As we go down the group the reactivity decreases because of the increasing size of the atoms. A halogen atom is able to attract an extra electron into its outermost shell to make eight electrons in total. It is the nucleus of each atom that attracts the extra electron.
As the atoms get bigger, their outer electron shell gets further away from the nucleus and hence the force of attraction for an electron decreases.
Therefore the atom gains an extra electron less readily.
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