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 super- critical 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

A critical mass is the minimum amount of nuclear fissile material required to sustain a chain reaction, which is essential in both energy production and atomic weapon functioning. Achieving a critical mass allows for a self-sustaining chain reaction, releasing large amounts of energy. The "gun" mechanism involves shooting one piece of fissionable material into another, while the compression mechanism involves detonating high explosives to compress the material. The latter method is considered more effective and efficient in achieving a super-critical mass and triggering a nuclear reaction.

Step-by-step solution

Critical Mass Concept

A critical mass is the minimum amount of nuclear fissile material required to sustain a chain reaction. A chain reaction is a sequence of nuclear reactions in which the product of one reaction triggers at least one more reaction, causing the process to continue. When the mass of the fissile material is less than the critical mass, the rate of neutron production will be lower than the rate at which neutrons are lost due to absorption or escaping the system. In this case, the chain reaction dies out over time. However, when the mass of the fissile material reaches or exceeds the critical mass, the neutrons produced will cause further nuclear reactions at a fast rate, leading to a sustained chain reaction.

Importance of Achieving Critical Mass

The ability to achieve a critical mass is essential to sustaining a nuclear reaction. If the mass of fissile material is below the critical mass, it cannot maintain a chain reaction, and the potential energy from the fission process is not efficiently released. By achieving the critical mass, a self-sustaining chain reaction can continue, releasing large amounts of energy in the form of a nuclear explosion. This principle is crucial for both energy production in nuclear reactors and for the functioning of atomic weapons.

'Gun' Mechanism

In the "gun" mechanism, one piece of fissionable material is shot into a cavity containing another piece of fissionable material. When the two pieces join together, their collective mass exceeds the critical mass, creating a super-critical system. Consequently, a nuclear chain reaction starts, resulting in a nuclear explosion. However, this method is relatively inefficient at producing a large explosion, as a significant portion of the fissile material may escape the system before complete detonation.

Compression Mechanism

The compression mechanism involves surrounding the fissionable material with a high explosive. When the high explosive is detonated, it compresses the fissionable material into a smaller volume, increasing the density and effectively increasing the mass per unit volume. This process results in a super-critical mass being created within the compressed volume, thereby initiating a nuclear chain reaction and a subsequent nuclear explosion. This method is considered more effective and efficient than the "gun" mechanism, as it can utilize a greater percentage of the fissionable material and create a larger explosion.

Key concepts

Critical Mass

Critical mass is a crucial term in nuclear physics, especially in the realm of nuclear reactions. It refers to the smallest amount of fissile material needed to maintain a continuous, self-sustaining nuclear chain reaction.
Critical mass depends on several factors:

• The type of fissile material used: Different materials have different critical masses based on their properties.
• The purity of the fissile material: Higher purity increases the likelihood of sustaining a reaction.
• The shape and configuration of the material: A spherical shape is often the most efficient for reaching critical mass due to optimal surface area-to-volume ratio.

When the fissile material's mass is below the critical mass, the reaction cannot sustain itself, as too many neutrons escape or are absorbed without causing further fissions.

Chain Reaction

A chain reaction is the core sequence of events that powers a nuclear reaction. It involves a series of fission events where each fission triggers further fissions, leading to a cascading series of reactions.
The process works as follows:

• A neutron collides with the nucleus of a fissile atom, causing it to split (fission).
• The fission releases additional neutrons along with energy.
• These newly released neutrons cause more fission events, and the cycle continues.

For a sustained chain reaction, at least one released neutron from each fission must cause another fission. Achieving critical mass allows this sustained chain of reactions to occur, maintaining the cycle and continuously releasing energy.

Fissile Material

Fissile materials are materials that are capable of sustaining a nuclear fission chain reaction with neutrons of any energy, typically thermal neutrons. Common fissile materials include uranium-235 and plutonium-239, both of which are used in nuclear reactors and nuclear weapons.
Essential characteristics of fissile materials include:

• The ability to capture and use neutrons effectively for sustaining chain reactions.
• A high probability of fission upon neutron absorption, which is pivotal for a successful chain reaction.

The choice of fissile material impacts the critical mass and the mechanism needed to maintain a nuclear reaction, making them vital for the effective operation of nuclear reactors and bombs.

Nuclear Fission

Nuclear fission is the process by which the nucleus of an atom splits into two or more smaller nuclei, along with the release of energy and additional neutrons. It is the foundational process for both nuclear reactors and nuclear weapons.
Key features of nuclear fission include:

• The splitting of heavy atomic nuclei into lighter fragments, like barium and krypton in uranium fission.
• Release of a vast amount of energy, because of the conversion of mass to energy as described by Einstein’s equation, \( E = mc^2 \).
• Release of additional neutrons, which can perpetuate further fission reactions, leading to a chain reaction.

Understanding nuclear fission is crucial to grasp how nuclear power and atomic explosions work, as they rely on the efficient release of energy from the fission process.

Atomic Bomb Mechanism

The mechanism behind an atomic bomb utilizes principles of nuclear fission and chain reactions to release a massive amount of energy explosively. Two primary types of mechanisms were developed during World War II: the "gun" type and the "implosion" type.
The "gun" mechanism involves shooting one sub-critical piece of fissile material into another to exceed critical mass.

• Once the combined mass becomes super-critical, a chain reaction is initiated, resulting in an explosion.

The "implosion" mechanism surrounds the fissile material with explosives, compressing it to reach super-critical conditions efficiently. This method maximizes the use of fissile material, making it more effective at producing larger explosions.
The understanding of each mechanism helps in appreciating how nuclear reactions can be controlled or unleashed, highlighting both civilian energy uses and military applications.