Multiple Choice
Which of the following best describes the possible values of the principal quantum number n in an atom?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Which of the following is a valid set of quantum numbers (n, l, m_l) for an electron in an atom?
A
n = 3, l = 2, m_l = -2
B
n = 1, l = 1, m_l = 0
C
n = 2, l = 2, m_l = 0
D
n = 4, l = 3, m_l = 4
Verified step by step guidance1
Recall the rules for quantum numbers: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)).
The azimuthal quantum number \(l\) can take integer values from \$0\( up to \)n-1\( for a given \)n\(. So, \)l$ must satisfy \(0 \leq l \leq n-1\).
The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), inclusive. So, \(m_l\) must satisfy \(-l \leq m_l \leq l\).
Check each set of quantum numbers against these rules: for example, for \(n=1\), \(l\) can only be 0; for \(n=2\), \(l\) can be 0 or 1; for \(n=4\), \(l\) can be 0, 1, 2, or 3.
Verify that \(m_l\) values fall within the allowed range for each \(l\). For instance, if \(l=3\), then \(m_l\) must be between \(-3\) and \(+3\). Any \(m_l\) outside this range is invalid.
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