Electron gain enthalpy of oxygen is less than sulphur's due to its compact nature (it will suffer interelectronic repulsion), but why does EGE become less negative after sulphur ? (Down the group, atomic size increases, so how can size be attributed to EGE in this case?) if it is not size, then what is the deciding factor?

 you should remember that oxygen ,being the first element of the group it is very small .hence a new electron will be suffer repulsions  from other electrons present in the orbits due to its small size. But as we go down the group the size increases, because of which affinity for incoming electron decreases. It will be more easier to remove the outermost electron.

Electrongativity is the tendency of an atom to attract an electron towards itself. So as we go down the group, the size increases therefore the electron density decreases,which in turn decreases the extent of attraction between the outermost electrons and the nucleus. So, as we move down a group, the size of atom increases and hence the tendency to gain electrons becomes less, but to lose electrons becomes more. 

A trend of decreasing Eea going down the groups in the periodic table would be expected. The additional electron will be entering an orbital farther away from the nucleus. Since this electron is farther from the nucleus it is less attracted to the nucleus and would release less energy when added

 

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