Question

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

Short answer

Critical mass is the minimum amount of fissionable material required to sustain a nuclear chain reaction. Achieving critical mass is essential for a nuclear reaction, as it allows for a self-sustaining chain reaction and a significant release of energy. In an atomic bomb context, gun-type bombs achieve this by shooting one piece of fissionable material into another, while implosion-type bombs compress fissionable material into a smaller volume via high explosives. Both methods aim to reach or exceed the critical mass, leading to a self-sustaining chain reaction and explosion.

Step-by-step solution

Define Critical Mass

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.

Explain the Importance of Critical Mass

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.

Analyze the Gun-Type Bomb

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.

Analyze the Implosion-Type Bomb

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.

Key concepts

Nuclear Chain Reaction

A nuclear chain reaction is a sequence of nuclear fission reactions where one fission event causes the release of additional neutrons, which then trigger further fission reactions. This process is central to the operation of nuclear reactors and atomic bombs.

In a controlled nuclear reactor, this reaction is carefully moderated to maintain a steady energy output. However, in an atomic bomb, the goal is to rapidly accelerate this process to release immense energy quickly.

For a chain reaction to sustain itself, each fission event must produce enough neutrons to continue the process. If each event leads to more reactions, the chain reaction will grow exponentially, releasing tremendous amounts of energy in a very short time span.

Fissionable Material

Fissionable material is a substance capable of sustaining a nuclear fission chain reaction when struck by neutrons. Common examples of such materials include Uranium-235 and Plutonium-239.

These materials have atoms with heavy nuclei, which can be split into smaller nuclei when bombarded by neutrons. This splitting, or fission, releases energy and more neutrons, which can go on to split additional nuclei, fueling a chain reaction.

The likelihood of fission increases with the density of the material. This is why atomic bomb mechanisms aim to bring fissionable material together in a dense configuration, often by combining separate pieces or compressing it with explosives, ensuring the reaction can sustain itself rapidly.

Atomic Bomb Mechanisms

Atomic bombs utilize mechanisms that quickly bring fissionable material to a supercritical state, allowing an explosive chain reaction.

• Gun-Type Bomb: This mechanism works by shooting one piece of sub-critical fissionable material into another using a high-speed gun assembly. When combined, the total mass slightly exceeds the critical mass, permitting the chain reaction to rapidly escalate, resulting in an explosion.


• Implosion-Type Bomb: This design surrounds the fissionable core with conventional high explosives. When detonated, these explosives compress the core to a smaller, denser state. This compression passes the critical threshold, triggering a nuclear explosion.

Both designs strive to maximize the neutron economy within their core to ensure the fission reactions sustain long enough for a significant explosion. The precise timing and mechanism of achieving supercriticality define the bomb's effectiveness.