Which set of quantum numbers correctly represents the two electrons in a 4s orbital?

• A. n = 4, l = 2, m_l = 0, m_s = +1/2 and n = 4, l = 2, m_l = 0, m_s = -1/2
• B. n = 4, l = 0, m_l = +1, m_s = +1/2 and n = 4, l = 0, m_l = -1, m_s = -1/2
• C. n = 4, l = 1, m_l = 0, m_s = +1/2 and n = 4, l = 1, m_l = 0, m_s = -1/2
• D. n = 4, l = 0, m_l = 0, m_s = +1/2 and n = 4, l = 0, m_l = 0, m_s = -1/2

Answer: (D)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) indicates the energy level or shell of the electron. For a 4s orbital, \(n = 4\).
2. The azimuthal quantum number \(l\) defines the subshell or shape of the orbital. For an s orbital, \(l = 0\); for p, \(l = 1\); for d, \(l = 2\).
3. The magnetic quantum number \(m_l\) specifies the orientation of the orbital within a subshell. For an s orbital (\(l=0\)), \(m_l\) can only be 0.
4. The spin quantum number \(m_s\) can be either \(+\frac{1}{2}\) or \(-\frac{1}{2}\), representing the two possible spin states of an electron in the same orbital.
5. Therefore, the two electrons in a 4s orbital must have quantum numbers \(n=4\), \(l=0\), \(m_l=0\), with one electron having \(m_s=+\frac{1}{2}\) and the other \(m_s=-\frac{1}{2}\).