In one atom, what is the maximum number of electrons that can have the principal quantum number n = 3?

• A. 10
• B. 6
• C. 18
• D. 8

Answer: (C)

Verified step by step guidance

1. Recall that the principal quantum number \( n \) defines the main energy level or shell of an electron in an atom. For \( n = 3 \), electrons can occupy all subshells with \( l = 0, 1, 2 \), which correspond to the 3s, 3p, and 3d orbitals respectively.
2. Determine the number of orbitals in each subshell: the number of orbitals is given by \( 2l + 1 \). For \( l = 0 \) (3s), there is 1 orbital; for \( l = 1 \) (3p), there are 3 orbitals; and for \( l = 2 \) (3d), there are 5 orbitals.
3. Calculate the total number of orbitals for \( n = 3 \) by summing the orbitals from all subshells: \( 1 + 3 + 5 = 9 \) orbitals.
4. Since each orbital can hold a maximum of 2 electrons (with opposite spins), multiply the total number of orbitals by 2 to find the maximum number of electrons: \( 9 \times 2 = 18 \).
5. Conclude that the maximum number of electrons with principal quantum number \( n = 3 \) is 18.