During the research that led to production of the two atomic bombs used against Japan in World War II, different mechanisms for obtaining a supercritical mass of fissionable material were investigated. In one type of bomb, a gun shot one piece of fissionable material into a cavity containing another piece of fissionable material. In the second type of bomb, the fissionable material was surrounded with a high explosive that, when detonated, compressed the fissionable material into a smaller volume. Discuss what is meant by critical mass, and explain why the ability to achieve a critical mass is essential to sustaining a nuclear reaction

Critical mass is the minimum amount of fissile, or fissionable, material required for a sustained nuclear chain reaction. When the amount of fissionable material is below this mass, the rate of fission reactions will decrease, and the chain reaction will eventually come to a halt. On the other hand, when the critical mass is reached or exceeded, the rate of fission reactions becomes self-sustaining, leading to a significant release of energy.

Achieving a critical mass is essential for sustaining a nuclear chain reaction. In the context of an atomic bomb, a sustained nuclear chain reaction leads to a rapid release of massive amount of energy and an explosion. If the amount of fissionable material is below the critical mass, the nuclear chain reaction will not be self-sustaining, and the bomb will not explode with full force.

In a gun-type atomic bomb, one piece of fissionable material is shot into another piece. The goal is to combine the two pieces and create a mass that is equal to or greater than the critical mass. As the two pieces come together, the total mass increases, and the probability of neutrons causing more fission reactions also increases. Once the critical mass is reached, the chain reaction becomes self-sustaining, leading to an explosion.

In an implosion-type atomic bomb, the fissionable material is surrounded by high explosives. When the explosives detonate, they compress the fissionable material into a smaller volume. This increases the density of the fissionable material, resulting in a greater number of fission reactions. The compression brings the mass and density of the fissionable material closer to, or beyond, the critical point, triggering a self-sustained nuclear chain reaction and explosion. In conclusion, critical mass plays a crucial role in nuclear reactions, such as those that occur in atomic bombs. Both the gun-type and implosion-type atomic bombs work on the principle of achieving a critical mass, which is necessary to initiate a self-sustaining chain reaction that leads to the release of massive amounts of energy and an explosion.