Explain the periodicity of electron gain enthalpy of elements in the periodic table.

(N/A) Electron gain enthalpy $(\Delta_{eg}H)$ shows less regularity compared to ionization enthalpy.
Across a period (left to right),electron gain enthalpy generally becomes more negative (increases in magnitude) with an increase in atomic number. This is because the effective nuclear charge increases,making it easier for an incoming electron to be added to the smaller atom,as the added electron is closer to the positively charged nucleus.

Group-$1$ Element $(\Delta_{eg} H)$	Group-$16$ Element $(\Delta_{eg} H)$	Group-$17$ Element $(\Delta_{eg} H)$	Group-$18$ Element $(\Delta_{eg} H)$
$H(-73)$	$-$	$-$	$He(+48)$
$Li(-60)$	$O(-141)$	$F(-328)$	$Ne(+116)$
$Na(-53)$	$S(-200)$	$Cl(-349)$	$Ar(+96)$
$K(-48)$	$Se(-195)$	$Br(-325)$	$Kr(+96)$
$Rb(-47)$	$Te(-190)$	$I(-295)$	$Xe(+77)$
$Cs(-46)$	$Po(-174)$	$At(-270)$	$Rn(+68)$

Down a group,the value of electron gain enthalpy generally becomes less negative (e.g.,$[S(-200), Se(-195), Te(-190), Po(-174)]$ and $[Cl(-349), Br(-325), I(-295), At(-270)]$). This occurs because the atomic volume increases,and the added electron is further from the nucleus.
Note: The electron gain enthalpy of oxygen is less negative than that of sulfur,and that of fluorine is less negative than that of chlorine. This is because when an electron is added to oxygen or fluorine ($n=2$ shell),it experiences significant inter-electronic repulsion due to the small size of the shell. In the $n=3$ shell (sulfur or chlorine),the added electron occupies a larger region of space,resulting in significantly less electron-electron repulsion.