Answer
$18.4\;T$
Work Step by Step
The energy difference between the two spin orientations or electron is:
$\Delta E=2\mu_BB$
or, $B=\frac{\Delta E}{2\mu_B}$
In the pervious section, we have obtained: $\Delta E=2.13\;meV=2.13\times10^{-3}\;eV$
Therefore,
$B=\frac{2.13\times10^{-3}\;eV}{2\times(5.788\times10^{-5}\;eV/T)}$
or, $B=18.4\;T$
Therefore, the magnetic field is $18.4\;T$
