In one atom, what is the maximum number of electrons that can have the principal quantum number n = 2?

• A. 6
• B. 4
• C. 8
• D. 2

Answer: (C)

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 \( l = 1 \). These correspond to the 2s and 2p subshells, respectively.
3. Calculate the number of orbitals in each subshell. For \( l = 0 \) (2s), there is 1 orbital. For \( l = 1 \) (2p), there are 3 orbitals because the magnetic quantum number \( m_l \) ranges from \( -l \) to \( +l \).
4. Find the total number of orbitals for \( n = 2 \) by adding the orbitals from both subshells: \( 1 + 3 = 4 \) orbitals.
5. Since each orbital can hold a maximum of 2 electrons (due to the two possible spin quantum numbers \( m_s = +\frac{1}{2} \) or \( -\frac{1}{2} \)), multiply the total orbitals by 2 to get the maximum number of electrons: \( 4 \times 2 = 8 \) electrons.