Multiple Choice
For a given principal quantum number n, what are the possible values of the angular momentum quantum number l?
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9. Quantum Mechanics
Quantum Numbers: Angular Momentum Quantum Number
Multiple Choice
In the third principal energy level (n = 3), how many different values of the angular momentum quantum number l are possible?
A
3
B
4
C
1
D
2
Verified step by step guidance1
Recall that the principal quantum number \(n\) determines the energy level and can take positive integer values: \(n = 1, 2, 3, \ldots\)
The angular momentum quantum number \(l\) depends on \(n\) and can take integer values from \$0\( up to \)n-1\(, inclusive. So, for a given \)n$, \(l = 0, 1, 2, \ldots, (n-1)\).
For \(n = 3\), list all possible values of \(l\): \(l = 0, 1, 2\).
Count the number of different \(l\) values: there are 3 values (\$0\(, \)1\(, and \)2$).
Therefore, the number of different angular momentum quantum numbers \(l\) possible for \(n = 3\) is 3.
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