The characteristic property of metals in their pure state observed during the activity is metallic luster. Metallic luster is the ability of metals to reflect light uniformly from their surfaces, giving them a shiny and reflective appearance. This property arises due to the free movement of electrons in the metallic structure. In the activity series, metals such as sodium, potassium, calcium, and aluminum exhibit a characteristic metallic luster. The presence of free electrons allows these metals to efficiently reflect light, contributing to their shiny and reflective nature in their pure, unoxidized states.