객관식
Which quantum number does not provide information about a specific individual orbital?
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9. Quantum Mechanics
Quantum Numbers: Angular Momentum Quantum Number
객관식
Which of the following combinations of principal quantum number n and angular momentum quantum number l are not allowed?
A
n = 1, l = 0
B
n = 2, l = 2
C
n = 4, l = 0
D
n = 3, l = 1
검증된 단계별 안내1
Recall the quantum number rules: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)), and the angular momentum quantum number \(l\) must satisfy \(0 \leq l \leq n - 1\).
For each given pair \((n, l)\), check if \(l\) is less than \(n\) and greater than or equal to zero. If \(l\) is outside this range, the combination is not allowed.
Evaluate \(n = 1, l = 0\): since \(l = 0\) and \(0 \leq 0 \leq 1 - 1 = 0\), this combination is allowed.
Evaluate \(n = 2, l = 2\): since \(l = 2\) but \(l\) must be less than or equal to \(n - 1 = 1\), this combination is not allowed.
Evaluate \(n = 4, l = 0\) and \(n = 3, l = 1\): both satisfy \(0 \leq l \leq n - 1\), so these combinations are allowed.
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