How many electrons can the n = 4 shell hold in an atom?

• A. 16
• B. 32
• C. 24
• D. 8

Answer: (B)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) defines the shell or energy level of an electron in an atom.
2. For a given shell \(n\), the number of subshells (or types of orbitals) is equal to \(n\). So for \(n=4\), the subshells are \(l = 0, 1, 2, 3\), corresponding to the \$4s\(, \)4p\(, \)4d\(, and \)4f$ orbitals.
3. Each subshell contains a certain number of orbitals: \(s\) has 1 orbital, \(p\) has 3 orbitals, \(d\) has 5 orbitals, and \(f\) has 7 orbitals.
4. Calculate the total number of orbitals in the \(n=4\) shell by summing the orbitals in each subshell: \$1 + 3 + 5 + 7$.
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 the \(n=4\) shell can hold.