Multiple Choice
How many electrons in an atom can have the quantum numbers n = 3, l = 2, m_l = 0?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
Multiple Choice
What is the maximum number of electrons that can have the principal quantum number n=2 in an atom?
A
6
B
2
C
4
D
8
Verified step by step guidance1
Recall that the principal quantum number \( n \) defines the main energy level or shell of an electron in an atom. For \( n=2 \), we are looking at the second energy level.
Determine the possible values of the azimuthal (angular momentum) quantum number \( l \) for \( n=2 \). Since \( l \) ranges from 0 to \( n-1 \), for \( n=2 \), \( l \) can be 0 or 1.
Identify the subshells corresponding to these \( l \) values: \( l=0 \) corresponds to the 2s subshell, and \( l=1 \) corresponds to the 2p subshell.
Calculate the number of orbitals in each subshell using the magnetic quantum number \( m_l \), which ranges from \( -l \) to \( +l \). For \( l=0 \), there is 1 orbital; for \( l=1 \), there are 3 orbitals.
Since each orbital can hold 2 electrons (with opposite spins), multiply the total number of orbitals by 2: \( (1 + 3) \times 2 = 8 \) electrons can have \( n=2 \).
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