# Particle Vibration

Bubonic Plague
Why do the particles of substances vibrate? Just where does that constant energy come from?

## Answers and Replies

It comes from thermal energy (aka heat), dude. We can approximate the atoms of a material and their bonds as an array of masses with each mass being coupled to its nearest neighbors by springs. The modes of vibration are known as phonons.

eNtRopY

Bubonic Plague
It comes from thermal energy (aka heat), dude. We can approximate the atoms of a material and their bonds as an array of masses with each mass being coupled to its nearest neighbors by springs. The modes of vibration are known as phonons.

Good. Let's say i were to put the substance in vacuum, will it's particles still vibrate, now that it has no source of heat? Let's also say that it is shielded from electromagnetic radiation.

Originally posted by Bubonic Plague
Good. Let's say i were to put the substance in vacuum, will it's particles still vibrate, now that it has no source of heat? Let's also say that it is shielded from electromagnetic radiation.

Yes.

Let's go a step further and say that you have put a substance in a vacuum and achieved a material temperature of zero kelvin. There would still be molecular vibration. This phonon mode is known as the the zero-point energy. It's a quantum mechanical thing, but conceptually it makes sense. There is a minimum amount of kinetic energy that must be present; otherwise, the atoms in the lattice will be highly unlocalized....

Remember the Heisenberg Uncertainty Principle:

delta x delta p ~ h.

So, having delta p at zero would cause delta x to tend towards infinite.

Anyway in case your interested, the zero-point energy of a simple harmonic oscillator is given as:

E0 = (1/2) hbar omega.

The energies of all higher modes are:

En = (n + 1/2) hbar omega.

eNtRopY

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