Walker, Halliday & Resnick — Maxwell's Equations; Magnetism of Matter: Problem 17

17 If an electron in an atom has an orbital angular momentum with \( m_\ell = 0 \), what are the components (a) \( L_{orb,z} \) and (b) \( \mu_{orb,z} \)? If the atom is in an external magnetic field \( \vec{B}_{ext} \) that has magnitude 52 mT and is directed along the \( z \) axis, what are (c) the energy \( U_{orb} \) associated with \( \vec{\mu}_{orb} \) and (d) the energy \( U_{spin} \) associated with \( \vec{\mu}_s \)? If, instead, the electron has \( m_\ell = -3 \), what are (e) \( L_{orb,z} \), (f) \( \mu_{orb,z} \), (g) \( U_{orb} \), and (h) \( U_{spin} \)?