What is the maximum number of electrons that can have the principal quantum number n = 3 in an atom?

• A. 8
• B. 10
• C. 18
• D. 6

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 \( n = 3 \), we are looking at the third shell.
2. Determine the possible values of the azimuthal quantum number \( l \) for \( n = 3 \). Since \( l \) ranges from 0 to \( n-1 \), the possible values are \( l = 0, 1, 2 \). These correspond to the subshells 3s, 3p, and 3d respectively.
3. Calculate the number of orbitals in each subshell using the formula: number of orbitals = \( 2l + 1 \). For \( l = 0 \) (3s), there is 1 orbital; for \( l = 1 \) (3p), there are 3 orbitals; for \( l = 2 \) (3d), there are 5 orbitals.
4. Sum the total number of orbitals for all subshells in the \( n = 3 \) shell: \( 1 + 3 + 5 = 9 \) orbitals.
5. 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: \( 9 \times 2 = 18 \) electrons.