Multiple Choice
Which principal quantum number (n) corresponds to the subshells in the sixth energy level of an atom?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Which of the following sets of quantum numbers is not allowed for an electron in an atom?
A
n = 4, l = 2, m_l = -2, m_s = -1/2
B
n = 3, l = 3, m_l = 0, m_s = +1/2
C
n = 2, l = 1, m_l = 0, m_s = +1/2
D
n = 1, l = 0, m_l = 0, m_s = -1/2
Verified step by step guidance1
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\( to \)n-1\(, the magnetic quantum number \)m_l\( ranges from \)-l\( to \)+l\(, and the spin quantum number \)m_s$ can be either \(+\frac{1}{2}\) or \(-\frac{1}{2}\).
Examine each set of quantum numbers to check if \(l\) is within the allowed range for the given \(n\). For example, verify if \(l \leq n-1\) for each set.
Check if the magnetic quantum number \(m_l\) lies within the range \(-l \leq m_l \leq +l\) for each set.
Confirm that the spin quantum number \(m_s\) is either \(+\frac{1}{2}\) or \(-\frac{1}{2}\) in each case.
Identify the set where any of these conditions fail. Specifically, look for a case where \(l\) is not less than \(n\), which would make the set of quantum numbers not allowed.
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