Final answer:
The most stable group of elements is the noble gases in Group 18 due to their full energy levels and adherence to the octet rule, which confers minimal reactivity.
Step-by-step explanation:
The most stable group of elements is the noble gases, which are found in Group 18 of the periodic table. These elements have full energy levels and adhere to the octet rule, meaning they have eight electrons in their outermost energy level, leading to great stability and minimal reactivity. Elements strive to achieve this stable configuration, and therefore, the noble gases do not react easily with other elements. In contrast, iron is noted for having the most stable nucleus due to its high binding energy, but when considering entire atoms, including electron configurations, the noble gases take precedence for overall elemental stability.