What you are thinking of is what's best described as "radical damage". All those free radicals you keep hearing about on TV? Yeah that's pretty much it. Basically what it is, is a atom (usually oxygen, although others do exist) that carries only one electron, this is a highly reactive species and will pretty much break into whatever structure it comes into contact with. Sometimes this causes cancer, other times it gets sequestered by the necessary enzymes/co-factors. Rarely though will you find just a stray radical oxygen atom, it's usually (I think) in a carbon structure, like the acyl radical. As for certain single atoms doing the damage, I don't think so. Cells move atoms (Chlorine, Sodium, Potassium) in and out of the cell at the rate of several hundred or more per second, if cancer could be induced by atoms bumping against things we'd have serious trouble. Maybe you were thinking of radiation? High energy radiation (mostly gamma and high doses of x-ray - UV radiation too) push out enough energy to physically mutate DNA and the cellular structure, destroying things like p53 proteins, and all those other things that keep the cell replicating normally.
I should add at this point that cancerous cells are so-called "immortal" cells because the mechanisms for inducing apoptosis are defunct in some way. Meaning that these cells reproduce till kingdom come, and don't die either. Which is why you need highly toxic treatments (stuff that basically kills cells - this is why chemo and radio therapies are dangerous) to kill the cancer.
As for the vibration theory, I'm not quite sure I understand where you're coming from, but I don't think that's a plausible idea. If vibrations were to be able to induce cancer, we'd not have invented things like rollercoasters or off-road vehicles, or even those funny vibrating thingies people stand on to get thinner. Maybe you're speaking of a different type of vibration though? I dunno, some quantum mechanics maybe? I know there's a group in the US that want to characterise the quantum processes behind cancer. Maybe they know of something.
Ultimately though, I think your case can best be explained by radiation.
@tya: Cancer itself is not hereditary, you can inherit genes giving you a higher chance of getting cancer though (I think you mentioned this) like the BRCA group of genes for example. But there are a myriad of epigenetic factors (and environmental) that are necessary to induce cancer. With specific mutations one might just need a lower dose for cells to become tumorigenic.