Which set of quantum numbers correctly describes an electron in a 4d orbital?

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

Answer: (C)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) indicates the energy level or shell of the electron. For a 4d orbital, \(n\) must be 4.
2. The azimuthal quantum number \(l\) defines the subshell or shape of the orbital. The values of \(l\) correspond to: \(l=0\) (s), \(l=1\) (p), \(l=2\) (d), \(l=3\) (f). Since the orbital is a 4d, \(l\) must be 2.
3. The magnetic quantum number \(m_l\) describes the orientation of the orbital and can take integer values from \(-l\) to \(+l\), including zero. For \(l=2\), \(m_l\) can be \(-2, -1, 0, 1,\) or \$2$.
4. Check each given set of quantum numbers against these rules: the set must have \(n=4\), \(l=2\), and \(m_l\) within the allowed range for \(l=2\).
5. Identify the set that matches all these criteria. The correct set will have \(n=4\), \(l=2\), and \(m_l\) equal to one of \(-2, -1, 0, 1,\) or \$2$.