Multiple Choice
For a principal quantum number n = 5, which of the following lists correctly represents all possible values of the angular momentum quantum number l?
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9. Quantum Mechanics
Quantum Numbers: Angular Momentum Quantum Number
Multiple Choice
Which of the following combinations of principal quantum number n and angular momentum quantum number l is impossible?
A
n = 1, l = 0
B
n = 4, l = 0
C
n = 2, l = 2
D
n = 3, l = 1
Verified step by step guidance1
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 \(l\) can take integer values from \$0\( up to \)n-1\( for each \)n$.
For each given pair \((n, l)\), check if \(l\) satisfies the condition \(0 \leq l \leq n-1\).
Evaluate \(n = 1, l = 0\): since \(l = 0\) and \(n-1 = 0\), this is allowed.
Evaluate \(n = 4, l = 0\): since \(l = 0\) and \(n-1 = 3\), this is allowed.
Evaluate \(n = 2, l = 2\): since \(l = 2\) but \(n-1 = 1\), \(l\) cannot be equal to or greater than \(n\), so this combination is impossible.
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