The reactivity goes up when you'r going down the column.
All group I elements have one single electron in their outmost orbit. If they can get rid of that they would have a noble gas configuration, and that is what every atom "wants".
As we go down in the group I, the number of electrons in the outermost shell remains the same i.e 1. But the no of shells increases ie - Li has 2 shells (K and L) and Na has 3 shells (K, L and M). So atomic radii increases as the nuclear pull towards the outermost shell and electron decreases.
So the lower in the column, the larger the atom, so the further away from the (positive) nucleus, so the less it pulls on that electron.