Chemical reactivity increases down a group in the periodic table primarily due to the atomic radius and the effect of electron shielding. As one moves down a group, the outer electrons are held less tightly by the nucleus, making them easier to transfer during chemical reactions. This decreased attraction results in higher reactivity. The comparison between elements like iodine and fluorine illustrates this trend, as iodine is more reactive than fluorine despite being lower in the group. Overall, the relationship between atomic structure and reactivity is crucial for understanding chemical behavior.