* Electron Configuration: Group 1 metals have one valence electron, which they readily lose to form a +1 cation. Group 13 metals have three valence electrons. While they can lose these electrons to form a +3 cation, it requires more energy to remove three electrons compared to one.

* Ionization Energy: Ionization energy is the energy required to remove an electron from an atom. Group 13 metals have higher ionization energies than group 1 metals, making them less likely to lose electrons.

* Metallic Character: As you move across a period in the periodic table, metallic character decreases. This means group 13 metals are less metallic and therefore less reactive than group 1 metals.

In summary, the reactivity of metals in the periodic table decreases as you move from left to right across a period (due to increasing ionization energy and decreasing metallic character).