Multiple Choice
Which of the following statements correctly describes the principal quantum number (n) for atomic orbitals?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Given n = 2, which of the following quantum numbers is NOT possible for an electron in this shell?
A
m_l = 0
B
l = 2
C
l = 0
D
l = 1
Verified step by step guidance1
Recall the relationship between the principal quantum number \(n\) and the azimuthal (angular momentum) quantum number \(l\): \(l\) can take integer values from \$0\( up to \)n-1$.
Given \(n = 2\), determine the possible values of \(l\). Since \(l\) ranges from \$0\( to \)n-1\(, the allowed values are \)l = 0\( and \)l = 1$.
Check each given \(l\) value against the allowed range for \(n=2\). The values \(l=0\) and \(l=1\) are possible, but \(l=2\) is not because it exceeds \(n-1\).
Understand that the magnetic quantum number \(m_l\) depends on \(l\) and can take integer values from \(-l\) to \(+l\). For example, if \(l=1\), then \(m_l\) can be \(-1, 0, +1\).
Conclude that since \(l=2\) is not allowed for \(n=2\), any quantum number set including \(l=2\) is not possible for an electron in the \(n=2\) shell.
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