Answer
See explanation.
Work Step by Step
The differing spin of the two states means they have a different z-component of spin angular momentum, by equation 41.36. In turn, the spin magnetic moment also differs when the electron is in the 2 states, by equation 41.38. The spin up state has a magnetic moment that points in the negative z direction.
Finally, when we put magnetic moments into magnetic fields, there is a torque exerted on them, and an associated potential energy, given by equation 41.28, $U=-\vec{\mu}\cdot \vec{B}$.
The magnetic moment that points opposite to $\vec{B}$ has a higher potential energy because the dot product is negative. That corresponds to the situation when the electron is in a spin up state.
