How many electrons can occupy all orbitals with the principal quantum number n = 5 in a neutral atom?

• A. 10
• B. 50
• C. 18
• D. 32

Answer: (B)

Verified step by step guidance

1. Recall that the principal quantum number \( n \) determines the energy level or shell of an electron in an atom. For \( n = 5 \), we are looking at the fifth shell.
2. Determine the possible values of the azimuthal quantum number \( l \) for \( n = 5 \). Since \( l \) ranges from 0 to \( n-1 \), the possible \( l \) values are 0, 1, 2, 3, and 4.
3. For each \( l \), calculate the number of orbitals using the formula: number of orbitals = \( 2l + 1 \). So for \( l = 0, 1, 2, 3, 4 \), the orbitals are 1, 3, 5, 7, and 9 respectively.
4. Sum the number of orbitals for all \( l \) values: \( 1 + 3 + 5 + 7 + 9 \). This gives the total number of orbitals in the \( n = 5 \) shell.
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 that can occupy all orbitals with \( n = 5 \).