How many electrons can occupy all orbitals with the principal quantum number n = 2 in an atom?

• A. 6
• B. 2
• C. 4
• D. 8

Answer: (D)

Verified step by step guidance

1. Recall that the principal quantum number \( n \) defines the energy level or shell of an electron in an atom. For \( n = 2 \), we are looking at the second energy level.
2. Determine the possible values of the azimuthal quantum number \( l \) for \( n = 2 \). Since \( l \) ranges from 0 to \( n-1 \), here \( l = 0 \) and \( l = 1 \).
3. Identify the orbitals corresponding to each \( l \) value: \( l = 0 \) corresponds to the 2s orbital (1 orbital), and \( l = 1 \) corresponds to the 2p orbitals (3 orbitals).
4. Calculate the total number of orbitals for \( n = 2 \) by adding the orbitals from each \( l \) value: \( 1 + 3 = 4 \) orbitals.
5. Since each orbital can hold 2 electrons (with opposite spins), multiply the total number of orbitals by 2 to find the total number of electrons: \( 4 \times 2 = 8 \) electrons.