Atoms of elements at the top of a group on the periodic table or smaller than the atoms of elements at the bottom of the group. how does this explain the difference in the reactivity of metals within a group?

Explanation:

Metals are the species or atoms which tend to lose their valence electrons in order to attain stability.

And, when we move down a group of metals then there occurs an increase in the size of atoms and along with it there occurs an increase in reactivity of metals.

This is because larger is the size of an element, lesser will be interaction between its valence electrons and nucleus. As a result, there is weak force of attraction between the nucleus of the atom and its valence electrons.

Hence, the metal is able to lose its valence electrons easily.

On the other hand, smaller is the size of a metal more strong will be the force of attraction between its nucleus and valence electrons. As a result, this metal will not easily lose its valence electrons.