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

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

Answer: (D)

Verified step by step guidance

1. Recall the meaning of each quantum number: \(n\) is the principal quantum number indicating the energy level, \(l\) is the azimuthal quantum number indicating the subshell (0 for s, 1 for p, 2 for d, etc.), \(m_l\) is the magnetic quantum number indicating the orbital orientation, and \(m_s\) is the spin quantum number indicating the electron spin (+1/2 or -1/2).
2. Identify the quantum numbers that correspond to a 4s electron. Since it is an s orbital, \(l\) must be 0. The principal quantum number \(n\) must be 4 to indicate the fourth energy level.
3. Check the allowed values of \(m_l\) for \(l=0\). Since \(m_l\) ranges from \(-l\) to \(+l\), for \(l=0\), \(m_l\) can only be 0.
4. Verify that the spin quantum number \(m_s\) can be either +1/2 or -1/2, so both are allowed for an electron in any orbital.
5. Compare each given set of quantum numbers to these criteria: the correct set must have \(n=4\), \(l=0\), \(m_l=0\), and \(m_s=+1/2\) (or -1/2). The set that matches these conditions describes a 4s electron.