Multiple Choice
What is the maximum number of electrons that can have the principal quantum number n=2 in an atom?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
Multiple Choice
What is the maximum number of electrons that can occupy the n = 3 shell?
A
10
B
8
C
18
D
6
Verified step by step guidance1
Recall that the principal quantum number \( n \) defines the shell or energy level of an electron in an atom.
For a given \( n \), the possible values of the azimuthal quantum number \( l \) range from \( 0 \) to \( n-1 \). For \( n = 3 \), \( l \) can be 0, 1, or 2, corresponding to the s, p, and d subshells respectively.
Each subshell has a specific number of orbitals: s has 1 orbital, p has 3 orbitals, and d has 5 orbitals. The total number of orbitals in the \( n = 3 \) shell is therefore \( 1 + 3 + 5 = 9 \).
Each orbital can hold a maximum of 2 electrons (due to the two possible spin states). So, multiply the total number of orbitals by 2 to find the maximum number of electrons in the \( n = 3 \) shell: \( 9 \times 2 \).
This calculation gives the maximum number of electrons that can occupy the \( n = 3 \) shell.
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