The size of an atomic orbital is primarily associated with which quantum number?

• A. Magnetic quantum number (m_l)
• B. Principal quantum number (n)
• C. Angular momentum quantum number (l)
• D. Spin quantum number (m_s)

Answer: (B)

Verified step by step guidance

1. Understand that atomic orbitals are described by four quantum numbers: the principal quantum number (\(n\)), the angular momentum quantum number (\(l\)), the magnetic quantum number (\(m_l\)), and the spin quantum number (\(m_s\)).
2. Recall that the principal quantum number (\(n\)) determines the main energy level or shell of an electron and is directly related to the size and energy of the orbital.
3. Recognize that as \(n\) increases, the orbital becomes larger and the electron is found farther from the nucleus, which means the size of the orbital increases with \(n\).
4. Note that the angular momentum quantum number (\(l\)) defines the shape of the orbital, the magnetic quantum number (\(m_l\)) defines the orientation of the orbital in space, and the spin quantum number (\(m_s\)) describes the electron's spin, none of which primarily affect the size.
5. Conclude that the size of an atomic orbital is primarily associated with the principal quantum number (\(n\)) because it determines the orbital's energy level and average distance of the electron from the nucleus.