Multiple Choice
Which of the following excited electrons has the lowest energy?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Which of the following sets of quantum numbers describes a valid orbital in an atom?
A
n = 2, l = 1, m_l = 0
B
n = 4, l = 0, m_l = 0
C
n = 1, l = 1, m_l = 0
D
n = 3, l = 2, m_l = 3
Verified step by step guidance1
Recall the rules for quantum numbers: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)).
The azimuthal quantum number \(l\) can take integer values from \(0\) up to \(n-1\) for a given \(n\). So, \(l\) must satisfy \(0 \leq l \leq n-1\).
The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), inclusive. So, \(m_l\) must satisfy \(-l \leq m_l \leq l\).
Check each set of quantum numbers against these rules: for example, for \(n=1\), \(l\) must be \(0\) (since \(l\) cannot be equal to \(n\)), so \(l=1\) is invalid for \(n=1\).
For the set \(n=3\), \(l=2\), \(m_l=3\), since \(m_l\) must be between \(-2\) and \(+2\), \(m_l=3\) is invalid. Use these checks to identify which sets are valid.
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