Use (IE) and (EA) listed below to determine
whether the following process is endothermic
exothermic.

$$\begin{gathered} {\mathrm{Mg}}_{\left(\mathrm{g}\right)}+2{\mathrm{F}}_{\left(\mathrm{g}\right)}\to {\mathrm{Mg}}^{2+}\left(\mathrm{g}\right)+2{\mathrm{F}}^{-}\left(\mathrm{g}\right) \\ (\mathrm{IE}{)}_1\text{of }{\mathrm{Mg}}_{\left(\mathrm{g}\right)}=737.7{\mathrm{kJmol}}^{-1} \\ (\mathrm{IE}{)}_2\text{ of }{\mathrm{Mg}}_{\left(\mathrm{g}\right)}=1451\mathrm{kJ}{\mathrm{mol}}^{-1} \\ \text{ (EA) of }{\mathrm{F}}_{\left(\mathrm{g}\right)}=-328\mathrm{kJ}{\mathrm{mol}}^{-1} \end{gathered}$$

We know that 

$\mathrm{Mg}\left(\mathrm{g}\right)\to {\mathrm{Mg}}^{+}\left(\mathrm{g}\right)+{\mathrm{e}}^{-}, 737.7 \mathrm{kJ}$

${\mathrm{Mg}}^{+}\left(\mathrm{g}\right)\to {\mathrm{Mg}}^{2+}\left(\mathrm{g}\right)+{\mathrm{e}}^{-}, 1451 \mathrm{kJ}$

$2 \mathrm{F}( \mathrm{g})+2{\mathrm{e}}^{-}\to 2{ \mathrm{F}}^{-}\left(\mathrm{g}\right)-328\times 2 \mathrm{kJ}$

$$\begin{gathered} \mathrm{Mg}\left(\mathrm{g}\right)+2 \mathrm{F}( \mathrm{g})\to {\mathrm{Mg}}^{2+}\left(\mathrm{g}\right)+2{ \mathrm{F}}^{-}\left(\mathrm{g}\right)\mathrm{\Delta H} \\ =\left({\mathrm{IP}}_1\right)\mathrm{Mg}+\left({\mathrm{IP}}_2\right)\mathrm{Mg}+2(\mathrm{E}.\mathrm{A})\mathrm{F}=1532.7 \mathrm{kJ} \end{gathered}$$

Therefore, the process is endothermic.

Hence, option(b) is the answer.