Multiple Choice
How many energy sublevels are present in the second principal energy level (n = 2)?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Which of the following sets correctly lists all possible orbitals for the principal quantum number n = 3?
A
3p and 3d only
B
3s, 3p, 3d, and 3f
C
3s, 3p, and 3d
D
3s and 3p only
Verified step by step guidance1
Recall that the principal quantum number \(n\) determines the energy level and the possible subshells (orbitals) within that level. For a given \(n\), the azimuthal quantum number \(l\) can take integer values from \$0\( to \)n-1$.
List the possible values of \(l\) for \(n=3\): \(l = 0, 1, 2\). Each value of \(l\) corresponds to a type of orbital: \(l=0\) is an \(s\) orbital, \(l=1\) is a \(p\) orbital, and \(l=2\) is a \(d\) orbital.
Identify the orbitals for \(n=3\) based on the \(l\) values: \$3s\( (for \)l=0\(), \)3p\( (for \)l=1\(), and \)3d\( (for \)l=2\(). Note that \)l=3\( (which would correspond to \)f\( orbitals) is not allowed for \)n=3\( because \)l\( must be less than \)n$.
Understand that \$3f\( orbitals do not exist because \)f\( orbitals start at \)n=4\( where \)l=3\( is allowed. Therefore, the set of orbitals for \)n=3\( includes only \)3s\(, \)3p\(, and \)3d$ orbitals.
Conclude that the correct set of orbitals for \(n=3\) is \$3s\(, \)3p\(, and \)3d\(, and options including \)3f\( or excluding \)3s$ are incorrect.
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