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They are both from the same group, yes. But F is above Cl so it means that the F's valence shell is nearer the nucleus (or at "lower level") than the valence shell in Cl, which causes F to have more effective nuclear charge.

This fact explains the more electron affinity* in F in relation to Cl and therefore F is more reactive.

* - electron affinity refers to a free atom. electronegativity refers to an atom in a molecule.

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