Group 1 and Group 17 elements exhibit vigorous reactivity due to their electronic configurations, which motivate them to attain a stable, fully filled outer shell.

Group 1 elements, commonly referred to as alkali metals, possess a single electron in their outermost shell. This characteristic renders them highly reactive, as they tend to lose this electron to achieve a stable electronic configuration akin to that of noble gases. The loss of this outer electron leads to the formation of a positive ion, or cation. The simplicity with which these elements can shed their outer electron makes them excellent reducing agents. For instance, when sodium ($\text{Na}$) reacts with chlorine ($\text{Cl}$), sodium loses its outer electron, forming $\text{Na}^+$, while chlorine gains this electron to become $\text{Cl}^-$. This reaction results in the formation of sodium chloride ($\text{NaCl}$), a stable ionic compound.

Conversely, Group 17 elements, known as halogens, have seven electrons in their outermost shell. They are only one electron short of achieving a stable, fully filled outer shell configuration. Consequently, halogens tend to gain an electron during chemical reactions, which makes them highly reactive and effective oxidizing agents. For example, when chlorine (a Group 17 element) reacts with sodium (a Group 1 element), chlorine acquires an electron from sodium, resulting in the formation of the chloride ion ($\text{Cl}^-$) and the compound sodium chloride ($\text{NaCl}$).

The reactivity of both Group 1 and Group 17 elements decreases as one moves down the group. For Group 1 elements, this decrease is attributed to an increase in atomic size and the shielding effect, which diminishes the nucleus’s ability to attract and lose the outermost electron. In the case of Group 17 elements, the larger atomic size and heightened shielding effect make it increasingly difficult for the atom to attract and gain an additional electron.

In summary, the electronic configurations of Group 1 and Group 17 elements play a crucial role in their reactivity. Group 1 elements, with one electron in their outer shell, tend to lose this electron to achieve stability, whereas Group 17 elements, with seven electrons in their outer shell, tend to gain an electron to complete their outer shell. This inherent drive toward stability is what makes these elements highly reactive.