If atoms are packed too tightly, they will not necessarily explode in the conventional sense. However, they can undergo a phenomenon known as nuclear fission, which can release a tremendous amount of energy.
Nuclear fission is a process where the nucleus of an atom splits into two or more smaller nuclei, accompanied by the release of a large amount of energy. This process can occur when certain heavy elements, such as uranium-235 or plutonium-239, absorb a neutron and become unstable. When the nucleus splits, additional neutrons are often emitted, which can then go on to initiate a chain reaction, causing more nuclei to undergo fission.
In order for a sustained chain reaction to occur, the packing of atoms needs to reach a critical mass. This critical mass is the minimum amount of fissile material required to maintain a self-sustaining chain reaction. If the packing of atoms falls below the critical mass, the chain reaction will not be sustained, and the process will cease.
If the packing of atoms exceeds the critical mass, an uncontrolled chain reaction can occur, leading to a release of a significant amount of energy in a short period of time. This is the principle behind nuclear reactors and atomic bombs.
In a nuclear reactor, the chain reaction is controlled to produce a steady release of energy for power generation. On the other hand, in an atomic bomb, the chain reaction is uncontrolled and leads to a rapid release of an enormous amount of energy, causing an explosion.
It's worth noting that the precise conditions required for a nuclear fission chain reaction depend on various factors, including the type of fissile material, its purity, the geometry of the material, and the presence of other substances. These factors determine whether a given packing of atoms will result in a sustained chain reaction, a limited reaction, or no reaction at all.