Multiple Choice
How many electrons could have the following set of quantum numbers: n = 3, l = 2, m_l = 1?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
How many electrons in an atom can have the principal quantum number n = 3?
A
6
B
10
C
2
D
18
Verified step by step guidance1
Understand that the principal quantum number \(n\) defines the main energy level or shell of an electron in an atom. For \(n = 3\), we are looking at the third shell.
Recall that each shell contains subshells defined by the azimuthal quantum number \(l\), which can take values from \$0\( to \)n-1\(. For \)n = 3\(, \)l\( can be \)0\(, \)1\(, or \)2\(, corresponding to the \)3s\(, \)3p\(, and \)3d$ subshells respectively.
Determine the number of orbitals in each subshell using the formula: number of orbitals = \$2l + 1\(. For \)l=0\( (3s), orbitals = 1; for \)l=1\( (3p), orbitals = 3; for \)l=2$ (3d), orbitals = 5.
Calculate the total number of orbitals in the \(n=3\) shell by summing the orbitals from all subshells: \$1 + 3 + 5 = 9$ orbitals.
Since each orbital can hold 2 electrons (with opposite spins), multiply the total number of orbitals by 2 to find the maximum number of electrons: \$9 \times 2 = 18$ electrons.
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