   # The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July 16, 1945. What percentage of the strontium-90 (t 1/2 = 28.9 years) originally produced by that explosion still remains as of July 16, 2015? ### 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 31E
Textbook Problem
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## The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July 16, 1945. What percentage of the strontium-90 (t1/2 = 28.9 years) originally produced by that explosion still remains as of July 16, 2015?

Interpretation Introduction

Interpretation: Date of detonation of first atomic bomb is given. Percentage of strontium 90 still remaining is to be stated.

Concept introduction: A process through which an unstable nuclide loses its energy due to excess of protons or neutrons is known as radioactive decay. Decay constant is the quantity that expresses the rate of decrease of number of atoms of a radioactive element per second. Half-life of radioactive sample is defined as the time required for the number of nuclides to reach half of the original value.

To determine: Percentage of strontium 90 remaining after the first explosion.

### Explanation of Solution

Explanation

Given

Half-life (t1/2) is 28.9 years .

The decay constant is calculated by the formula,

λ=0.693t1/2

Where

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

Substitute the value of half-life in the above formula.

λ=0.69328.9years-1=0.02397 years-1

The decay constant is 0.02397years-1 .

The amount of strontium 90 still remaining is calculated by the formula,

ln(nn0)=kt

Where

• n0 is the original amount of strontium 90 in the first atomic explosion.
• n is the amount of strontium 90 still remaining.
• t is the decay time.

The value of t is 20151945=70 years.

Substitute the values of t and decay constant in the above equation

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