Multiple Choice
What is the maximum number of electrons that can have the principal quantum number n = 3 in an atom?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
Multiple Choice
How many electrons in an atom can have the quantum numbers n = 3, l = 2, m_l = 0?
A
2
B
1
C
6
D
4
Verified step by step guidance1
Understand the meaning of each quantum number: \(n\) is the principal quantum number indicating the energy level, \(l\) is the azimuthal (angular momentum) quantum number indicating the subshell or orbital shape, and \(m_l\) is the magnetic quantum number indicating the orientation of the orbital within the subshell.
Given \(n = 3\), \(l = 2\), and \(m_l = 0\), identify the type of orbital: \(l = 2\) corresponds to a d orbital, and \(m_l = 0\) specifies one particular orientation of that d orbital.
Recall that each orbital (defined by \(n\), \(l\), and \(m_l\)) can hold a maximum of 2 electrons, which differ by their spin quantum number \(m_s\) (either \(+\frac{1}{2}\) or \(-\frac{1}{2}\)).
Since \(m_l = 0\) specifies a single orbital within the d subshell, the number of electrons that can have these quantum numbers is the number of possible spins for that orbital, which is 2.
Therefore, the maximum number of electrons with \(n = 3\), \(l = 2\), and \(m_l = 0\) is 2.
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