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What is the maximum number of f orbitals that can exist in a given shell?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Which of the following combinations of quantum numbers is allowed for an electron in an atom?
A
n = 1, l = 1, m_l = 0, m_s = -1/2
B
n = 4, l = 0, m_l = 0, m_s = -1/2
C
n = 2, l = 1, m_l = 0, m_s = +1/2
D
n = 3, l = 2, m_l = 3, m_s = +1/2
검증된 단계별 안내1
Recall the allowed ranges for each quantum number: 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 \(-l \leq m_l \leq l\).
The spin quantum number \(m_s\) can only be \(+\frac{1}{2}\) or \(-\frac{1}{2}\).
Check each set of quantum numbers against these rules to determine if they are allowed. For example, if \(n=1\), then \(l\) must be \(0\); if \(l=2\), then \(m_l\) must be between \(-2\) and \(+2\).
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