Answer
Binding energy$=-1.7394\times10^{11}\,kJ/mol$
$=-7.3086\times10^{8}\,kJ/mol\,nucleon$
Work Step by Step
Mass defect, $\Delta m= Mass \,^{238}U-[(Z\times\,^{1}_{1}H)+(A-Z)\,^{1}_{0}n]= 238.0508\,g/mol-[(92\times1.00783\,g/mol)+(238-92)1.00867\,g/mol]$
$=-1.9354\,g/mol=-0.0019354\,kg/mol$
Binding energy $E_{b}=\Delta m c^{2}$
$=-0.0019354\times(2.99792458\times 10^{8}m/s)^{2}$$=-1.7394\times10^{14}\,J/mol$
$=-1.7394\times10^{11}\,kJ/mol$
Negative sign indicates that the energy is released when constituent protons and neutrons combine to form $^{238}U$.
Binding energy per nucleon, $E_{bn}= \frac{E_{b}}{number\,of\,nucleons}=\frac{E_{b}}{mass\, number}$
$=\frac{-1.739451\times10^{11}\,kJ/mol}{238 nucleons}$$=-7.3086\times10^{8}\,kJ/mol\,nucleon$
