Multiple Choice
What is the maximum number of electrons that can occupy the third energy level (n = 3) in an atom?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
Multiple Choice
How many orbitals in an atom can have the quantum numbers n = 3 and l = 2?
A
3
B
1
C
7
D
5
Verified step by step guidance1
Understand the meaning of the quantum numbers: \(n\) is the principal quantum number indicating the energy level, and \(l\) is the azimuthal (angular momentum) quantum number indicating the subshell or shape of the orbital.
For \(n = 3\), the possible values of \(l\) range from 0 to \(n-1\), so \(l\) can be 0, 1, or 2. Here, \(l = 2\) corresponds to the d subshell.
The magnetic quantum number \(m_l\) determines the orientation of the orbital and can take integer values from \(-l\) to \(+l\), including zero.
Since \(l = 2\), \(m_l\) can be \(-2, -1, 0, +1, +2\), which means there are 5 possible values of \(m_l\).
Each unique set of quantum numbers \((n, l, m_l)\) corresponds to one orbital, so the number of orbitals with \(n=3\) and \(l=2\) is 5.
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