How many electrons in an atom can have the principal quantum number n = 5?

• A. 18
• B. 32
• C. 10
• D. 50

Answer: (D)

Verified step by step guidance

1. Recall that the principal quantum number \( n \) defines the main energy level or shell of an electron in an atom.
2. For a given \( n \), the possible values of the azimuthal quantum number \( l \) range from 0 to \( n-1 \). So for \( n = 5 \), \( l = 0, 1, 2, 3, 4 \).
3. Each \( l \) corresponds to a subshell with a specific number of orbitals: the number of orbitals in a subshell is given by \( 2l + 1 \). Calculate the number of orbitals for each \( l \) value and sum them up.
4. Since each orbital can hold 2 electrons (due to the two possible spin quantum numbers \( m_s = +\frac{1}{2} \) or \( -\frac{1}{2} \)), multiply the total number of orbitals by 2 to find the maximum number of electrons for \( n = 5 \).
5. Sum all the electrons from each subshell to get the total number of electrons that can have the principal quantum number \( n = 5 \).