What is the state of matter where atoms are free to move independently of one another?

In the state of matter known as gas, the atoms and molecules are indeed free to move independently of one another. This high degree of freedom allows gas particles to spread out and occupy the entire volume of their container, which is a characteristic feature of gases. The kinetic energy of gas particles is relatively high compared to those in solids and liquids, enabling them to overcome intermolecular forces and travel in various directions without being held closely together.

In contrast, in solids, the atoms are tightly packed in a fixed arrangement and can only vibrate in place. In liquids, while the atoms are closer together compared to gases, they do have some freedom to move around each other, but they are still influenced by intermolecular forces that keep them in close proximity. Plasma, while also composed of free-moving particles, is a state in which the gas has been energized to the point that electrons are freed from atoms, resulting in ionized gas. However, when discussing the independence of atomic movement, the gas state is the most accurate answer.