Which set of quantum numbers correctly designates the energy level, subshell shape, orbital orientation, and electron spin for an electron in an atom?

• A. The principal quantum number n defines orbital orientation; l defines energy level; m_l defines orbital shape; m_s is electron spin.
• B. The principal quantum number n defines energy level; l defines subshell shape (0 = s, 1 = p, 2 = d, 3 = f); m_l defines orbital orientation; m_s is electron spin (+1/2 or -1/2).
• C. The azimuthal quantum number l defines energy level; principal quantum number n defines subshell shape; m_l defines spin orientation; m_s defines occupation number.
• D. The magnetic quantum number m_l defines energy level; n defines orientation; l defines spin; m_s defines subshell.

Answer: (B)

The idea is that each electron in an atom is described by four quantum numbers that assign its energy, the shape of its orbital, its orientation in space, and its spin. The energy level comes from the principal quantum number, n. The shape of the orbital, or subshell, is set by the azimuthal quantum number, l (0 for s, 1 for p, 2 for d, 3 for f). The specific orbital within that subshell and its orientation in space is given by the magnetic quantum number, m_l (ranging from −l to +l). The electron’s spin is described by the spin quantum number, m_s, which can be +1/2 or −1/2. Therefore, the correct designation uses n for energy level, l for subshell shape, m_l for orbital orientation, and m_s for spin. For example, a 3d electron has n = 3, l = 2, and m_l could be −2, −1, 0, 1, or 2, with m_s equal to +1/2 or −1/2. The other options swap or misassign these roles, so they don’t consistently label all four features.