Multiple Choice
Which of the following lists all the allowed values of the angular momentum quantum number, l, when the principal quantum number n = 5?
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9. Quantum Mechanics
Quantum Numbers: Angular Momentum Quantum Number
Multiple Choice
Which of the following correctly represents the subshell with principal quantum number n = 2 and angular momentum quantum number l = 1?
A
1p
B
2s
C
2d
D
2p
Verified step by step guidance1
Recall that the principal quantum number \(n\) indicates the energy level or shell of an electron in an atom. Here, \(n = 2\) means we are looking at the second energy level.
The angular momentum quantum number \(l\) determines the subshell or shape of the orbital. The possible values of \(l\) range from \(0\) to \(n-1\). For \(n = 2\), \(l\) can be \(0\) or \(1\).
Each value of \(l\) corresponds to a specific subshell letter: \(l = 0\) corresponds to an \(s\) subshell, \(l = 1\) corresponds to a \(p\) subshell, \(l = 2\) corresponds to a \(d\) subshell, and so on.
Since \(l = 1\) for this problem, the subshell is a \(p\) subshell. Combining this with \(n = 2\), the correct notation for the subshell is \$2p$.
Check the options given: \$1p\( is invalid because \)l = 1\( is not possible for \)n = 1\( (since \)l\( must be less than \)n\(), \)2s\( corresponds to \)l = 0\(, and \)2d\( is invalid because \)l = 2\( is not allowed for \)n = 2\(. Therefore, \)2p$ is the correct representation.
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