How many electrons can occupy all orbitals with the principal quantum number n = 3 in an atom?

• A. 10
• B. 18
• C. 8
• D. 6

Answer: (B)

Verified step by step guidance

1. Recall that the principal quantum number \( n \) defines the energy level or shell of an electron in an atom. For \( n = 3 \), we need to consider all orbitals in the third shell.
2. Determine the possible values of the azimuthal quantum number \( l \) for \( n = 3 \). Since \( l \) ranges from 0 to \( n-1 \), here \( l = 0, 1, 2 \), corresponding to the 3s, 3p, and 3d subshells respectively.
3. Calculate the number of orbitals in each subshell: - For \( l = 0 \) (3s), there is 1 orbital. - For \( l = 1 \) (3p), there are 3 orbitals. - For \( l = 2 \) (3d), there are 5 orbitals. Total orbitals = 1 + 3 + 5 = 9 orbitals.
4. Recall that each orbital can hold a maximum of 2 electrons (due to the two possible spin states). Therefore, total electrons = number of orbitals \( \times 2 \).
5. Multiply the total number of orbitals (9) by 2 to find the maximum number of electrons that can occupy all orbitals with \( n = 3 \).