객관식
Which of the following sets of quantum numbers is valid for an electron in an atom?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
객관식
Which of the following orbitals cannot exist according to the rules for the principal quantum number n and the angular momentum quantum number l?
A
4f
B
3p
C
1s
D
2d
검증된 단계별 안내1
Recall the quantum number rules: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)), and the angular momentum quantum number \(l\) can take integer values from \(0\) up to \(n-1\) for each \(n\).
Identify the possible values of \(l\) for each given \(n\). For example, if \(n=2\), then \(l\) can be \(0\) or \(1\) only.
Match each orbital notation to its corresponding \(n\) and \(l\) values: the letter corresponds to \(l\) as follows: \(s \rightarrow l=0\), \(p \rightarrow l=1\), \(d \rightarrow l=2\), \(f \rightarrow l=3\).
Check if the given \(l\) value is allowed for the specified \(n\). For example, for \$2d\(, \)n=2\( and \)l=2\(, but since \)l\( must be less than \)n\(, \)l=2\( is not allowed when \)n=2$.
Conclude that orbitals where \(l \geq n\) cannot exist, so the \$2d$ orbital is invalid according to the quantum number rules.
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