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Chapter 21: Problem 8

The diagram shown here illustrates a fission process. \begin{equation} \begin{array}{l}{\text { (a) What is the unidentified product of the fission? }} \\ {\text { (b) Use Figure } 21.2 \text { to predict whether the nuclear products }} \\ \quad {\text { of this fission reaction are stable. [ Section } 21.7 ]}\end{array} \end{equation}

Short Answer

Expert verified
In summary, to identify the unknown product in a fission process, apply the conservation of mass number and conservation of atomic number equations to find its atomic number and mass number. For example, with a given fission process \(\ce{^{A_1}_{Z_1}X + ^{1}_{0}n -> ^{A_2}_{Z_2}Y + ^{A_3}_{Z_3}Z + 2 ^{1}_{0}n}\), solve \( A_1 + 1 = A_2 + A_3 \) and \( Z_1 + 0 = Z_2 + Z_3 \) for the unknown product X. Next, consult Figure 21.2 to determine the stability of the nuclear products. If they lie on or near the stability curve, they are stable; otherwise, they will be unstable or radioactive.

Step by step solution

01

Analyzing the given fission process

Analyze the fission process diagram which should consist of a certain nucleus undergoing fission and the products after the fission. Identify the unknown product by using its symbol, such as X. Also, identify the other products and the initial nucleus. Consider an example where the fission process is as follows: \[\ce{^{A_1}_{Z_1}X + ^{1}_{0}n -> ^{A_2}_{Z_2}Y + ^{A_3}_{Z_3}Z + 2 ^{1}_{0}n}\] Here, X is the initial nucleus, Y and Z are the fission products, and n is a neutron.
02

Applying conservation laws to find the unidentified product

Apply conservation of mass number and conservation of atomic number in the fission process: 1. Conservation of mass number (number of protons and neutrons): The sum of mass numbers on the left side is equal to the sum of mass numbers on the right side. \( A_1 + 1 = A_2 + A_3 \) 2. Conservation of atomic number (number of protons): The sum of atomic numbers on the left side is equal to the sum of atomic numbers on the right side. \( Z_1 + 0 = Z_2 + Z_3 \) Now, using the given nucleus Y and Z's atomic number and mass number, solve for the unknown product X's atomic number and mass number, which will give you the complete identity of the unknown fission product.
03

Consult Figure 21.2 to determine if the products are stable or not

Now that we have identified our nuclear products, refer to Figure 21.2 to determine whether the products are stable or not. Look at the stability curve and locate the identified nuclear products. If the products lie close to or on the stability curve, they are stable. If they lie away from the stability curve, they will be unstable or radioactive. #Conclusion# Following the steps given above, a student should be able to identify an unknown nuclear product in a fission process and determine its stability using Figure 21.2. The most important part in solving this problem is applying the conservation laws wisely to find the unknown product.

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Most popular questions from this chapter

Potassium-40 decays to argon-40 with a half-life of \(1.27 \times 10^{9}\) yr. What is the age of a rock in which the mass ratio of \(^{40} \mathrm{Ar}\) to \(^{40} \mathrm{K}\) is 4.2?

Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of Nal, in which only a small fraction of the iodide is radioactive. (a) Why is Nal a good choice for the source of iodine? (b) If a Geiger counter is placed near the person's thyroid (which is near the neck) right after the sodium iodide solution is taken, what will the data look like as a function of time? (c) A normal thyroid will take up about 12\(\%\) of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01\(\%\) of the original amount?

It has been suggested that strontium-90 (generated by nuclear testing deposited in the hot desert will undergo radioactive decay more rapidly because it will be exposed to much higher average temperatures. (a) Is this a reasonable suggestion? (b) Does the process of radioactive decay have an activation energy, like the Arrhenius behavior of many chemical reactions (Section 14.5\()?\)

(a) Which of the following are required characteristics of an isotope to be used as a fuel in a nuclear power reactor? (i) It must emit gamma radiation. (ii) On decay, it must release two or more neutrons. (iii) It must have a half-life less than one hour. (iv) It must undergo fission upon the absorption of a neutron. (b) What is the most common fissionable isotope in a commercial nuclear power reactor?

Complete and balance the nuclear equations for the following fission reactions: \begin{equation}(a) ^{2235} \mathrm{U}+_{0}^{1} \mathrm{n} \longrightarrow _{62}^{160} \mathrm{Sm}+ _{30}^{72} \mathrm{Zn}+_{0}^{1} \mathrm{n}\end{equation}\begin{equation} (b)^{239} \mathrm{Pu}+_{0}^{1} \mathrm{n} \longrightarrow _{58}^{144} \mathrm{Ce}+ 2 _{0}^{1} \mathrm{n} \end{equation}
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