Which set of quantum numbers is possible for an electron in a 2s orbital?

• A. n = 2, l = 0, m_l = 0, m_s = +1/2
• B. n = 1, l = 0, m_l = 1, m_s = -1/2
• C. n = 2, l = 1, m_l = 0, m_s = +1/2
• D. n = 2, l = 0, m_l = 1, m_s = -1/2

Answer: (A)

Verified step by step guidance

1. Recall the four quantum numbers that describe an electron in an atom: the principal quantum number \(n\), the azimuthal (angular momentum) quantum number \(l\), the magnetic quantum number \(m_l\), and the spin quantum number \(m_s\).
2. For a 2s orbital, the principal quantum number \(n\) must be 2, since the electron is in the second energy level.
3. The azimuthal quantum number \(l\) defines the shape of the orbital. For an s orbital, \(l\) must be 0. This means for a 2s orbital, \(l = 0\).
4. The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\). Since \(l = 0\) for an s orbital, \(m_l\) must be 0.
5. The spin quantum number \(m_s\) can be either \(+\frac{1}{2}\) or \(-\frac{1}{2}\), representing the two possible spin states of the electron.