An atom's reactivity is determined by the number of electrons in its outermost shell. Because the outer shell can hold up to eight electrons and not all elements are able to fill these shells to capacity, the fullness of the shells will determine the volatility of the atom's reactive properties as a result of the number of electrons required to complete the shell.
Atoms with low reactivity have full atom shells. The noble gases, including neon, argon and krypton, fall into this category, as they are atoms that naturally present with full electron shells and are not looking to gain or lose electrons to achieve a balanced outer shell.
Atoms with high reactivity have outer shells that are imbalanced because of a low number of electrons (one or two) or a higher but not full number (six or seven). The most highly reactive elements are halogens, which are looking to gain one more electron, and alkali metals, which are looking to lose the single electron in their outer shells.