Halliday, Resnick & Walker — Maxwell's Equations; Magnetism of Matter: Problem 44

44 Figure 32-29a is a one-axis graph along which two of the allowed energy values (levels) of an atom are plotted. When the atom is placed in a magnetic field of 0.800 T, the graph changes to that of Fig. 32-29b because of the energy associated with \(\vec{\mu}_{orb} \cdot \vec{B}\). (We neglect \(\vec{\mu}_s\).) Level \(E_1\) is unchanged, but level \(E_2\) splits into a (closely spaced) triplet of levels. What are the allowed values of \(m_\ell\) associated with (a) energy level \(E_1\) and (b) energy level \(E_2\)? (c) In joules, what amount of energy is represented by the spacing between the triplet levels?