Which property of an electron in an atom is determined by the magnetic quantum number (m_l)?

• A. The shape of the orbital
• B. The energy level of the electron
• C. The orientation of the orbital in space
• D. The spin direction of the electron

Answer: (C)

Verified step by step guidance

1. Recall that the magnetic quantum number, denoted as \(m_l\), is one of the four quantum numbers used to describe the unique quantum state of an electron in an atom.
2. Understand that \(m_l\) specifically determines the orientation of the orbital in space relative to an external magnetic field. It can take integer values ranging from \(-l\) to \(+l\), where \(l\) is the azimuthal (angular momentum) quantum number.
3. Note that the shape of the orbital is determined by the azimuthal quantum number \(l\), not \(m_l\).
4. Recognize that the energy level of the electron is primarily determined by the principal quantum number \(n\), and sometimes influenced by \(l\) and \(m_l\) in multi-electron atoms, but \(m_l\) itself directly corresponds to orientation.
5. Remember that the spin direction of the electron is described by the spin quantum number \(m_s\), which is separate from \(m_l\).