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Chapter 18: Problem 34

Balance the following nuclear reactions. \begin{equation}a. \quad_{93}^{239} \mathrm{Np} \longrightarrow_{-1}^{0} e+?\end{equation} \begin{equation}\begin{array}{l}{\text { b. }_{4}^{9} \mathrm{Be}+_{2}^{4} \mathrm{He} \longrightarrow ?} \\ {\text { c. } _{15}^{32} \mathrm{P}+? \longrightarrow_{15}^{33} \mathrm{P}}\end{array}\end{equation} \begin{equation}d. _{92}^{236} \mathrm{U} \longrightarrow_{36}^{94} \mathrm{Kr}+?+3_{0}^{1} n\end{equation}

Short Answer

Expert verified
The balanced nuclear reactions are: \n (a) \(_{93}^{239} \mathrm{Np} \longrightarrow_{-1}^{0} e + _{94}^{239} \mathrm{Pu}\) \n (b) \(_{4}^{9} \mathrm{Be}+_{2}^{4}\mathrm{He} \longrightarrow _{6}^{13}\mathrm{C}\) \n (c) \(_{15}^{32} \mathrm{P}+_{0}^{1}\mathrm{n} \longrightarrow_{15}^{33} \mathrm{P}\) \n (d) \(_{92}^{236} \mathrm{U} \longrightarrow_{36}^{94}\mathrm{Kr}+_{56}^{139} \mathrm{Ba}+3_{0}^{1} n\)

Step by step solution

01

Balancing the first nuclear reaction

To balance this nuclear reaction \(_{93}^{239} \mathrm{Np} \longrightarrow_{-1}^{0} e+?\), we need to identify the missing product. This can be done by ensuring that the atomic and mass numbers are balanced. The atomic number will be \(93 - (-1) = 94\), and the mass number will be \(239 - 0 = 239\). Therefore, the missing product is \(_{94}^{239} \mathrm{Pu}\).
02

Balancing the second nuclear reaction

In the reaction \(_{4}^{9} \mathrm{Be}+_{2}^{4}\mathrm{He} \longrightarrow ?\), we need to find the missing product. Adding atomic numbers gives \(4 + 2 = 6\), and adding the mass numbers results in \(9 + 4 = 13\), yielding a product of \(_{6}^{13}\mathrm{C}\).
03

Balancing the third nuclear reaction

For the reaction \(_{15}^{32} \mathrm{P}+? \longrightarrow_{15}^{33} \mathrm{P}\), we need to find the missing reactant. Subtracting the atomic numbers gives \(15 - 15 = 0\) and subtracting the mass numbers gives \(33 - 32 = 1\). Thus, the missing reactant is \(_{0}^{1}n\), a neutron.
04

Balancing the fourth nuclear reaction

In the reaction \(_{92}^{236} \mathrm{U} \longrightarrow_{36}^{94}\mathrm{Kr}+?+3_{0}^{1}\mathrm{n}\), we have to find the missing product. For atomic numbers, this gives \(92 - 36 - 3*0 = 56\). For mass numbers, we get \(236 - 94 - 3*1 = 139\). This gives the product \(_{56}^{139} \mathrm{Ba}\).

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Most popular questions from this chapter

Design an experiment that illustrates the concept of half-life.

The half-life of tritium, \(_{1}^{3} \mathrm{H},\) is 12.3 \(\mathrm{y} .\) How long will it take for seven-eighths of the sample to decay?

Suppose you are an energy consultant who has been asked to evaluate a proposal to build a power plant in a remote area of the desert. Research the requirements for each of the following types of power plant: nuclear-fission power plant, coal-burning power plant, solar-energy farm. Decide which of these power plants would be best for its surroundings, and write a paragraph supporting your decision.

Research some important historical findings that have been validated through radioactive dating. Report your findings to the class.

Calculating the Amount of Radioactive Material The graphing calculator can run a program that graphs the relationship between the amount of radioactive material and elapsed time. Given the half-life of the radioactive material and the initial amount of material in grams, you will graph the relationship between the amount of radioactive material and the elapsed time. Then, with the elapsed time, you will trace the graph to calculate the amount of radioactive material. Go to Appendix C. If you are using a TI-83 Plus, you can download the program RADIOACT and run the application as directed. If you are using another calculator, your teacher will provide you with key-strokes and data sets to use. After you have run the program, answer these questions. a. Determine the amount of neptunium-235 left after 2.0 years, given the half- life of neptunium-235 is 1.08 years and the initial amount was 8.00 g. b. Determine the amount of neptunium-235 left after 5.0 years, given the half- life of neptunium-235 is 1.08 years and the initial amount was 8.00 g. c. Determine the amount of uranium-232 left after 100 years, given the half- life of uranium-232 is 69 years and the initial amount was 10.0 g.
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