We know that lithium, sodium and potassium tarnish when exposed to air, but rubidium and cesium catch on fire. Why is there such a huge jump in reactivity between Rb and K?
Good question. Because going down in the periodic system, the ions get bigger and bigger, ionization energies become smaller. So it's easier to start a reaction with the bigger guys.
Does that make it clearer ?
BvU has it right. There's not really a "huge jump" in reactivity ... it's just a matter of reaching a threshold in the rate of energy release, to a point where things proceed differently. Expose K to hot air, or to a higher concentration of oxygen, and it will behave like Rb.