The electrons that gain enthalpy for metals is positive and negative for non metals. Also, if metals are bigger in size than non metals then, how can electrons gain enthalpy is inversely proportional to the atomic size?

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The answer is simple, like you are hungry you can pay more to get the food than that of the person who is less hungry,

Similarily here the non metals want electrons thus they spend the energy more , or they release the energy. By this they lose the energy.

So smaller is the size more is the non metallic character and this way energy will be negative as the energy is released by the system.

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