Multiple Choice
Which of the following correctly describes the allowed values for 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 combinations of principal quantum number n and angular momentum quantum number l represent possible atomic orbitals?
A
n = 3, l = 2
B
n = 1, l = 1
C
n = 2, l = 2
D
n = 4, l = 3
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\( for a given \)n$.
For each pair \((n, l)\), check if \(l\) satisfies the condition \(0 \leq l \leq n-1\). If this condition is true, the combination represents a possible atomic orbital.
Evaluate \(n = 3, l = 2\): since \(l = 2\) and \(n - 1 = 2\), this is valid because \(2 \leq 2\).
Evaluate \(n = 1, l = 1\): here, \(n - 1 = 0\), but \(l = 1\) which is greater than \$0$, so this is not valid.
Evaluate \(n = 2, l = 2\): here, \(n - 1 = 1\), but \(l = 2\) which is greater than \$1\(, so this is not valid. Similarly, \)n = 4, l = 3$ is valid because \(3 \leq 4 - 1 = 3\).
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