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Chapter 19: Problem 61

Uranium-235 undergoes many different fission reactions. For one such reaction, when \(^{235} \mathrm{U}\) is struck with a neutron, \(^{144}\mathrm{Ce}\) and \(^{90}\mathrm{Sr}\) are produced along with some neutrons and electrons. How many neutrons and \(\beta\) -particles are produced in this fission reaction?

Short Answer

Expert verified
In the given fission reaction of Uranium-235, 2 neutrons and 4 β-particles are produced along with Cerium-144 and Strontium-90.

Step by step solution

01

Determine the mass numbers and atomic numbers of the initial and final products

In this fission reaction, Uranium-235 is hit with a neutron, and the products are Cerium-144 and Strontium-90 along with some neutrons and beta particles. First, let's note down the mass numbers (A) and atomic numbers (Z) of each element involved in the reaction. - Uranium-235 (U): A = 235, Z = 92 - Neutron (n): A = 1, Z = 0 - Cerium-144 (Ce): A = 144, Z = 58 - Strontium-90 (Sr): A = 90, Z = 38 - Neutrons: A = 1, Z = 0 (each) - Beta particles (β): A = 0, Z = -1 (each, since it is an electron emitted) We will denote the number of neutrons produced as x, and the number of beta particles produced as y.
02

Apply the conservation of mass number and atomic number

In order for the reaction to conserve mass number and atomic number, we need to satisfy the following equations: 1. Mass number conservation: 235 + 1 = 144 + 90 + x (U + n = Ce + Sr + neutrons) 2. Atomic number conservation: 92 = 58 + 38 + y (U = Ce + Sr + beta particles)
03

Solve the equations for x and y

Now, let's solve the equations to find x and y: 1. From the mass number conservation equation: 236 = 234 + x x = 2 (2 neutrons are produced) 2. From the atomic number conservation equation: 92 = 96 + y y = -4 (4 beta particles are produced) (Note that the negative sign indicates that 4 electrons are emitted as β-particles during the fission reaction.) #Conclusion# In this fission reaction of Uranium-235, 2 neutrons and 4 β-particles are produced along with Cerium-144 and Strontium-90.

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Most popular questions from this chapter

Naturally occurring uranium is composed mostly of \(^{238} \mathrm{U}\) and $235 \mathrm{U},\( with relative abundances of 99.28\)\%\( and \)0.72 \%,$ respectively. The half-life for \(^{238} \mathrm{U}\) is \(4.5 \times 10^{9}\) years, and the half-life for 235 \(\mathrm{U}\) is \(7.1 \times 10^{8}\) years. Assuming that the earth was formed 4.5 billion years ago, calculate the relative abundances of the 28 \(\mathrm{U}\) and \(^{235} \mathrm{U}\) isotopes when the earth was formed.

In the bismuth-214 natural decay series, Bi-214 initially undergoes \(\beta\) decay, the resulting daughter emits an \(\alpha\) particle, and the succeeding daughters emit a \(\beta\) and a \(\beta\) particle in that order. Determine the product of each step in the Bi-214 decay series.

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.\(_{1}^{3} \mathrm{H}(\beta)\) b. \(_{3}^{8} \operatorname{Li}(\beta \text { followed by } \alpha)\) c. \(\quad_{4}^{7}\) Be (electron capture) d. \(_{5}^{8} \mathrm{B}(\text { positron })\)

Consider the following graph of binding energy per nucleon as a function of mass number a. What does this graph tell us about the relative half-lives of the nuclides? Explain your answer. b. Which nuclide shown is the most thermodynamically stable? Which is the least thermodynamically stable? c. What does this graph tell us about which nuclides undergo fusion and which undergo fission to become more stable? Support your answer.

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