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.