Multiple Choice
How many electrons can occupy all orbitals with the principal quantum number n = 5 in a neutral atom?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
Multiple Choice
How many electrons can occupy all orbitals with the principal quantum number n = 3 in an atom?
A
10
B
18
C
8
D
6
Verified step by step guidance1
Recall that the principal quantum number \( n \) defines the energy level or shell of an electron in an atom. For \( n = 3 \), we need to consider all orbitals in the third shell.
Determine the possible values of the azimuthal quantum number \( l \) for \( n = 3 \). Since \( l \) ranges from 0 to \( n-1 \), here \( l = 0, 1, 2 \), corresponding to the 3s, 3p, and 3d subshells respectively.
Calculate the number of orbitals in each subshell:
- For \( l = 0 \) (3s), there is 1 orbital.
- For \( l = 1 \) (3p), there are 3 orbitals.
- For \( l = 2 \) (3d), there are 5 orbitals.
Total orbitals = 1 + 3 + 5 = 9 orbitals.
Recall that each orbital can hold a maximum of 2 electrons (due to the two possible spin states). Therefore, total electrons = number of orbitals \( \times 2 \).
Multiply the total number of orbitals (9) by 2 to find the maximum number of electrons that can occupy all orbitals with \( n = 3 \).
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