Final answer:
In a gaseous state, particles are separated by large distances compared to solids and liquids, and they occupy the entire volume of their container, which makes it the state of matter with particles spread the furthest apart.
Step-by-step explanation:
The state of matter that has particles spread the furthest apart is gas. In the gaseous state, the individual particles are separated by distances that are much larger than the size of the particles themselves, and they can move about freely. This movement causes the particles in a gas to be spread out and occupy the entire volume of their container, making the distance between them substantially greater than in solids or liquids. If we consider other states of matter mentioned in the reference materials provided, such as plasma, we'll see that in plasma, the gas is ionized and particles are also very far apart, possibly even more so due to the high energy levels involved. However, for the options listed in the question, gas is the correct answer as it is the most common state of matter we encounter daily where particles are spread out the most, aside from plasma which is not listed.