# Half-Life I-131 has a half-life of 8.04 days. If a sample initially contains 20.0 g of I-131, approximately how much I-131 will be left after 32 days?

### Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692

Chapter
Section

### Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692
Chapter 8, Problem 39E
Textbook Problem
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## Half-LifeI-131 has a half-life of 8.04 days. If a sample initially contains 20.0 g of I-131, approximately how much I-131 will be left after 32 days?

Interpretation Introduction

Interpretation:

The amount of I-131 left after 32 days is to be determined.

Concept Introduction:

The time required by a radioactive sample to decompose to half of its mass is called its half-life.

In every half-life, the sample is reduced to half of its mass that was taken initially in the current decay.

### Explanation of Solution

The half-life of I-131 is 8.04 days. Therefore, the number of half-lives (n) of I-131 is calculated as follows:

n=328.04n=3.98

Therefore, the number of half-lives is approximately 4.

Since, in every half-life, the sample is reduced to half of its mass that was taken initially in the current decay, the initial mass of I-131 is 20 g.

The mass of I-131 (m1) left after the first half-life is calculated as follows:

m1=20 g2=10 g.

The mass of I-131 (m2) left after the second half-life is calculated as follows:

m2=10 g2=5 g

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