Mastering Chemistry with Pearson eText -- Standalone Access Card -- for Fundamentals of General, Organic, and Biological Chemistry (8th Edition)
Mastering Chemistry with Pearson eText -- Standalone Access Card -- for Fundamentals of General, Organic, and Biological Chemistry (8th Edition)
8th Edition
ISBN: 9780134283180
Author: John E. McMurry, David S. Ballantine, Carl A. Hoeger, Virginia E. Peterson
Publisher: PEARSON
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Textbook Question
Chapter 11, Problem 11.21UKC

Magnesium-28 decays by β emission to give aluminum-28. If yellow spheres represent 12 28 Mg atoms and blue spheres represent 13 28 Al atoms, how many half-lives have passed in the following sample?

Chapter 11, Problem 11.21UKC, Magnesium-28 decays by  emission to give aluminum-28. If yellow spheres represent 1228Mg atoms and

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation:

The number of half-lives when Mg-28 decays by β-emission to give Al-28 has to be calculated.

Concept Introduction:

Half-life:

The time required to reduce a radioactive isotope to half of its initial value.

Explanation of Solution

Mastering Chemistry with Pearson eText -- Standalone Access Card -- for Fundamentals of General, Organic, and Biological Chemistry (8th Edition), Chapter 11, Problem 11.21UKC

Figure 1

From the above figure,

We know that, yellow spheres are representing 1228Mg and blue spheres are 1328Al

The total number of yellow spheres present in first box is 16

The number of yellow spheres present in second box after beta decay is 4

16100%β1half-life850%β2 half-life425%

So, the number of half-lives needed is 2

Conclusion

The number of half-lives when Mg-28 decays by β-emission to give Al-28 was calculated as two half-lives.

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Chapter 11 Solutions

Mastering Chemistry with Pearson eText -- Standalone Access Card -- for Fundamentals of General, Organic, and Biological Chemistry (8th Edition)

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