds to s orbitals.
- When \( l = 1 \), it corresponds to p orbitals.
- When \( l = 2 \), it corresponds to d orbitals.
Hence, the types of orbitals found in the \( n = 3 \) energy level are: s, p, and d orbitals.
Therefore, the correct answer is [tex]\( \boxed{2} \)[/tex], which corresponds to option B: s, p, and d.
