Two orbitals are described as 2s and 3s. Which quantum number(s) would be different for these two orbitals?

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

Answer: (B)

Verified step by step guidance

1. Identify the quantum numbers associated with each orbital: the principal quantum number (\(n\)), the azimuthal quantum number (\(l\)), the magnetic quantum number (\(m_l\)), and the spin quantum number (\(m_s\)).
2. Recall that the principal quantum number (\(n\)) indicates the main energy level or shell of the electron and is represented by the number before the letter in the orbital notation (e.g., 2 in 2s, 3 in 3s).
3. Understand that the azimuthal quantum number (\(l\)) defines the shape of the orbital and depends on the type of orbital: for s orbitals, \(l = 0\) regardless of \(n\).
4. Recognize that the magnetic quantum number (\(m_l\)) specifies the orientation of the orbital in space and can range from \(-l\) to \(+l\). For s orbitals where \(l=0\), \(m_l\) is always 0.
5. Note that the spin quantum number (\(m_s\)) describes the spin of the electron and can be either \(+\frac{1}{2}\) or \(-\frac{1}{2}\), which is independent of the orbital type or energy level.