Reactivity increases going down Group 1 because the atoms lets larger so the single electron in the outer most shellis attracted less strongly to the positive nucelus.
The electrostatic attraction with the nucleus gets weaker because the distance between the outer electrons and nucleus increases.
Also the outer electron experiences a sheilding effect from inner shells of electrons. This reduces the attraction between the oppositely charged outer electrons in the nucleus.
The size of the positive charge on the nucleus does become larger as you go down a group, as more protons are present inside the nucleus. This suggests tee attraction for the outer electron should get stronger.
However, the greater distance and sheilding effect of inner electrons outweigh the increasing nuclear charge.
Therefore, in Group 1, the outer electron gets easier to remove going down the group and the elements et more and more reactive.
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