In the quantum mechanical model of the atom, what does the principal quantum number n represent?

• A. The spin direction of the electron
• B. The energy level or shell in which an electron resides
• C. The shape of the orbital occupied by the electron
• D. The orientation of the orbital in space

Answer: (B)

Verified step by step guidance

1. Understand that the principal quantum number, denoted as \(n\), is one of the four quantum numbers used to describe the unique quantum state of an electron in an atom.
2. Recognize that \(n\) primarily indicates the energy level or shell of the electron, which corresponds to the average distance of the electron from the nucleus.
3. Recall that as \(n\) increases, the electron's energy and its average distance from the nucleus also increase, meaning electrons in higher \(n\) levels are less tightly bound to the nucleus.
4. Differentiate \(n\) from other quantum numbers: the azimuthal quantum number \(l\) describes the shape of the orbital, the magnetic quantum number \(m_l\) describes the orientation of the orbital, and the spin quantum number \(m_s\) describes the spin direction of the electron.
5. Conclude that the principal quantum number \(n\) represents the energy level or shell in which an electron resides.