Final answer:
Particles in a gas state have the freedom to vibrate, rotate, and translate due to minimal intermolecular forces, unlike particles in solid and liquid states. Option 2 is correct.
Step-by-step explanation:
Particles are free to vibrate, rotate, and translate predominantly in a gas state of matter. In a solid, particles are closely packed together and can only vibrate in place due to strong intermolecular forces. On the other hand, in a liquid, particles have enough energy to move around each other but still remain in close contact, although they do not have enough energy to completely escape the influence of neighboring particles as they do in a gas.
The gaseous state allows the most freedom of movement, with particles moving independently and colliding in a random fashion due to minimal intermolecular forces acting upon them. As a result, gases can expand to fill their container, are compressible, and have neither a fixed shape nor a fixed volume. Thus, the correct answer to which state of matter allows particles to be free to vibrate, rotate, and translate is gas.
The state of matter in which particles are free to vibrate, rotate, and translate is gas. In the gas state, the particles have enough energy to move freely and do not have a fixed shape or volume. They move randomly and only come into contact with each other when they collide.