Electron affinity is defined as the change in energy (in kJ/mole) of a neutral atom (in the gaseous phase) when an electron is added to the atom to form a negative ion.
In other words, the neutral atom's likelihood of gaining an electron.
Na(g)→Na+(g)+e−;
1st ionisation energy ; ΔHIE(1)=+5.1eV
Electron gaining is the reversed reaction of ionization. Hence, electron gain enthalpy is ;
∣IENa∣=∣EANa+∣
Na+(g)+e−→Na
So, ΔHeg=−5.1eV