Answer
$
\Delta U=4.64 \times 10^{-24} \mathrm{~J} .
$
Work Step by Step
For any pair of adjacent levels in the triplet, $\left|\Delta m_f\right|=1$. Thus, the spacing is given by
$$
\Delta U=\left|\Delta\left(-m_{\ell} \mu_B B\right)\right|=\left|\Delta m_{\ell}\right| \mu_B B=\mu_B B=\left(9.27 \times 10^{-24} \mathrm{~J} / \mathrm{T}\right)(0.50 \mathrm{~T})=4.64 \times 10^{-24} \mathrm{~J} .
$$
