The
question though is how come reactivity of halogens decreases going down
the group whereas reactivity of group 1 metals increases going down
the group?
You are reminded here once again that
elements react with other elements because they are energetically unstable.
Atoms of noble gases are energetically
stable while the rest of the elements in the periodic table are
not.
So, all atoms of other elements try to
attain a similar electronic structure as those of noble gases and they do so by
reacting with other elements.
Now,
the halogens also have two options for achieving the same electronic
structure as a noble gas: gain 1 electron or lose 7 electrons.