How many different orbitals in an atom have a principal quantum number n = 3?

• A. 9
• B. 6
• C. 18
• D. 3

Answer: (A)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) determines the energy level or shell of an electron in an atom. For \(n = 3\), we are looking at the third shell.
2. The angular momentum quantum number \(l\) can take integer values from \$0\( to \)n-1\(. For \)n = 3\(, \)l\( can be \)0\(, \)1\(, or \)2$.
3. Each value of \(l\) corresponds to a subshell: \(l=0\) is the s subshell, \(l=1\) is the p subshell, and \(l=2\) is the d subshell.
4. The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), inclusive. The number of orbitals in each subshell is therefore \$2l + 1$.
5. Calculate the total number of orbitals for \(n=3\) by summing the orbitals in each subshell: for \(l=0\), orbitals = \$1\(; for \)l=1\(, orbitals = \)3\(; for \)l=2\(, orbitals = \)5\(. Total orbitals = \)1 + 3 + 5$.