When an atom bomb goes off some matter is converted to energy according to $E = m c^2$.
I'd like to know exactly what matter in the original atom bomb is converted to energy. Is it protons, neutrons, electrons? Is it a collection of atoms? What goes?
Take a nucleus of U-235 and determine its mass. Induce it to fission by firing a neutron at it. When it does so, collect all the pieces (except the extra neutron) and determine their total mass. You will find that all the pieces weigh just a hair less than original nucleus. The difference is the "binding energy", also previously known as the "packing fraction", and is the mass that was converted to energy.
Iron has the highest binding energy. Atoms heavier than iron will release energy when split. Atoms lighter than iron will release energy when fused together. Fuse two deuterium nuclei into a helium nucleus and you will find that the helium weighs just a little less than two deuteriums (deuteria?). It takes a lot of energy to get the two deuteriums close enough to fuse, but if you manage to do it (with a fission bomb as the trigger of a hydrogen bomb) you get quite a bit of energy out.
One does not simply vanish mass, you'd have to provide the respective antiparticles to obtain Annihilation, converting the entire mass into energy. What does happen in nuclear reactions is that the elements obtained afterwards have a total mass $m_\text{new}$ that is lower* than the one $m_\text{old}$ before. This is due to the different binding energies involved, causing the so-called mass-defect. This missing mass $\Delta m=m_\text{new}-m_\text{old}$ is what is converted into energy $E=\Delta m c^2$, which is partially set free as kinetic energy of the new matter (including $\alpha$ (He nuclei) and $\beta^\pm$ (Positrons, electrons) particles), and partly into the creation of $\gamma$ particles (Photons, i.e. radiation).
* Not always, it can be higher as well, the basic rule is that the binding energy per nucleus particle increases towards iron from both sides, i.e. in order to convert iron into hydrogen or oxygen, you'd need to invest energy. This is shown in the following image, with the notable exceptions of the rather important elements Oxygen, Carbon and Helium:
If you take a proton or something and make it go really, really fast – give it lots of kinetic energy then relativity says it gets heavier. In the same way if you’ve got lots of potential energy if you put it into a really big heavy atom like uranium then it will also get heavier. When you split up that big atom you get less potential energy and that means that the resultants (all of the protons and all of the neutrons inside) are lighter than they were before because they have less potential energy.
So there are actually the same number of constituents, but the sum total weight is decreased.
The rest mass of Nuclear Binding Energy is converted into external energy of destruction in fission-based nuclear bombs.
