Chapter 21: Problem 89
The nuclide \(^{247 \mathrm{Es}}\) is made by bombardment of \(^{238} \mathrm{U}\) in a reaction that emits five neutrons. Identify the bombarding particle.
Short Answer
Expert verified
The bombarding particle is a nitrogen-14 nucleus, represented as \[\begin{equation} ^{14}_{7}N \end{equation}\].
Step by step solution
01
Understand the Nuclear Reaction
Nuclear reactions follow the law of conservation of mass and charge. The equation describing the reaction for the formation of the nuclide must account for the mass and atomic numbers of the reactants (uranium and the bombarding particle) and products (einsteinium and emitted neutrons).
02
Write the General Reaction
Express the nuclear reaction in terms of the unknown bombarding particle (X) which has an unknown mass number (A) and atomic number (Z): \[\begin{equation} ^{238}_{92}U + ^A_ZX \rightarrow ^{247}_{99}Es + 5^1_0n \end{equation}\]
03
Solve for the Mass Number of the Bombarding Particle
For the mass numbers (top numbers), apply the conservation law: \[\begin{equation} 238 + A = 247 + 5 \times 1 \end{equation}\] Therefore, \[\begin{equation} A = 247 + 5 - 238 \end{equation}\] \[\begin{equation} A = 14 \end{equation}\]
04
Solve for the Atomic Number of the Bombarding Particle
For the atomic numbers (bottom numbers), apply the conservation law: \[\begin{equation} 92 + Z = 99 + 5 \times 0 \end{equation}\] Therefore, \[\begin{equation} Z = 99 - 92 \end{equation}\] \[\begin{equation} Z = 7 \end{equation}\]
05
Identify the Bombarding Particle
The bombarding particle has a mass number of 14 and an atomic number of 7, which corresponds to the element nitrogen (N): \[\begin{equation} ^{14}_{7}N \end{equation}\]
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Law of Conservation of Mass and Charge
In the realm of nuclear chemistry, the law of conservation of mass and charge plays a pivotal role. It holds that during a nuclear reaction, like the one involving uranium and einsteinium, the total mass and the total charge must remain constant before and after the reaction occurs.
This concept is crucial when balancing nuclear equations. For example, if an element like uranium (( ^{238}_{92}U )) undergoes a transformation to produce einsteinium (( ^{247}_{99}Es )) while emitting neutrons, the sum of the mass numbers and the sum of the atomic numbers on both sides of the equation must be equal.
This concept is crucial when balancing nuclear equations. For example, if an element like uranium (( ^{238}_{92}U )) undergoes a transformation to produce einsteinium (( ^{247}_{99}Es )) while emitting neutrons, the sum of the mass numbers and the sum of the atomic numbers on both sides of the equation must be equal.
- The mass number represents the total number of protons and neutrons in the nucleus.
- The atomic number reflects the total number of protons, which also defines the identity of the element.
Neutron Emission
Neutron emission is a type of radioactive decay or nuclear reaction process where one or several neutrons are expelled from the nucleus of an atom. It is significant in various nuclear reactions, including the production of new nuclides.
In our nuclear equation involving the bombardment of uranium to form einsteinium, five neutrons are emitted. This emission alters the mass number of the product since neutrons contribute to the overall mass of the nucleus, but as they carry no charge, the atomic number, which refers to the number of protons, remains unaffected.
In our nuclear equation involving the bombardment of uranium to form einsteinium, five neutrons are emitted. This emission alters the mass number of the product since neutrons contribute to the overall mass of the nucleus, but as they carry no charge, the atomic number, which refers to the number of protons, remains unaffected.
- Each neutron has a mass number of 1 and an atomic number of 0 (( ^1_0n )).
- The emitted neutrons need to be accounted for when balancing the nuclear equation by the conservation of mass and charge.
Nuclide Identification
Nuclide identification is the process of determining the identity of a nuclide based on its mass number (A) and atomic number (Z). In the given problem, we sought to identify the bombarding particle used to transmute uranium into einsteinium.
The mass number provides information about the total number of protons and neutrons in the nuclide, while the atomic number tells us the number of protons, which is directly tied to the element's place on the periodic table.
In the exercise, we determined that the bombarding particle had a mass number of 14 and an atomic number of 7. Using the periodic table, we can then identify the particle as nitrogen (( ^{14}_{7}N )), which aligns with the conservation of mass and charge by completing the nuclear reaction equation previously unbalanced.
Identifying nuclides is fundamental in nuclear chemistry, as it leads us to understand the transformation of elements and the creation of novel substances through nuclear reactions.
The mass number provides information about the total number of protons and neutrons in the nuclide, while the atomic number tells us the number of protons, which is directly tied to the element's place on the periodic table.
In the exercise, we determined that the bombarding particle had a mass number of 14 and an atomic number of 7. Using the periodic table, we can then identify the particle as nitrogen (( ^{14}_{7}N )), which aligns with the conservation of mass and charge by completing the nuclear reaction equation previously unbalanced.
Identifying nuclides is fundamental in nuclear chemistry, as it leads us to understand the transformation of elements and the creation of novel substances through nuclear reactions.