Answer
See the answer below.
Work Step by Step
$\lambda_1=589.00\ nm=0.58900\times10^{-6}\ m$
$\lambda_2=589.59\ nm=0.58959\times10^{-6}\ m$
$c=\lambda\times\nu$
$\nu_1=5.09\times10^{14}\ s^{-1}$
$\nu_2=5.08\times10^{14}\ s^{-1}$
$E=h\times\nu$
$E_1=3.37\times10^{-19}\ J$
$E_2=3.36\times10^{-19}\ J$
$E_1-E_2=3.375\times10^{-22}\ J$