Can atoms be destroyed?

Chris Smith put this question from listener Rheboth to physicist Adam Murphy. 

Adam - It depends sort of on what you mean by destroy. If you mean just break it into bits then yeah you can. A lot of the history of signs has been oh, we can't divide this thing any further - oh no wait, yes we can. Atom comes from the Greek meaning indivisible but we've learnt that we can break atoms up into protons, neutrons, and electrons. We learnt that those can be divided further into things called quarks and so far we think that's the bottom layer but we could be wrong again.

But there's another layer to that which is if you go to Einstein's work you get his big famous equation which is e=mc squared - energy is mass times the speed of light squared. Basically energy and  of the same thing so you can convert mass into energy and there's a lot of energy in a tiny amount of mass. If you took 1 kg and converted it all into energy you get about 25 billion kilo-watt-hours. If you took 1 g of stuff and turn that all into energy, that's what happened at Nagasaki in 1945 with the atomic bomb.

Chris - So one tiny component of you could destroy an entire city if we realised all of the energy that's in it? But you mentioned radioactivity because that bomb was the process which is that it was a nuclear bomb which is, in some cases, you can make a nuclear bomb by splitting atoms apart, you actually make them fall apart so atoms can in that sense be destroyed, can't they, if they radioactively decay? Other bombs are made by joining the atoms together to make bigger ones so we can actually take one atom and turn it into another kind of atom by radioactivity?

Adam - Absolutely. And you find if you take those two atoms and smash them together that new atom will be a tiny tiny bit lighter than the other two put together because that little bit of mass has turned into energy.