   # A proposed system for storing nuclear wastes involves storing the radioactive material in caves or deep mine shafts. One of the most toxic nuclides that must be disposed of is plutonium-239, which is produced in breeder reactors and has a half-life of 24, 100 years. A suitable storage place must be geologically stable long enough for the activity of plutonium-239 to decrease to 0.1% of its original value. How long is this for plutonium-239? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 64AE
Textbook Problem
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## A proposed system for storing nuclear wastes involves storing the radioactive material in caves or deep mine shafts. One of the most toxic nuclides that must be disposed of is plutonium-239, which is produced in breeder reactors and has a half-life of 24, 100 years. A suitable storage place must be geologically stable long enough for the activity of plutonium-239 to decrease to 0.1% of its original value. How long is this for plutonium-239?

Interpretation Introduction

Interpretation: Half-life of plutonium- 239 is given. Time required for it to decrease its activity to 0.1% of its original value is to be calculated.

Concept introduction: The process in which a given nucleus undergoes decomposition leading to the formation of another nucleus is known as radioactive decay. The cause of instability of a nuclide is its inefficiency in holding the nucleus together. Half-life of plutonium is very long.

To determine: Time required for it to decrease its activity to 0.1% of its original value.

### Explanation of Solution

Explanation

The decay constant is calculated by the formula given below.

λ=0.693t1/2

Where

• t1/2 is the half-life of nuclide.
• λ is decay constant.

The value of t1/2 is 24100years

Substitute the value of half life in the above formula.

λ=0.69324100year-1=2.8755×10-5year-1_

Explanation

Decay time is calculated by the formula,

t=2.303λlog(n0n)

Where

• n0 is the number of atoms of plutonium initially present.
• n is the number of atoms of plutonium after time ‘t’

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