Which of the following sets of quantum numbers can describe the location of a 4s electron?

• A. n = 4, l = 0, m_l = 0, m_s = +1/2
• B. n = 4, l = 1, m_l = 0, m_s = +1/2
• C. n = 4, l = 2, m_l = 1, m_s = -1/2
• D. n = 3, l = 0, m_l = 0, m_s = -1/2

Answer: (A)

Verified step by step guidance

1. Recall the four quantum numbers that describe an electron's state: 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. Identify the quantum numbers for an electron in a 4s orbital: since the principal quantum number \(n\) corresponds to the shell number, for 4s, \(n = 4\).
3. For an s orbital, the azimuthal quantum number \(l\) is always 0, because \(l\) ranges from 0 to \(n-1\) and s orbitals correspond to \(l=0\).
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 \(-\frac{1}{2}\), so both spin states are possible for the electron.