Step 1: Understand electron gain enthalpy.
Electron gain enthalpy is the enthalpy change when an electron is added to an isolated gaseous atom.
More negative electron gain enthalpy means greater tendency to accept an electron.
Step 2: Compare fluorine and chlorine.
Although fluorine is more electronegative, chlorine has more negative electron gain enthalpy than fluorine.
This is because the incoming electron in fluorine enters the compact \(2p\) orbital where electron-electron repulsion is very high.
In chlorine, the added electron enters the larger \(3p\) orbital where repulsion is comparatively less.
Hence,
\[
\Delta H_{eg}(\text{Cl})\lt \Delta H_{eg}(\text{F})
\]
Therefore, fluorine has smaller negative electron gain enthalpy than chlorine.
So, Assertion (A) is correct.
Step 3: Examine the reason statement.
The reason states that electron-electron repulsion is higher in chlorine than in fluorine.
This is incorrect.
Actually, electron-electron repulsion is higher in fluorine because of its very small atomic size and compact \(2p\) orbital.
Therefore, Reason (R) is incorrect.
Step 4: Final conclusion.
Hence,
\[
\boxed{\text{(A) is correct but (R) is incorrect}}
\]