$\mathrm{AB}$, ${\mathrm{A}}_2$and ${\mathrm{B}}_2$are diatomic molecules. If the bond enthalpies of ${\mathrm{A}}_2 ,\mathrm{AB}$ and ${\mathrm{B}}_2$ are in the ratio 1: 1: 0.5 and enthalpy of formation of $\mathrm{AB}$from ${\mathrm{A}}_2$and ${\mathrm{B}}_2$is $-100\mathrm{kJ}/{\mathrm{mol}}^{-1}$ . What is the bond enthalpy of ${\mathrm{A}}_2$?