The reactivity or passiveness of an element depends solely on how close it is to attain a noble gas configuration. This means the closer an element is to attain a noble gas configuration, the greater its reactivity in both direction, positively or negatively.
Alkali metals belong to group 1 of the periodic table while halogens belong to group 17 of the periodic table. This means they are just one electron away from achieving the stability of a noble gas configuration. While alkali metals need to lose one electron to form a univalent positive ion, halogens news to gain one electron to form a univalent negative ion.
They tend to go about this vigorously and as such undergo several chemical reactions because of that single electron they neeed.
