
Philip P. answered 05/17/17
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Temperature is a measure of the average kinetic energy of the particles in a substance, be it a gas, liquid, or solid. The formula for kinetic energy (KE) is:
KE = mv2/2
where m is the particle's mass and v is its velocity. If the temperature (T) is not zero (Kelvin or absolute scale), then the KE is not zero and v cannot be zero. So if T>0, there is motion. In a gas or liquid, the particles move about freely. In a solid, they are held in place in the solid's lattice structure but vibrate around their fixed position.
At a temperature of absolute zero (T = 0), it implies that the kinetic energy is also zero and hence the velocity of the particles is zero. However, the 3rd Law of Thermodynamics tells us that you can never quite get to absolute zero; hence there is always some residual motion.
In Quantum Mechanics, a temperature of absolute zero means that all particles are in their lowest energy states, but the Heisenberg Uncertainty Principle means that there will always be some uncertainty in the particle's position and momentum, hence in its velocity.
So the bottom line is yes, the particles in any substance are in constant motion.