Answer
$2.13\;meV$
Work Step by Step
The difference in energy between the two upper energy levels is
$\Delta E=\frac{ch}{\lambda_2}-\frac{ch}{\lambda_1}$
or, $\Delta E=\frac{1240\;eV-nm}{\lambda_2\; (nm)}-\frac{1240\;eV-nm}{\lambda_1\;(nm)}$
or, $\Delta E=\frac{1240\;eV-nm}{588.995\; nm}-\frac{1240\;eV-nm}{589.592\;nm}$
or, $\Delta E=2.13\times10^{-3}\;eV$
or, $\Delta E=2.13\;meV$
