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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