Multiple Choice
For a principal quantum number n = 3, which of the following lists correctly represents all possible values of the angular momentum quantum number l?
9. Quantum Mechanics
Quantum Numbers: Angular Momentum Quantum Number
Multiple Choice
Which of the following correctly describes the allowed values for the angular momentum quantum number l in an atom?
A
l can be any positive integer.
B
l can be any integer from 0 up to n.
C
l can be any integer from 0 up to n - 1, where n is the principal quantum number.
D
l can be any integer from 1 up to n.
Verified step by step guidance1
Recall that the angular momentum quantum number \(l\) is related to the shape of the atomic orbital and depends on the principal quantum number \(n\).
Understand that for a given principal quantum number \(n\), the allowed values of \(l\) start from 0 and go up to \(n - 1\).
Express this relationship mathematically as: \(l = 0, 1, 2, \ldots, (n - 1)\).
Note that \(l\) cannot be equal to \(n\) or greater than \(n - 1\), and it cannot be negative, so it must be a non-negative integer less than \(n\).
Therefore, the correct description is that \(l\) can be any integer from 0 up to \(n - 1\), where \(n\) is the principal quantum number.
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