Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 21: Problem 22

One nuclide in each of these pairs is radioactive. Predict which is radioactive and which is stable: \((\mathbf{a}){ }_{20}^{40} \mathrm{Ca}\) and \({ }_{20}^{45} \mathrm{Ca},\) (b) \({ }^{12} \mathrm{C}\) and \({ }^{14} \mathrm{C}\) (c) lead-206 and thorium-230. Explain your choice in each case.

Short Answer

Expert verified
The stable isotopes are \({_{20}^{40} \mathrm{Ca}}\), \({^{12} \mathrm{C}}\), and Lead-206, while the radioactive isotopes are \({_{20}^{45} \mathrm{Ca}}\), \({^{14} \mathrm{C}}\), and Thorium-230. This is based on the magic numbers concept and the known stability of specific isotopes.

Step by step solution

01

Identifying the Basics of Isotopes and Magic Numbers

A stable isotope has a balanced ratio of protons and neutrons to maintain stability. The magic numbers provide a guideline for stability: 2, 8, 20, 28, 50, 82, and 126. Isotopes with magic number of protons and/or neutrons generally tend to be more stable.
02

Comparing Isotopes of Ca (Calcium)

\({_{20}^{40} \mathrm{Ca}}\) has 20 protons and 20 neutrons, and \({_{20}^{45} \mathrm{Ca}}\) has 20 protons and 25 neutrons. Both isotopes have a magic number of protons, but only \({_{20}^{40} \mathrm{Ca}}\) also has a magic number of neutrons. As a result, \({_{20}^{40} \mathrm{Ca}}\) is the stable isotope, and \({_{20}^{45} \mathrm{Ca}}\) is the radioactive isotope.
03

Comparing Isotopes of C (Carbon)

\({^{12} \mathrm{C}}\) has 6 protons and 6 neutrons, and \({^{14} \mathrm{C}}\) has 6 protons and 8 neutrons. While many elements tend to be more stable with an even number of both protons and neutrons, \({^{12} \mathrm{C}}\) is the stable isotope, while \({^{14} \mathrm{C}}\) is radioactive.
04

Comparing Lead-206 and Thorium-230

Lead-206 has 82 protons and 124 neutrons, and Thorium-230 has 90 protons and 140 neutrons. Lead-206 has a magic number of protons, while Thorium-230 does not. Moreover, it is known that isotope leads are stable elements. Thus, Lead-206 is the stable isotope, and Thorium-230 is radioactive.
05

Conclusion

To summarize, we've determined the stability of isotope pairs based on their position around magic numbers and other knowledge about the isotopes. - \({_{20}^{40} \mathrm{Ca}}\) is stable, and \({_{20}^{45} \mathrm{Ca}}\) is radioactive. - \({^{12} \mathrm{C}}\) is stable, and \({^{14} \mathrm{C}}\) is radioactive. - Lead-206 is stable, and Thorium-230 is radioactive.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write balanced nuclear equations for the following processes: (a) radon-198 undergoes alpha emission; (b) thorium-234 undergoes beta emission; (c) copper-61 undergoes positron emission; (d) silver-106 undergoes electron capture.

(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?

Chlorine has two stable nuclides, \({ }^{35} \mathrm{Cl}\) and ${ }^{37} \mathrm{Cl}\(. In contrast, \){ }^{36} \mathrm{Cl}$ is a radioactive nuclide that decays by beta emission. (a) What is the product of decay of \({ }^{36} \mathrm{Cl}\) ? (b) Based on the empirical rules about nuclear stability, explain why the nucleus of \({ }^{36} \mathrm{Cl}\) is less stable than either ${ }^{35} \mathrm{Cl}\( or \){ }^{37} \mathrm{Cl}$.

Write balanced equations for each of the following nuclear reactions: $(\mathbf{a}){ }_{92}^{238} \mathrm{U}(\mathrm{n}, \gamma){ }^{239} \mathrm{U},(\mathbf{b}){ }_{82}^{16} \mathrm{O}(\mathrm{p}, \alpha){ }^{13} \mathrm{~N},\( (c) \){ }_{8}^{18} \mathrm{O}\left(\mathrm{n}, \beta^{-}\right){ }^{19} \mathrm{~F}$.

It takes 180 minutes for a 200 -mg sample of an unknown radioactive substance to decay to \(112 \mathrm{mg}\). What is the halflife of this substance?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

Physical Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

Kinetics

Read Explanation

Organic Chemistry

Read Explanation

Chemical Reactions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free