Chapter 21: Problem 89
The number of neutrons accompanying the formation of \(_{34} \mathrm{Xe}^{139}\) and \(\mathrm{Sr}^{94}\) from the absorption of slow neutron by \({ }_{92} \mathrm{U}^{235}\) followed by nuclear fission is (a) 0 (b) 2 (c) 1 (d) 3
Short Answer
Expert verified
The number of neutrons released is 3.
Step by step solution
01
Understand the Problem Statement
We need to determine the number of neutrons released during the nuclear fission of uranium-235 when it absorbs a slow-moving neutron, leading to the formation of xenon-139 and strontium-94.
02
Write the Nuclear Equation
The nuclear reaction for the fission of uranium-235 after absorbing a neutron can be represented as:\[_{92}^{235}\text{U} + _{0}^{1}\text{n} \rightarrow _{54}^{139}\text{Xe} + _{38}^{94}\text{Sr} + x \ _{0}^{1}\text{n}\] Here, \( x \) represents the number of neutrons released.
03
Apply Conservation of Mass and Atomic Numbers
The sum of the atomic numbers before and after the fission must be equal, as must the sum of the mass numbers. The initial atomic number on the left is 92 (from uranium), and on the right, it is 54 (from xenon) + 38 (from strontium), which adds up to 92. For mass numbers, the sum initially is 236 (235 from uranium + 1 from neutron), and on the right side it is 233 (139 from xenon + 94 from strontium) + x, thus leading us to solve for \( x \).
04
Solve for Neutrons Released
Set up the equation for mass numbers: 236 = 233 + x. Solving it gives:\[ x = 236 - 233 = 3 \] Hence, 3 neutrons are released in this reaction.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Neutron Absorption
Neutron absorption is a key process in nuclear reactions, particularly in nuclear fission. It occurs when a neutron collides with a nucleus and is absorbed into it. This alters the composition of the nucleus, often leading to its instability. When a neutron is absorbed by a fissile material, such as uranium-235, it can lead to a chain reaction.
During neutron absorption, the target nucleus captures the neutron, adding to its mass. This increase in mass and the potential change in nuclear structure can make the nucleus unstable, prompting it to undergo fission. In nuclear reactors, controlled neutron absorption is harnessed to produce energy, as the reaction releases a large amount of heat.
Understanding neutron absorption helps in comprehending how fission reactions are initiated and sustained, especially in practical applications like nuclear power generation.
During neutron absorption, the target nucleus captures the neutron, adding to its mass. This increase in mass and the potential change in nuclear structure can make the nucleus unstable, prompting it to undergo fission. In nuclear reactors, controlled neutron absorption is harnessed to produce energy, as the reaction releases a large amount of heat.
Understanding neutron absorption helps in comprehending how fission reactions are initiated and sustained, especially in practical applications like nuclear power generation.
Uranium-235
Uranium-235 (
_{92}^{235} ext{U}
) is a naturally occurring isotope of uranium, notable for its role in nuclear fission. It accounts for about 0.7% of natural uranium and is highly sought after for nuclear power and weapons due to its fissile properties.
In nuclear physics, uranium-235 is vital because of its ability to sustain a chain reaction. When it absorbs a neutron, it becomes uranium-236, an unstable isotope prone to splitting apart. This fission results in the release of enormous amounts of energy and additional neutrons, which can further propagate the chain reaction if absorbed by other uranium-235 nuclei. This self-sustaining series of reactions is fundamental to both nuclear reactors and nuclear bombs.
Thus, mastering the properties of uranium-235 is crucial for understanding how nuclear energy is produced and the principles behind nuclear chain reactions.
In nuclear physics, uranium-235 is vital because of its ability to sustain a chain reaction. When it absorbs a neutron, it becomes uranium-236, an unstable isotope prone to splitting apart. This fission results in the release of enormous amounts of energy and additional neutrons, which can further propagate the chain reaction if absorbed by other uranium-235 nuclei. This self-sustaining series of reactions is fundamental to both nuclear reactors and nuclear bombs.
Thus, mastering the properties of uranium-235 is crucial for understanding how nuclear energy is produced and the principles behind nuclear chain reactions.
Nuclear Equation
A nuclear equation is a symbolic representation of a nuclear reaction. It shows how nuclear components like protons, neutrons, and atomic nuclei change during a reaction.
For instance, the absorption of a neutron by uranium-235 and its subsequent fission can be written as:\[_{92}^{235}\text{U} + _{0}^{1}\text{n} \rightarrow _{54}^{139}\text{Xe} + _{38}^{94}\text{Sr} + x \ _{0}^{1}\text{n}\]
In this equation, the reactants on the left combine to form new products on the right. In our example, uranium-235 and a neutron yield xenon-139, strontium-94, and a certain number of neutrons (represented by \( x \)). By conserving mass numbers and atomic numbers on both sides, one can solve for \( x \), determining the amount of neutron released.
This equation underscores the principles of conservation in physics, maintaining the balance of energy and matter before and after the reaction.
For instance, the absorption of a neutron by uranium-235 and its subsequent fission can be written as:\[_{92}^{235}\text{U} + _{0}^{1}\text{n} \rightarrow _{54}^{139}\text{Xe} + _{38}^{94}\text{Sr} + x \ _{0}^{1}\text{n}\]
In this equation, the reactants on the left combine to form new products on the right. In our example, uranium-235 and a neutron yield xenon-139, strontium-94, and a certain number of neutrons (represented by \( x \)). By conserving mass numbers and atomic numbers on both sides, one can solve for \( x \), determining the amount of neutron released.
This equation underscores the principles of conservation in physics, maintaining the balance of energy and matter before and after the reaction.
Xenon-139 and Strontium-94 Formation
When uranium-235 undergoes fission, it typically splits into two smaller nuclei and a few free neutrons. In our specific example, the products of this reaction are xenon-139 and strontium-94. These are known as fission fragments and are highly energetic due to their unstable nature.
The formation of these isotopes can be represented in the nuclear equation where xenon-139 ( _{54}^{139} ext{Xe} ) and strontium-94 ( _{38}^{94} ext{Sr} ) appear on the right side. These isotopes are part of a broad array of possible fission fragments, quite common in the splitting of uranium-235.
These newly formed nuclei may undergo further radioactive decay until they reach stable forms. This decay process releases additional energy, which is harnessed in nuclear reactors. Thus, understanding the specifics of xenon-139 and strontium-94, along with other potential fission products, helps in grasping how energy is released and utilized in nuclear fission.
The formation of these isotopes can be represented in the nuclear equation where xenon-139 ( _{54}^{139} ext{Xe} ) and strontium-94 ( _{38}^{94} ext{Sr} ) appear on the right side. These isotopes are part of a broad array of possible fission fragments, quite common in the splitting of uranium-235.
These newly formed nuclei may undergo further radioactive decay until they reach stable forms. This decay process releases additional energy, which is harnessed in nuclear reactors. Thus, understanding the specifics of xenon-139 and strontium-94, along with other potential fission products, helps in grasping how energy is released and utilized in nuclear fission.
