How many electrons in an atom can have the principal quantum number n = 3?

• A. 6
• B. 18
• C. 10
• D. 2

Answer: (B)

Verified step by step guidance

1. Understand 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. Recall that each shell contains one or more subshells characterized by the azimuthal quantum number \(l\), which can take values from \$0\( to \)n-1\(. For \)n = 3\(, \)l\( can be \)0\(, \)1\(, or \)2\(, corresponding to the \)3s\(, \)3p\(, and \)3d$ subshells respectively.
3. Determine 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. Calculate the total number of orbitals in the \(n=3\) shell by summing the orbitals from all subshells: \$1 + 3 + 5 = 9$ orbitals.
5. Since each orbital can hold 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.