Which of the following is a correct set of quantum numbers for an electron in a 5f orbital?

• A. n = 4, l = 3, m_l = +3, m_s = +1/2
• B. n = 5, l = 1, m_l = +1, m_s = -1/2
• C. n = 5, l = 3, m_l = -2, m_s = +1/2
• D. n = 5, l = 2, m_l = 0, m_s = -1/2

Answer: (C)

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 (orbital shape), \(m_l\) is the magnetic quantum number indicating the orientation of the orbital, and \(m_s\) is the spin quantum number indicating the electron's spin.
2. Identify the values of \(n\) and \(l\) for a 5f orbital. The principal quantum number \(n\) corresponds to the main energy level, so for 5f, \(n = 5\). The azimuthal quantum number \(l\) corresponds to the type of orbital: \(l = 0\) for s, \(l = 1\) for p, \(l = 2\) for d, and \(l = 3\) for f orbitals. Therefore, for an f orbital, \(l = 3\).
3. Check the allowed range of \(m_l\) values for \(l = 3\). The magnetic quantum number \(m_l\) can take integer values from \(-l\) to \(+l\), so for \(l = 3\), \(m_l\) can be \(-3, -2, -1, 0, +1, +2, +3\).
4. Verify the spin quantum number \(m_s\). The spin quantum number can only be \(+\frac{1}{2}\) or \(-\frac{1}{2}\), representing the two possible spin states of an electron.
5. Compare each given set of quantum numbers to these rules to determine which set correctly corresponds to an electron in a 5f orbital.