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

Answer: (C)

Verified step by step guidance

1. 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$.
2. 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.
3. 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$.
4. 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.
5. Conclude that the correct set of orbitals for \(n=3\) is \$3s\(, \)3p\(, and \)3d\(, and options including \)3f\( or excluding \)3s$ are incorrect.