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"Can you use particle accelerators to break up molecules into their elements?"

The short answer is yes.

The long answer is more complicated. You can think of molecules as wads of warm taffy with marbles in it (where the marbles are the atoms, and the warm taffy is what keeps them together). If you look at a marble (atom), you find that it has BB's inside, but they're held together with cold taffy (meaning they are held more firmly). If you continue to look at smaller pieces, you find that they are also made up of smaller things, each held together with stronger material. You could imagine that inside the pieces of the atoms (the BB's, really the electrons, protons and neutrons) that these are made of smaller things. For instance, the proton might be made up of little flecks of dust held together with steel.

So the pieces of a molecule are made up of smaller things, each of which are made of even smaller things, and so on. As things get smaller, the stuff holding them together gets stronger.

Molecules are very weakly held together. The typical energy that binds them together is about 0.25 electron Volt (eV) (don't worry how big an eV is.... just use it for a number you can compare). The Fermilab accelerator is 1,000,000,000,000 eV. Even the particle accelerator in the back of your TV is about 10,000 eV. So you could take particles moving very fast from an accelerator, smash them into a molecule and the molecule would most likely be broken up. But other bad things might happen too.

Imagine you are in a biology class and want to disassemble a chicken skeleton. You could do it in many ways. One way is to grab each bone and carefully detach it. Another way is to strap the skeleton to the front of the fastest rocket you can find, aim the rocket at the face of a very tall cliff and smash the skeleton into the cliff. Both of these methods will work, but in one case you'll have all of the parts and in the other you probably won't be able to find all of the bones, plus some of the bones will be broken, etc.

The point is that sometimes your hammer can be too big.

One final thought. A particle coming out of an accelerator is typically very small. So the particle doesn't hit the entire molecule, just a piece. An analogy is shooting a rifle bullet at a slab of jello. The bullet certainly has enough energy to liquify the jello, but what it often does is simply punch a hole in one place and make the rest of the jello jiggle. So when you hit a molecule with a fast moving particle, the damage is more likely to be localized.

So you can use a particle acclerator to split apart molecules. But there are much easier ways.

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