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 fissionable material required to sustain a nuclear chain reaction. A chain reaction occurs when one nuclear reaction causes an average of one or more subsequent nuclear reactions, releasing a large amount of energy.

Achieving a critical mass is crucial for a nuclear reaction to become self-sustaining. If the mass of the fissionable material is below the critical mass, the number of released neutrons will not be enough to sustain the chain reaction, and the reaction will eventually stop. When the mass is equal to or greater than the critical mass, the reaction can continuously produce energy by converting the mass of the fissionable material into energy, following Einstein's famous equation \(E = mc^2\), where E is energy, m is mass, and c is the speed of light.

The two mechanisms mentioned in the exercise were developed to achieve a supercritical mass, which is essential for a successful atomic bomb. 1. Gun-type assembly: In the gun-type bomb, two sub-critical pieces of fissionable material (usually uranium-235) are brought together at high speed. One piece is shot into a cavity containing the other piece. The collision creates a supercritical mass, initiating a chain reaction and producing a nuclear explosion. 2. Implosion-type assembly: In the implosion-type bomb, a sub-critical mass of fissionable material (usually plutonium-239) is surrounded by a high explosive. When the explosive is detonated, it compresses the fissionable material into a smaller volume, making it denser and increasing its probability to achieve a supercritical mass. This process results in a nuclear chain reaction and a powerful explosion. By understanding the concept of critical mass and the methods used to achieve it, we can appreciate the importance of critical mass in sustaining a nuclear chain reaction and its role in the development of nuclear weapons.