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Chapter 38: Problem 36

Write a complete equation for neutron-induced fission of plutonium-239 that yields barium-143, two neutrons, and another nucleus.

Short Answer

Expert verified
The balanced nuclear equation for neutron-induced fission of plutonium-239 resulting in barium-143, two neutrons, and another nucleus is: \(^{1}_{0}\mathrm{n} + ^{239}_{94}\mathrm{Pu} \to ^{143}_{56}\mathrm{Ba} + 2(^{1}_{0}\mathrm{n}) + ^{96}_{38}\mathrm{Kr}\).

Step by step solution

01

Understanding Nuclear Fission of Plutonium-239

In this case, a neutrons impacts a plutonium-239 nucleus causing it to split into two smaller nuclei along with two additional neutrons. One of the resulting nuclei is barium-143.
02

Writing the Initial Reaction

Initially, write down what's given. The fission of plutonium-239 (\(^{239}_{94}\mathrm{Pu}\)) induced by a neutron (\(^{1}_{0}\mathrm{n}\)) results in barium-143 (\(^{143}_{56}\mathrm{Ba}\)), two neutrons (2\(^{1}_{0}\mathrm{n}\)), and an unknown nucleus (\(^{A}_{Z}\mathrm{X}\)). So write the initial equation as: \(^{1}_{0}\mathrm{n} + ^{239}_{94}\mathrm{Pu} \to ^{143}_{56}\mathrm{Ba} + 2(^{1}_{0}\mathrm{n}) + ^{A}_{Z}\mathrm{X}\)
03

Balancing the Nuclear Equation

In nuclear reactions, both the total atomic number (the subscript, representing the number of protons) and the total mass number (the superscript, representing the sum of protons and neutrons) must be conserved. The atomic number on the left side of the equation (94) must equal that on the right, and similarly, the mass number on the left (240, accounting for the additional neutron) must be equal to that on the right. Solving these equations, you would find \(^{96}_{38}\mathrm{Kr}\) as the unknown nucleus.

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Most popular questions from this chapter

Why are fission fragments necessarily radioactive?

Which model, liquid-drop or nuclear shell, does a better job explaining (a) nuclear fission and (b) gamma-ray spectra?

The proton-proton cycle consumes four protons while producing 27 MeV of energy. (a) At what rate must the Sun consume protons to produce its power output of \(4 \times 10^{26} \mathrm{W?}\) (b) The present phase of the Sun's life will end when it has consumed about \(10 \%\) of its original protons. Estimate how long this phase will last, assuming the Sun's \(2 \times 10^{30}-\mathrm{kg}\) mass was initially \(71 \%\) hydrogen.

Neutron-induced fission of \(^{235} \mathrm{U}\) yields fission products iodine- 139 and yttrium- \(95 .\) How many neutrons are released?

(a) Example 38.6 explains that the number of fission events in a chain reaction increases by a factor \(k\) with each generation. Show that the total number of fission events in \(n\) generations is \(N=\left(k^{n+1}-1\right) /(k-1) \cdot(b)\) In a typical nuclear explosive, \(k\) is about 1.5 and the generation time is about 10 ns. Use the result from (a) to calculate the time for all the nuclei in a 10 -kg mass \(^{235} \mathrm{U}\) to fission. Hint: Sum a series in part (a), and neglect 1 compared with \(N\) in part (b).
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