Answer
See explanation.
Work Step by Step
The interaction energy between an external magnetic field and the orbital angular momentum is given by $U=m_l\mu_B B$.
a. The 5g level is split into 9 levels by the magnetic field.
For the 5g level, $l=4$ and there are $2l+1 = 9$ different $m_l$ values/states.
b. Each $m_l$ level is shifted in energy an amount given by $U=m_l\mu_B B$, so adjacent levels differ in energy by $\Delta U= \mu_B B$.
$$\Delta U =(5.79\times10^{-5}eV/T)(0.600T)= 3.47\times10^{-5}eV $$
c. There are 9 equally-spaced levels, and we just calculated the energy separation between adjacent levels. The separation between the highest energy ($m_l=4$) and the lowest energy ($m_l=-4$) is $\Delta U= 8 \mu_B B$.
$$\Delta U =8(5.79\times10^{-5}eV/T)(0.600T)= 2.78\times10^{-4}eV $$
