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Chapter 19: Problem 56

Breeder reactors are used to convert the nonfissionable nuclide \({ }_{92}^{238} \mathrm{U}\) to a fissionable product. Neutron capture of the \({ }_{92}^{238} \mathrm{U}\) is followed by two successive beta decays. What is the final fissionable product?

Short Answer

Expert verified
The final fissionable product formed from the neutron capture and two successive beta decays of \(_{92}^{238} \mathrm{U}\) is \(_{94}^{239} \mathrm{Pu}\) (Plutonium).

Step by step solution

01

Determine the isotope formed after neutron capture

: When a nuclide captures a neutron, its mass number increases by 1 while its atomic number remains the same. The captured neutron increases the number of neutrons by 1. So the isotope after neutron capture will be \(_{92}^{239} \mathrm{U}\).
02

Determine the first isotope formed after the first beta decay

: In a beta decay, a neutron is converted into a proton, while an electron (beta particle) is emitted. This causes the atomic number of the nuclide to increase by 1 while the mass number remains unchanged. Thus, after the first beta decay, the isotope formed will be \(_{93}^{239} \mathrm{Np}\) (Neptunium).
03

Determine the final fissionable product formed after the second beta decay

: After the second beta decay, the atomic number of the isotope will again increase by 1 while the mass number remains unchanged. This results in the formation of the isotope \(_{94}^{239} \mathrm{Pu}\) (Plutonium) as the final fissionable product. So, the final fissionable product formed from the neutron capture and two successive beta decays of \(_{92}^{238} \mathrm{U}\) is \(_{94}^{239} \mathrm{Pu}\).

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Most popular questions from this chapter

Radioactive copper-64 decays with a half-life of \(12.8\) days. a. What is the value of \(k\) in \(\mathrm{s}^{-1}\) ? b. A sample contains \(28.0 \mathrm{mg}^{64} \mathrm{Cu}\). How many decay events will be produced in the first second? Assume the atomic mass of \({ }^{64} \mathrm{Cu}\) is \(64.0 \mathrm{u}\). c. A chemist obtains a fresh sample of \({ }^{64} \mathrm{Cu}\) and measures its radioactivity. She then determines that to do an experiment, the radioactivity cannot fall below \(25 \%\) of the initial measured value. How long does she have to do the experiment?

The binding energy per nucleon for magnesium- 27 is \(1.326\) \(\times 10^{-12} \mathrm{~J} /\) nucleon. Calculate the atomic mass of \({ }^{27} \mathrm{Mg} .\)

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

The curie (Ci) is a commonly used unit for measuring nuclear radioactivity: 1 curie of radiation is equal to \(3.7 \times 10^{10}\) decay events per second (the number of decay events from \(1 \mathrm{~g}\) radium in \(1 \mathrm{~s}\) ). A 1.7-mL sample of water containing tritium was injected into a 150 -lb person. The total activity of radiation injected was \(86.5 \mathrm{mCi}\). After some time to allow the tritium activity to equally distribute throughout the body, a sample of blood plasma containing \(2.0 \mathrm{~mL}\) water at an activity of \(3.6 \mu \mathrm{Ci}\) was removed. From these data, calculate the mass percent of water in this 150 -lb person.

When nuclei undergo nuclear transformations, \(\gamma\) rays of characteristic frequencies are observed. How does this fact, along with other information in the chapter on nuclear stability, suggest that a quantum mechanical model may apply to the nucleus?
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