객관식
When two electrons are shared in the same orbital, what is the relationship between their spin quantum numbers?
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9. Quantum Mechanics
Quantum Numbers: Spin Quantum Number
객관식
Which of the following set of quantum numbers is possible for an electron in a set of 6f orbitals?
A
n = 6, l = 3 , mll = 0, ms = 0
B
n = 6, l = 2, ml = 1, ms = –1/2
C
n = 9, l = 1, ml = –2, ms = +1/2
D
n = 6, l = 3, ml = 0, ms = +1/2
E
n = 4, l = 2, ml = –2, ms = +1
검증된 단계별 안내1
Recall the four quantum numbers: the principal quantum number \(n\), the azimuthal (angular momentum) quantum number \(l\), the magnetic quantum number \(m_l\), and the spin quantum number \(m_s\).
Understand the allowed ranges for each quantum number: \(n\) is a positive integer (\(n = 1, 2, 3, \ldots\)), \(l\) ranges from \(0\) to \(n-1\), \(m_l\) ranges from \(-l\) to \(+l\) in integer steps, and \(m_s\) can only be \(+\frac{1}{2}\) or \(-\frac{1}{2}\).
Check the given quantum numbers for the 6f orbital: since \(f\) orbitals correspond to \(l = 3\), verify that \(n = 6\) and \(l = 3\) are consistent, which they are because \(l\) must be less than \(n\).
Verify that \(m_l\) is within the allowed range for \(l = 3\), so \(m_l\) must be one of \(-3, -2, -1, 0, 1, 2, 3\). The value \(m_l = 0\) is valid.
Confirm that \(m_s\) is either \(+\frac{1}{2}\) or \(-\frac{1}{2}\). The value \(m_s = 0\) or \(+1\) is not allowed, so only \(m_s = +\frac{1}{2}\) or \(-\frac{1}{2}\) are valid spin quantum numbers.
