Each row on the periodic table represents a new energy level/electron shell. So as you go down the group there are more energy levels, increasing the atomic radius. The first electron to react will be on the outer shell.

The reactivity increases down the group from Mg to Ba. This is because the further away an electron is from the nucleus, the weaker its attraction and the more likely it is to react with another atom. More energy levels also means there is more nuclear ‘shielding’ from other electrons, further weakening the outer electrons’ attraction to the nuclei.