What is electron gain enthalpy?

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(N/A) Electron gain enthalpy $(\Delta_{eg}H)$ is defined as the change in enthalpy when an electron is added to a neutral gaseous atom $(X)_{(g)}$ to convert it into a negative ion $(X)_{(g)}^{-}$.
The process is represented as: $X_{(g)} + e^{-} \rightarrow X_{(g)}^{-}; \Delta_{eg}H$.
The value of $\Delta_{eg}H$ can be either negative or positive depending on the element.

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In which of the following,elements are arranged in the correct order of their electron gain enthalpies?

The set containing the elements with positive electron gain enthalpies is

The formation of the oxide ion,$O^{2-}_{(g)}$ from an oxygen atom requires first an exothermic and then an endothermic step as shown below:
$O_{(g)} + e^- \to O^{-}_{(g)} ; \Delta_f H^o = -141 \ kJ \ mol^{-1}$
$O^{-}_{(g)} + e^- \to O^{2-}_{(g)} ; \Delta_f H^o = +780 \ kJ \ mol^{-1}$
Thus,the process of formation of $O^{2-}$ in the gas phase is unfavourable even though $O^{2-}$ is isoelectronic with neon. This is due to the fact that,

The formation of the oxide ion,$O^{2-}_{(g)}$,from oxygen atom requires first an exothermic and then an endothermic step as shown below:
$O_{(g)} + e^- \to O^{-}_{(g)} ; \Delta_f H^{\Theta} = -141 \ kJ \ mol^{-1}$
$O^{-}_{(g)} + e^- \to O^{2-}_{(g)} ; \Delta_f H^{\Theta} = +780 \ kJ \ mol^{-1}$
Thus,the process of formation of $O^{2-}$ in gas phase is unfavourable even though $O^{2-}$ is isoelectronic with neon. It is due to the fact that,

Knowing the electron gain enthalpy values for $O \rightarrow O^{-}$ and $O \rightarrow O^{2-}$ as $-141 \ kJ \ mol^{-1}$ and $702 \ kJ \ mol^{-1}$ respectively,how can you account for the formation of a large number of oxides having $O^{2-}$ species and not $O^{-}$?
(Hint: Consider lattice energy factor in the formation of compounds).

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