Elements in the halogen group want to gain an electron in order to complete an electron shell. Therefore they all have high electron affinities.
The general trend of electron affinities is that it falls going down a group. This is because:
1. Going down a group the atoms gets bigger, so the electron that is added is farther from the positive charges in the nucleus, so there's less attraction.
2. Going down a group, more electrons are present in the atoms, so their repulsion for any extra electron grows.
In the case of fluorine, the volume of the atom is very small compared with chlorine. So, even though chlorine has more electrons than fluorine, they repel the extra electron less because they are much more spread out than in fluorine.
The extra electron feels more repulsion from the densely packed negative charges in fluorine than it does from the more spread out negative charges in chlorine. Therefore fluorine's electron affinity is lower than chlorine's.
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