Which sample is likely to be the least dense and has the fastest motion and most energy?

The correct answer highlights the properties of gases in relation to density, motion, and energy. In a gas, molecules are much further apart compared to solids and liquids, which significantly decreases the overall density of the gas. This reduced density is a result of the fact that particles in a gaseous state are not held closely together by intermolecular forces, allowing them to move freely and rapidly.

Furthermore, the kinetic energy of gas molecules is generally higher than that of molecules in solids or liquids. This is because, in a gas, the kinetic energy is determined by the temperature and the speed of molecular motion. As the molecules collide and bounce off each other, they maintain a high rate of motion. This rapid movement contributes to the gas having the least density while possessing a lot of energy.

In contrast, solids have tightly packed molecules that vibrate in place, resulting in higher density and lower energy compared to gases. Liquids have intermediate properties, with molecules that are closer than gases but still able to move around, leading to moderate density and energy levels. Hence, the characteristics of gases as described in the correct answer establish them as having low density, rapid molecular motion, and high energy relative to the other states of matter.