The factors affecting electron gain enthalpy and the trend in its variation in the periodic table are:

1)ATOMIC SIZE

As we go down the group electron gain enthalpy decreases as the distance of the nucleus from the outermost shell increases which decreases its tendency to gain electron and electron gain enthalpy becomes less negative.

2)EFFECTIVE NUCLEAR CHARGE

As we go from left to right in a period the effective nuclear charge increases and when we move down the group it decreases which results in the attraction of electrons from the outermost shell.

3) ELECTRONIC CONFIGURATION

The tendency to gain electrons depends upon the stability of an element. Elements having completely or half filled stable orbitals have very low tendency to gain electron thus they have very low electron gain enthalpy.

TRENDS

Across a period: electron gain enthalpy becomes more negative.

Down the group: electron gain enthalpy becomes less negative.