If the principal quantum number n equals 3, which of the following statements is correct?

• A. The value of the angular momentum quantum number l must be 3.
• B. The electron must be in an s orbital.
• C. The maximum number of electrons in this shell is 6.
• D. The electron can be found in the third energy level.

Answer: (D)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) defines the main energy level or shell of an electron in an atom. For \(n=3\), the electron is in the third energy level.
2. Understand that the angular momentum quantum number \(l\) can take integer values from \$0\( up to \)n-1\(. So for \)n=3\(, \)l\( can be \)0\(, \)1\(, or \)2\(, but not \)3$.
3. Recognize that the value of \(l\) determines the type of orbital: \(l=0\) corresponds to an s orbital, \(l=1\) to a p orbital, and \(l=2\) to a d orbital. Therefore, the electron is not restricted to an s orbital when \(n=3\).
4. Calculate the maximum number of electrons in the third shell by summing the electrons in all possible orbitals for \(n=3\). The orbitals are: 3s (\(l=0\)), 3p (\(l=1\)), and 3d (\(l=2\)). Each orbital can hold 2 electrons, so total electrons = \$2(1 + 3 + 5) = 18$.
5. Conclude that the correct statement is that the electron can be found in the third energy level, as this aligns with the definition of the principal quantum number \(n\).