객관식
How many electrons in an atom can have the principal quantum number n = 3?
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9. Quantum Mechanics
Quantum Numbers: Number of Electrons
객관식
Which of the following sets of quantum numbers is not 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 = 3, l = 2, m_l = -2, m_s = -1/2
D
n = 2, l = 1, m_l = 0, m_s = +1/2
검증된 단계별 안내1
Recall the rules for allowed quantum numbers for electrons in atoms: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)), the azimuthal quantum number \(l\) must be an integer such that \(0 \leq l \leq n-1\), the magnetic quantum number \(m_l\) must satisfy \(-l \leq m_l \leq +l\), and 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. For the first set: \(n = 1\), \(l = 1\), \(m_l = 0\), \(m_s = +\frac{1}{2}\). Since \(l\) must be less than \(n\), verify if \(l = 1\) is allowed when \(n = 1\).
For the second set: \(n = 4\), \(l = 0\), \(m_l = 0\), \(m_s = -\frac{1}{2}\). Confirm that \(l = 0\) is valid for \(n = 4\), and that \(m_l\) and \(m_s\) values are within allowed ranges.
For the third set: \(n = 3\), \(l = 2\), \(m_l = -2\), \(m_s = -\frac{1}{2}\). Check if \(l = 2\) is valid for \(n = 3\), and if \(m_l = -2\) is within \(-l\) to \(+l\).
For the fourth set: \(n = 2\), \(l = 1\), \(m_l = 0\), \(m_s = +\frac{1}{2}\). Verify that all quantum numbers satisfy the allowed ranges for \(n = 2\).
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