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Chapter 18: Problem 68

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

Expert verified
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

01

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.
02

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.
03

'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.
04

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.

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Most popular questions from this chapter

Each of the following isotopes has been used medically for the purpose indicated. Suggest reasons why the particular element might have been chosen for this purpose. a. cobalt-57, for study of the body's use of vitamin \(\mathbf{B}_{12}\) b. calcium- \(47,\) for study of bone metabolism c. iron-59, for study of red blood cell function

A small atomic bomb releases energy equivalent to the detonation of 20,000 tons of TNT; a ton of TNT releases \(4 \times 10^{9} \mathrm{J}\) of energy when exploded. Using \(2 \times 10^{13} \mathrm{J} / \mathrm{mol}\) as the energy released by fission of \(^{235} \mathrm{U},\) approximately what mass of \(^{235} \mathrm{U}\) undergoes fission in this atomic bomb?

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a. \(^{68}\) Ga (electron capture) b. \(^{62} \mathrm{Cu}\) (positron) c. \(^{212} \operatorname{Fr}(\alpha)\) d. \(^{129} \operatorname{Sb}(\beta)\)

Calculate the binding energy per nucleon for \(\frac{2}{1} \mathrm{H}\) and \(^{3}_{1}\) \(\mathrm{H}\). The atomic masses are \(\frac{2}{1} \mathrm{H}, 2.01410 \mathrm{u} ;\) and \(\frac{3}{1} \mathrm{H}, 3.01605 \mathrm{u}\)

In each of the following radioactive decay processes, supply the missing particle. a. \(^{60} \mathrm{Co} \rightarrow^{60} \mathrm{Ni}+?\) b. \(^{97} \mathrm{Tc}+? \rightarrow^{97} \mathrm{Mo}\) c. \(^{99} \mathrm{Tc} \rightarrow^{99} \mathrm{Ru}+?\) d. \(^{239} \mathrm{Pu} \rightarrow^{235} \mathrm{U}+?\)
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