Quote - When an atomic bomb explodes neither a single electron vanishes transformed into energy
.When the nuclear fission happens the uranium nucleous is divided in two giving two other elements. If we add the number of protons, neutons and electrons that the uranium atom has before the fision and we compare to the sum of protonts, neutrons and electrons of both elements produced by the fision and add the two liberated neutrons we shall find that are the same, no proton, no neutron, no electron has dissapeared, matter was preserved after the explosion.
So if no matter has vanished from where do come the energy liberated by the explosion?
The answer is that the energy stored in the uranium nucleous is bigger than the sum of energies stored in the nucleum of the produced elements.
 The energy stored in the nucleums we measure as mass and this is what is converted or liberated as energy, only a question of units.
Matter (protons, neutrons) is preserved by the explosion, a fraction of the internal energy (mass) is converted or liberated as energy.
Relativity tell us that mass increase with speed, but it doesn't mean that a plane flying becomes bigger than is on ground, it only means that a plane that is flying has more inertia than when is on ground.

 

Last point first. The relativistic mass increase at high velocities is more than the kinetic energy increase predicted from Newtonian physics. This is observable in the real world in supercolliders. First point--I'm not sure what you are talking about regarding fission and fusion. In fusion, there is a conversion of protons+electrons into neutrons. The fusion of two hydrogen atoms into the heavy isotope (deutrinium) of hydrogen takes two protons and two electrons and ends up with one proton, one neutron, and one electron. In fission, the atomic numbers of the fission products do not always sum up to the atomic number of the original atom, typically neutrons get converted into protons and electrons. However, there is a conservation of charge and of baryon (heavy particle) numbers.

The energy liberated in fusion, and fission, is not, however affected by proton+electron to neutron conversion. (At a given atomic weight of an atom, a neutron has the same mass as a proton and an electron combined.) The actual mass of protons and neutrons varies with the atomic mass of the atom they reside in. A neutron in a Plutonium atom has a little more mass than one in a Uranium atom, and a neutron in a hydrogen atom has a little more mass than one in a Helium atom. The point at which an atomic particle has the lowest mass is, IIRC, in an iron atom, which is one reason why atoms with higher atomic numbers are very rare (universaly speaking) -- they don't get formed by normal fusion (actually, it requires a pretty hot star on it's way to becoming a Nova to fuse anything much other than hydrogen to helium), and probably only get formed in Supernovas, where fusion (of heavy atoms) actually requires additional energy.

Anyway, the energy liberated in fusion of hydrogen to helium is because a helium atom (atomic mass 4) has slightly less mass than four hydrogen atoms (atomic mass 1). Similarly for fission byproducts, or, for that matter, normal radioactive decay. When an atom of Uranium-238 gives of an alpha particle (essentially a helium nucleus) to form Thorium-234, each proton and neutron in the Thorium masses slightly less than its counterpart in the Uranium. (The ones in the alpha particle mass more, but the net of all the mass changes is a decrease in mass, which is libereated as kinetic energy of the alpha particle.) Note that in fission and decay, a lot of the energy is liberated as kinetic energy. Look up "decay chain" in Wikipedia for more details.